Wu, Sheng-Jhih; Chu, Moody T.
2017-08-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.
International Nuclear Information System (INIS)
Wu, Sheng-Jhih; Chu, Moody T
2017-01-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing–Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations. (paper)
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
Directory of Open Access Journals (Sweden)
Fatemeh Mohammad
2014-05-01
Full Text Available In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011 1697-1715]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
Preconditioned Krylov subspace methods for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Wu, Kesheng; Saad, Y.; Stathopoulos, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
Lanczos algorithm is a commonly used method for finding a few extreme eigenvalues of symmetric matrices. It is effective if the wanted eigenvalues have large relative separations. If separations are small, several alternatives are often used, including the shift-invert Lanczos method, the preconditioned Lanczos method, and Davidson method. The shift-invert Lanczos method requires direct factorization of the matrix, which is often impractical if the matrix is large. In these cases preconditioned schemes are preferred. Many applications require solution of hundreds or thousands of eigenvalues of large sparse matrices, which pose serious challenges for both iterative eigenvalue solver and preconditioner. In this paper we will explore several preconditioned eigenvalue solvers and identify the ones suited for finding large number of eigenvalues. Methods discussed in this paper make up the core of a preconditioned eigenvalue toolkit under construction.
AMDLIBF, IBM 360 Subroutine Library, Eigenvalues, Eigenvectors, Matrix Inversion
International Nuclear Information System (INIS)
Wang, Jesse Y.
1980-01-01
Description of problem or function: AMDLIBF is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne. This subset includes library category F: Identification/Description: F152S F SYMINV: Invert sym. matrices, solve lin. systems; F154S A DOTP: Double plus precision accum. inner prod.; F156S F RAYCOR: Rayleigh corrections for eigenvalues; F161S F XTRADP: A fast extended precision inner product; F162S A XTRADP: Inner product of two DP real vectors; F202S F1 EIGEN: Eigen-system for real symmetric matrix; F203S F: Driver for F202S; F248S F RITZIT: Largest eigenvalue and vec. real sym. matrix; F261S F EIGINV: Inverse eigenvalue problem; F313S F CQZHES: Reduce cmplx matrices to upper Hess and tri; F314S F CQZVAL: Reduce complex matrix to upper Hess. form; F315S F CQZVEC: Eigenvectors of cmplx upper triang. syst.; F316S F CGG: Driver for complex general Eigen-problem; F402S F MATINV: Matrix inversion and sol. of linear eqns.; F403S F: Driver for F402S; F452S F CHOLLU,CHOLEQ: Sym. decomp. of pos. def. band matrices; F453S F MATINC: Inversion of complex matrices; F454S F CROUT: Solution of simultaneous linear equations; F455S F CROUTC: Sol. of simultaneous complex linear eqns.; F456S F1 DIAG: Integer preserving Gaussian elimination
Inversion for Eigenvalues and Modes Using Sierra-SD and ROL.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Aquino, Wilkins [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kouri, Drew Philip [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
In this report we formulate eigenvalue-based methods for model calibration using a PDE-constrained optimization framework. We derive the abstract optimization operators from first principles and implement these methods using Sierra-SD and the Rapid Optimization Library (ROL). To demon- strate this approach, we use experimental measurements and an inverse solution to compute the joint and elastic foam properties of a low-fidelity unit (LFU) model.
Eigenvalue translation method for mode calculations
International Nuclear Information System (INIS)
Gerck, E.; Cruz, C.H.B.
1978-11-01
A new method is described for the first few modes calculations in a interferometer that has several advantages over the ALLMAT subroutine, the Prony Method and the Fox and Li Method. In the illustrative results shown for the same cases it can be seen that the eigenvalue translation method is typically 100 fold times faster than the usual Fox and Li Method and 10 times faster than ALLMAT [pt
Application of collocation meshless method to eigenvalue problem
International Nuclear Information System (INIS)
Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki
2012-01-01
The numerical method for solving the nonlinear eigenvalue problem has been developed by using the collocation Element-Free Galerkin Method (EFGM) and its performance has been numerically investigated. The results of computations show that the approximate solution of the nonlinear eigenvalue problem can be obtained stably by using the developed method. Therefore, it can be concluded that the developed method is useful for solving the nonlinear eigenvalue problem. (author)
Cakoni, Fioralba; Haddar, Houssem
2013-10-01
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission
A numerical method to compute interior transmission eigenvalues
International Nuclear Information System (INIS)
Kleefeld, Andreas
2013-01-01
In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)
A method for the solution of the RPA eigenvalue
International Nuclear Information System (INIS)
Hoffman, M.J.H.; De Kock, P.R.
1986-01-01
The RPA eigenvalue problem requires the diagonalization of a 2nx2n matrix. In practical calculations, n (the number of particle-hole basis states) can be a few hundred and the diagonalization of such a large non-symmetric matrix may take quite a long time. In this report we firstly discuss sufficient conditions for real and non-zero RPA eigenvalues. The presence of zero or imaginary eigenvalues is related to the relative importance of the groundstate correlations to the total interaction energy. We then rewrite the RPA eigenvalue problem for the cases where these conditions are fulfilled in a form which only requires the diagonalization of two symmetric nxn matrices. The extend to which this method can be applied when zero eigenvalues occur, is also discussed
Guliyev, Namig J.
2008-01-01
International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.
Efficient methods for time-absorption (α) eigenvalue calculations
International Nuclear Information System (INIS)
Hill, T.R.
1983-01-01
The time-absorption eigenvalue (α) calculation is one of the options found in most discrete-ordinates transport codes. Several methods have been developed at Los Alamos to improve the efficiency of this calculation. Two procedures, based on coarse-mesh rebalance, to accelerate the α eigenvalue search are derived. A hybrid scheme to automatically choose the more-effective rebalance method is described. The α rebalance scheme permits some simple modifications to the iteration strategy that eliminates many unnecessary calculations required in the standard search procedure. For several fast supercritical test problems, these methods resulted in convergence with one-fifth the number of iterations required for the conventional eigenvalue search procedure
The nonconforming virtual element method for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications
2018-02-05
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L^{2}-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.
Methods of intermediate problems for eigenvalues
Weinstein, Alexander
1972-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group
International Nuclear Information System (INIS)
Wang, S.J.
1993-04-01
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)
A method for eigenvalues of sparse lambda-matrices
International Nuclear Information System (INIS)
Yang, W.H.
1982-01-01
The matrix N(lambda) whose elements are functions of a parameter lambda is called the lambda-matrix. Those values of lambda that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a lambda-matrix is presented. A simple explicit convergence criterion is given as well as the algorithm and two numerical examples
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
A multilevel, level-set method for optimizing eigenvalues in shape design problems
International Nuclear Information System (INIS)
Haber, E.
2004-01-01
In this paper, we consider optimal design problems that involve shape optimization. The goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible. To achieve this goal we combine two new ideas for an efficient solution of the problem. First, we replace the eigenvalue problem with an approximation by using inverse iteration. Second, we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques. Combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem
Energy Technology Data Exchange (ETDEWEB)
Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática
2017-07-01
We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)
A numerical method for eigenvalue problems in modeling liquid crystals
Energy Technology Data Exchange (ETDEWEB)
Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A. [Kent State Univ., OH (United States); Calvetti, D. [Stevens Inst. of Technology, Hoboken, NJ (United States)
1996-12-31
Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.
Jacobi-Davidson methods for generalized MHD-eigenvalue problems
J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)
1995-01-01
textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The
An algorithm of α-and γ-mode eigenvalue calculations by Monte Carlo method
International Nuclear Information System (INIS)
Yamamoto, Toshihiro; Miyoshi, Yoshinori
2003-01-01
A new algorithm for Monte Carlo calculation was developed to obtain α- and γ-mode eigenvalues. The α is a prompt neutron time decay constant measured in subcritical experiments, and the γ is a spatial decay constant measured in an exponential method for determining the subcriticality. This algorithm can be implemented into existing Monte Carlo eigenvalue calculation codes with minimum modifications. The algorithm was implemented into MCNP code and the performance of calculating the both mode eigenvalues were verified through comparison of the calculated eigenvalues with the ones obtained by fixed source calculations. (author)
International Nuclear Information System (INIS)
Lomnitz-Adler, J.; Brink, D.M.
1976-01-01
A generating function for the eigenvalues of the RGM Normalization Kernel is expressed in terms of the diagonal matrix elements of thw GCM Overlap Kernel. An asymptotic expression for the eigenvalues is obtained by using the Method of Steepest Descent. (Auth.)
Supersymmetry, reflectionless symmetric potentials and the inverse method
International Nuclear Information System (INIS)
Bagchi, B.
1990-01-01
The role of inverse scattering method is illustrated to examine the connection between the multi-soliton solutions of Korteweg-de Vries (KdV) equation and discrete eigenvalues of Schrodinger equation. The necessity of normalization of the Schrodinger wave functions, which are constructed purely from a supersymmetric consideration is pointed out
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering
Pelinovsky, Dmitry E.; Sulem, Catherine
A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.
Gould, S H
1966-01-01
The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. This second edition presents new developments in the framework of the material contained in the first edition, which is retained in somewhat modified form.
Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.
2011-01-01
The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William; Sacks, Paul
2013-01-01
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative
International Nuclear Information System (INIS)
Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-01-01
By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained
Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems
International Nuclear Information System (INIS)
Yavuz, Musa
1998-01-01
We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods
Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems
International Nuclear Information System (INIS)
Yavuz, M.
1997-01-01
We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods. (author)
Directory of Open Access Journals (Sweden)
Leszek Majkut
Full Text Available In the work, the problems of the beam structural modification through coupling the additional mass or elastic support, as well as the problem of diagnostics of the beam cracks, are discussed. The common feature for both problems is that the material parameters in each of the discussed cases change only in one point (additional mass, the support in one point, the crack described by the elastic joint. These systems, after determination of the value of additional element and its localization, should have a given natural vibration frequency. In order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity, the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity as a function of its localization so that the system has the free vibration frequency, which is desired in the modification problem or measured on the object in the diagnostics.
Directory of Open Access Journals (Sweden)
Leszek Majkut
Full Text Available In the work, in order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity, the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity as a function of its localization so that the free vibration frequency changes to desirable value. The criteria for choice of the “proper” pair (mass - its position, including the criterion allowing changing the position of the vibration node of the second mode of the free vibrations, were given. Analysis of the influence of uncertainties in the determination of the additional quantity value and its position on the desired free vibration frequency was carried out, too. The proposed beam inverse model can be employing to identification of the beam cracks. In such a case, the input quantity is free vibration frequency measured on the damaged object. Each determined free-vibration frequency allows determining the flexibility curve for the spring modeling crack as a function of its position. The searched parameters of the crack (its depth and position are indicated by the common point of two arbitrary curves. Accuracy of crack parameters determination depends on accuracy (uncertainty of frequency measurement. Only some regions containing the searched crack parameters can be obtained in such a situation.
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William
2013-04-23
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative: the Dirichlet spectrum from the clamped end-point conditions is insufficient. There are many known ways to add additional information to gain a positive answer, and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode-the so-called norming constants. We make the assumption that neither of these changes are possible. Instead we will add known mass-densities to the string in a way we can prescribe and remeasure the Dirichlet spectrum. We will not be able to answer the uniqueness question in its most general form, but will give some insight to what "added masses" should be chosen and how this can lead to a reconstruction of the original string density. © 2013 Society for Industrial and Applied Mathematics.
The method of fundamental solutions for computing acoustic interior transmission eigenvalues
Kleefeld, Andreas; Pieronek, Lukas
2018-03-01
We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.
A Decentralized Eigenvalue Computation Method for Spectrum Sensing Based on Average Consensus
Mohammadi, Jafar; Limmer, Steffen; Stańczak, Sławomir
2016-07-01
This paper considers eigenvalue estimation for the decentralized inference problem for spectrum sensing. We propose a decentralized eigenvalue computation algorithm based on the power method, which is referred to as generalized power method GPM; it is capable of estimating the eigenvalues of a given covariance matrix under certain conditions. Furthermore, we have developed a decentralized implementation of GPM by splitting the iterative operations into local and global computation tasks. The global tasks require data exchange to be performed among the nodes. For this task, we apply an average consensus algorithm to efficiently perform the global computations. As a special case, we consider a structured graph that is a tree with clusters of nodes at its leaves. For an accelerated distributed implementation, we propose to use computation over multiple access channel (CoMAC) as a building block of the algorithm. Numerical simulations are provided to illustrate the performance of the two algorithms.
The discontinuous finite element method for solving Eigenvalue problems of transport equations
International Nuclear Information System (INIS)
Yang, Shulin; Wang, Ruihong
2011-01-01
In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)
A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems
Directory of Open Access Journals (Sweden)
Muhammed I. Syam
2017-11-01
Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.
Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry
International Nuclear Information System (INIS)
Anistratov, D. Y.; Gol'din, V. Y.
2009-01-01
A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)
MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems
International Nuclear Information System (INIS)
Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.
1986-01-01
1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real
An iterative method for determination of a minimal eigenvalue
DEFF Research Database (Denmark)
Kristiansen, G.K.
1968-01-01
Kristiansen (1963) has discussed the convergence of a group of iterative methods (denoted the Equipoise methods) for the solution of reactor criticality problems. The main result was that even though the methods are said to work satisfactorily in all practical cases, examples of divergence can be...
Kernel based eigenvalue-decomposition methods for analysing ham
DEFF Research Database (Denmark)
Christiansen, Asger Nyman; Nielsen, Allan Aasbjerg; Møller, Flemming
2010-01-01
methods, such as PCA, MAF or MNF. We therefore investigated the applicability of kernel based versions of these transformation. This meant implementing the kernel based methods and developing new theory, since kernel based MAF and MNF is not described in the literature yet. The traditional methods only...... have two factors that are useful for segmentation and none of them can be used to segment the two types of meat. The kernel based methods have a lot of useful factors and they are able to capture the subtle differences in the images. This is illustrated in Figure 1. You can see a comparison of the most...... useful factor of PCA and kernel based PCA respectively in Figure 2. The factor of the kernel based PCA turned out to be able to segment the two types of meat and in general that factor is much more distinct, compared to the traditional factor. After the orthogonal transformation a simple thresholding...
Deflation of eigenvalues for iterative methods in lattice QCD
International Nuclear Information System (INIS)
Darnell, Dean; Morgan, Ronald B.; Wilcox, Walter
2004-01-01
Work on generalizing the deflated, restarted GMRES algorithm, useful in lattice studies using stochastic noise methods, is reported. We first show how the multi-mass extension of deflated GMRES can be implemented. We then give a deflated GMRES method that can be used on multiple right-hand sides of Aχ = b in an efficient manner. We also discuss and give numerical results on the possibilty of combining deflated GMRES for the first right hand side with a deflated BiCGStab algorithm for the subsequent right hand sides
Hybrid subgroup decomposition method for solving fine-group eigenvalue transport problems
International Nuclear Information System (INIS)
Yasseri, Saam; Rahnema, Farzad
2014-01-01
Highlights: • An acceleration technique for solving fine-group eigenvalue transport problems. • Coarse-group quasi transport theory to solve coarse-group eigenvalue transport problems. • Consistent and inconsistent formulations for coarse-group quasi transport theory. • Computational efficiency amplified by a factor of 2 using hybrid SGD for 1D BWR problem. - Abstract: In this paper, a new hybrid method for solving fine-group eigenvalue transport problems is developed. This method extends the subgroup decomposition method to efficiently couple a new coarse-group quasi transport theory with a set of fixed-source transport decomposition sweeps to obtain the fine-group transport solution. The advantages of the quasi transport theory are its high accuracy, straight-forward implementation and numerical stability. The hybrid method is analyzed for a 1D benchmark problem characteristic of boiling water reactors (BWR). It is shown that the method reproduces the fine-group transport solution with high accuracy while increasing the computational efficiency up to 12 times compared to direct fine-group transport calculations
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1996-01-01
The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Macdonald, Colin B.
2011-06-01
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.
International Nuclear Information System (INIS)
Lay-Ekuakille, Aimé; Pariset, Carlo; Trotta, Amerigo
2010-01-01
The FDM (filter diagonalization method), an interesting technique used in nuclear magnetic resonance data processing for tackling FFT (fast Fourier transform) limitations, can be used by considering pipelines, especially complex configurations, as a vascular apparatus with arteries, veins, capillaries, etc. Thrombosis, which might occur in humans, can be considered as a leakage for the complex pipeline, the human vascular apparatus. The choice of eigenvalues in FDM or in spectra-based techniques is a key issue in recovering the solution of the main equation (for FDM) or frequency domain transformation (for FFT) in order to determine the accuracy in detecting leaks in pipelines. This paper deals with the possibility of improving the leak detection accuracy of the FDM technique thanks to a robust algorithm by assessing the problem of eigenvalues, making it less experimental and more analytical using Tikhonov-based regularization techniques. The paper starts from the results of previous experimental procedures carried out by the authors
Extending the subspace hybrid method for eigenvalue problems in reactor physics calculation
International Nuclear Information System (INIS)
Zhang, Q.; Abdel-Khalik, H. S.
2013-01-01
This paper presents an innovative hybrid Monte-Carlo-Deterministic method denoted by the SUBSPACE method designed for improving the efficiency of hybrid methods for reactor analysis applications. The SUBSPACE method achieves its high computational efficiency by taking advantage of the existing correlations between desired responses. Recently, significant gains in computational efficiency have been demonstrated using this method for source driven problems. Within this work the mathematical theory behind the SUBSPACE method is introduced and extended to address core wide level k-eigenvalue problems. The method's efficiency is demonstrated based on a three-dimensional quarter-core problem, where responses are sought on the pin cell level. The SUBSPACE method is compared to the FW-CADIS method and is found to be more efficient for the utilized test problem because of the reason that the FW-CADIS method solves a forward eigenvalue problem and an adjoint fixed-source problem while the SUBSPACE method only solves an adjoint fixed-source problem. Based on the favorable results obtained here, we are confident that the applicability of Monte Carlo for large scale reactor analysis could be realized in the near future. (authors)
International Nuclear Information System (INIS)
Qiu, Yishu; She, Ding; Tang, Xiao; Wang, Kan; Liang, Jingang
2016-01-01
Highlights: • A new algorithm is proposed to reduce memory consumption for sensitivity analysis. • The fission matrix method is used to generate adjoint fission source distributions. • Sensitivity analysis is performed on a detailed 3D full-core benchmark with RMC. - Abstract: Recently, there is a need to develop advanced methods of computing eigenvalue sensitivity coefficients to nuclear data in the continuous-energy Monte Carlo codes. One of these methods is the iterated fission probability (IFP) method, which is adopted by most of Monte Carlo codes of having the capabilities of computing sensitivity coefficients, including the Reactor Monte Carlo code RMC. Though it is accurate theoretically, the IFP method faces the challenge of huge memory consumption. Therefore, it may sometimes produce poor sensitivity coefficients since the number of particles in each active cycle is not sufficient enough due to the limitation of computer memory capacity. In this work, two algorithms of the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method, namely, the collision-event-based algorithm (C-CLUTCH) which is also implemented in SCALE and the fission-event-based algorithm (F-CLUTCH) which is put forward in this work, are investigated and implemented in RMC to reduce memory requirements for computing eigenvalue sensitivity coefficients. While the C-CLUTCH algorithm requires to store concerning reaction rates of every collision, the F-CLUTCH algorithm only stores concerning reaction rates of every fission point. In addition, the fission matrix method is put forward to generate the adjoint fission source distribution for the CLUTCH method to compute sensitivity coefficients. These newly proposed approaches implemented in RMC code are verified by a SF96 lattice model and the MIT BEAVRS benchmark problem. The numerical results indicate the accuracy of the F-CLUTCH algorithm is the same as the C
Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods
International Nuclear Information System (INIS)
Roberts, Jeremy A.; Forget, Benoit
2011-01-01
The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)
International Nuclear Information System (INIS)
Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.
1995-07-01
In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)
International Nuclear Information System (INIS)
Abreu, M.P.; Filho, H.A.; Barros, R.C.
1993-01-01
The authors describe a new nodal method for multigroup slab-geometry discrete ordinates S N eigenvalue problems that is completely free from all spatial truncation errors. The unknowns in the method are the node-edge angular fluxes, the node-average angular fluxes, and the effective multiplication factor k eff . The numerical values obtained for these quantities are exactly those of the dominant analytic solution of the S N eigenvalue problem apart from finite arithmetic considerations. This method is based on the use of the standard balance equation and two nonstandard auxiliary equations. In the nonmultiplying regions, e.g., the reflector, we use the multigroup spectral Green's function (SGF) auxiliary equations. In the fuel regions, we use the multigroup spectral diamond (SD) auxiliary equations. The SD auxiliary equation is an extension of the conventional auxiliary equation used in the diamond difference (DD) method. This hybrid characteristic of the SD-SGF method improves both the numerical stability and the convergence rate
Institute of Scientific and Technical Information of China (English)
Tang Wen-Lin; Tian Gui-Hua
2011-01-01
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
An eigenvalue approach to quantum plasmonics based on a self-consistent hydrodynamics method.
Ding, Kun; Chan, C T
2018-02-28
Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or empirical Feibelman d-parameters have been used to explore the quantum correction of plasmonic resonances. However, most of these methods are formulated within the quasi-static framework. The self-consistent hydrodynamics model offers a reliable approach to study quantum plasmonics because it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent manner. Instead of the standard scattering method, we formulate the self-consistent hydrodynamics method as an eigenvalue problem to study quantum plasmonics with electrons and photons treated on the same footing. We find that the eigenvalue approach must involve a global operator, which originates from the energy functional of the electron gas. This manifests the intrinsic nonlocality of the response of quantum plasmonic resonances. Our model gives the analytical forms of quantum corrections to plasmonic modes, incorporating quantum electron spill-out effects and electrodynamical retardation. We apply our method to study the quantum surface plasmon polariton for a single flat interface.
The Path Resistance Method for Bounding the Smallest Nontrivial Eigenvalue of a Laplacian
Guattery, Stephen; Leighton, Tom; Miller, Gary L.
1997-01-01
We introduce the path resistance method for lower bounds on the smallest nontrivial eigenvalue of the Laplacian matrix of a graph. The method is based on viewing the graph in terms of electrical circuits; it uses clique embeddings to produce lower bounds on lambda(sub 2) and star embeddings to produce lower bounds on the smallest Rayleigh quotient when there is a zero Dirichlet boundary condition. The method assigns priorities to the paths in the embedding; we show that, for an unweighted tree T, using uniform priorities for a clique embedding produces a lower bound on lambda(sub 2) that is off by at most an 0(log diameter(T)) factor. We show that the best bounds this method can produce for clique embeddings are the same as for a related method that uses clique embeddings and edge lengths to produce bounds.
Energy Technology Data Exchange (ETDEWEB)
Stathopoulos, A.; Fischer, C.F. [Vanderbilt Univ., Nashville, TN (United States); Saad, Y.
1994-12-31
The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
A Schur Method for Designing LQ-optimal Systems with Prescribed Eigenvalues
Directory of Open Access Journals (Sweden)
David Di Ruscio
1990-01-01
Full Text Available In this paper a new algorithm for solving the LQ-optimal pole placement problem is presented. The method studied is a variant of the classical eigenvector approach and instead uses a set of Schur vectors, thereby gaining substantial numerical advantages. An important task in this method is the LQ-optimal pole placement problem for a second order (sub system. The paper presents a detailed analytical solution to this problem. This part is not only important for solving the general n-dimensional problem but also provides an understanding of the behaviour of an optimal system: The paper shows that in some cases it is an infinite number; in others a finite number, and in still others, non state weighting matrices Q that give the system a set of prescribed eigenvalues. Equations are presented that uniquely determine these state weight matrices as a function of the new prescribed eigcnvalues. From this result we have been able to derive the maximum possible imaginary part of the eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen.
International Nuclear Information System (INIS)
Eaker, C.W.; Schatz, G.C.; De Leon, N.; Heller, E.J.
1984-01-01
Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method
An algebraic sub-structuring method for large-scale eigenvalue calculation
International Nuclear Information System (INIS)
Yang, C.; Gao, W.; Bai, Z.; Li, X.; Lee, L.; Husbands, P.; Ng, E.
2004-01-01
We examine sub-structuring methods for solving large-scale generalized eigenvalue problems from a purely algebraic point of view. We use the term 'algebraic sub-structuring' to refer to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to provide approximate solutions to the original problem. We are interested in the question of which spectral components one should extract from each sub-structure in order to produce an approximate solution to the original problem with a desired level of accuracy. Error estimate for the approximation to the smallest eigenpair is developed. The estimate leads to a simple heuristic for choosing spectral components (modes) from each sub-structure. The effectiveness of such a heuristic is demonstrated with numerical examples. We show that algebraic sub-structuring can be effectively used to solve a generalized eigenvalue problem arising from the simulation of an accelerator structure. One interesting characteristic of this application is that the stiffness matrix produced by a hierarchical vector finite elements scheme contains a null space of large dimension. We present an efficient scheme to deflate this null space in the algebraic sub-structuring process
A Bootstrap Approach to Eigenvalue Correction
Hendrikse, A.J.; Spreeuwers, Lieuwe Jan; Veldhuis, Raymond N.J.
2009-01-01
Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Directory of Open Access Journals (Sweden)
Wei Wang
2014-01-01
Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.
On Selberg's small eigenvalue conjecture and residual eigenvalues
DEFF Research Database (Denmark)
Risager, Morten S.
2011-01-01
We show that Selberg’s eigenvalue conjecture concerning small eigenvalues of the automorphic Laplacian for congruence groups is equivalent to a conjecture about the non-existence of residual eigenvalues for a perturbed system. We prove this using a combination of methods from asymptotic perturbat...
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
Energy Technology Data Exchange (ETDEWEB)
Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC
2009-02-15
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
International Nuclear Information System (INIS)
Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.
2009-02-01
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)
Lectures on the inverse scattering method
International Nuclear Information System (INIS)
Zakharov, V.E.
1983-06-01
In a series of six lectures an elementary introduction to the theory of inverse scattering is given. The first four lectures contain a detailed theory of solitons in the framework of the KdV equation, together with the inverse scattering theory of the one-dimensional Schroedinger equation. In the fifth lecture the dressing method is described, while the sixth lecture gives a brief review of the equations soluble by the inverse scattering method. (author)
Energy Technology Data Exchange (ETDEWEB)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Programa de Pos-Graduacao em Modelagem Computacional
2015-07-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S{sub N}) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S{sub N} discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S{sub N} transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S{sub N} eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Silva, Davi Jose M.; Alves Filho, Hermes; Barros, Ricardo C.
2015-01-01
A spectral nodal method is developed for multigroup x,y-geometry discrete ordinates (S N ) eigenvalue problems for nuclear reactor global calculations. This method uses the conventional multigroup SN discretized spatial balance nodal equations with two non-standard auxiliary equations: the spectral diamond (SD) auxiliary equations for the discretization nodes inside the fuel regions, and the spectral Green's function (SGF) auxiliary equations for the non-multiplying regions, such as the baffle and the reactor. This spectral nodal method is derived from the analytical general solution of the SN transverse integrated nodal equations with constant approximations for the transverse leakage terms within each discretization node. The SD and SGF auxiliary equations have parameters, which are determined to preserve the homogeneous and the particular components of these local general solutions. Therefore, we refer to the offered method as the hybrid SD-SGF-Constant Nodal (SD-SGF-CN) method. The S N discretized spatial balance equations, together with the SD and the SGF auxiliary equations form the SD-SGF-CN equations. We solve the SD-SGF-CN equations by using the one-node block inversion inner iterations (NBI), wherein the most recent estimates for the incoming group node-edge average or prescribed boundary conditions are used to evaluate the outgoing group node-edge average fluxes in the directions of the S N transport sweeps, for each estimate of the dominant eigenvalue in the conventional Power outer iterations. We show in numerical calculations that the SD-SGF-CN method is very accurate for coarse-mesh multigroup S N eigenvalue problems, even though the transverse leakage terms are approximated rather simply. (author)
International Nuclear Information System (INIS)
Emel'yanenko, G.A.; Sek, I.E.
1988-01-01
Many correctable unknown methods for eigenvalue calculation of general tridiagonal matrices with real elements; criteria of singular tridiagonal matrices; necessary and sufficient conditions of tridiagonal matrix degeneracy; process with boundary conditions according to calculation processes of general upper and lower tridiagonal matrix minors are obtained. 6 refs
Jarlebring, E.; Hochstenbach, M.E.
2009-01-01
Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called
International Nuclear Information System (INIS)
Abreu, M.P. de
1994-01-01
The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)
An inverse method for radiation transport
Energy Technology Data Exchange (ETDEWEB)
Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)
2004-01-01
Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.
Eigenvalue routines in NASTRAN: A comparison with the Block Lanczos method
Tischler, V. A.; Venkayya, Vipperla B.
1993-01-01
The NASA STRuctural ANalysis (NASTRAN) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this paper is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the Block Lanczos algorithm by Boeing Computer Services (BCS). This eigenvalue routine is now available in the BCS mathematics library as well as in several commercial versions of NASTRAN. In addition, CRAY maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The Block Lanczos algorithm was found to be extremely efficient, in particular, for very large size problems.
Directory of Open Access Journals (Sweden)
Winfried Auzinger
2006-01-01
Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
International Nuclear Information System (INIS)
Petersen, Claudio Zen; Vilhena, Marco T.; Barros, Ricardo C.
2009-01-01
In this paper the application of the Laplace transform method is described in order to determine the energy-dependent albedo matrix that is used in the boundary conditions multigroup neutron diffusion eigenvalue problems in slab geometry for nuclear reactor global calculations. In slab geometry, the diffusion albedo substitutes without approximation the baffle-reflector system around the active domain. Numerical results to typical test problems are shown to illustrate the accuracy and the efficiency of the Chebysheff acceleration scheme. (orig.)
2017-09-01
features can be evaluated such a welds and bolted connections. With these situations investigated, test articles with more complex geometry can be used...become more capable. Despite these advancements, the construction of physical prototypes remains an essential aspect of design and testing . FEM...prototype, there may be design deficiencies that cannot be identified until the prototype is tested . Using eigenvalue sensitivities, enhanced by
A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.
Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas
2015-12-01
Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.
The Schrodinger Eigenvalue March
Tannous, C.; Langlois, J.
2011-01-01
A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…
Ensemble Kalman methods for inverse problems
International Nuclear Information System (INIS)
Iglesias, Marco A; Law, Kody J H; Stuart, Andrew M
2013-01-01
The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen 1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. In this paper we propose the application of an iterative ensemble Kalman method for the solution of a wide class of inverse problems. In this context we show that the estimate of the unknown function that we obtain with the ensemble Kalman method lies in a subspace A spanned by the initial ensemble. Hence the resulting error may be bounded above by the error found from the best approximation in this subspace. We provide numerical experiments which compare the error incurred by the ensemble Kalman method for inverse problems with the error of the best approximation in A, and with variants on traditional least-squares approaches, restricted to the subspace A. In so doing we demonstrate that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Furthermore, we also demonstrate that the accuracy is of the same order of magnitude as that achieved by the best approximation. Three examples are used to demonstrate these assertions: inversion of a compact linear operator; inversion of piezometric head to determine hydraulic conductivity in a Darcy model of groundwater flow; and inversion of Eulerian velocity measurements at positive times to determine the initial condition in an incompressible fluid. (paper)
Energy Technology Data Exchange (ETDEWEB)
Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics
1997-11-01
The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.
Miyazaki, Yoshinori
2000-01-01
This paper is strongly based on two powerful general theorems proved by Ikebe, et. al in 1993[15] and 1996[13], which will be referred to as Theorem A and Theorem B in this paper. They were recently published and justify the approximate computations of simple eigenvalues of infinite matrices of certain types by truncation, giving an extremely accurate error estimates. So far, they have applied to some important problems in engineering, such as computing the zeros of some special functions, an...
International Nuclear Information System (INIS)
Jiang Bin; Zhang Yejing; Wang Yufei; Liu Anjin; Zheng Wanhua
2012-01-01
We present the extended Dirichlet-to-Neumann wave vector eigenvalue equation (DtN-WVEE) method to calculate the equi-frequency contour (EFC) of square lattice photonic crystals (PhCs). With the extended DtN-WVEE method and Snell's law, the effective refractive index of the mode with a circular EFC can be obtained, which is further validated with the refractive index weighted by the electric field or magnetic field. To further verify the EFC calculated by the DtN-WVEE method, the finite-difference time-domain method is also used. Compared with other wave vector eigenvalue equation methods that calculate EFC directly, the size of the eigenmatrix used in the DtN-WVEE method is much smaller, and the computation time is significantly reduced. Since the DtN-WVEE method solves wave vectors for given arbitrary frequencies, it can also find applications in studying the optical properties of a PhC with dispersive, lossy and magnetic materials. (paper)
Kinetic equation solution by inverse kinetic method
International Nuclear Information System (INIS)
Salas, G.
1983-01-01
We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance
Schwartz, L M; Bergman, D J; Dunn, K J; Mitra, P P
1996-01-01
Random walk computer simulations are an important tool in understanding magnetic resonance measurements in porous media. In this paper we focus on the description of pulsed field gradient spin echo (PGSE) experiments that measure the probability, P(R,t), that a diffusing water molecule will travel a distance R in a time t. Because PGSE simulations are often limited by statistical considerations, we will see that valuable insight can be gained by working with simple periodic geometries and comparing simulation data to the results of exact eigenvalue expansions. In this connection, our attention will be focused on (1) the wavevector, k, and time dependent magnetization, M(k, t); and (2) the normalized probability, Ps(delta R, t), that a diffusing particle will return to within delta R of the origin after time t.
Babaee, Hessam; Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em
2017-09-01
We develop a new robust methodology for the stochastic Navier-Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods [1-3]. Both approaches are variants of a generalized Karhunen-Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent [3], but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes [4]. We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we
International Nuclear Information System (INIS)
Ito, Motohiro; Endo, Tomohiro; Yamamoto, Akio; Kuroda, Yusuke; Yoshii, Takashi
2017-01-01
The bias factor method based on the random sampling technique is applied to the benchmark problem of Peach Bottom Unit 2. Validity and availability of the present method, i.e. correction of calculation results and reduction of uncertainty, are confirmed in addition to features and performance of the present method. In the present study, core characteristics in cycle 3 are corrected with the proposed method using predicted and 'measured' critical eigenvalues in cycles 1 and 2. As the source of uncertainty, variance-covariance of cross sections is considered. The calculation results indicate that bias between predicted and measured results, and uncertainty owing to cross section can be reduced. Extension to other uncertainties such as thermal hydraulics properties will be a future task. (author)
Inverse amplitude method and Adler zeros
International Nuclear Information System (INIS)
Gomez Nicola, A.; Pelaez, J. R.; Rios, G.
2008-01-01
The inverse amplitude method is a powerful unitarization technique to enlarge the energy applicability region of effective Lagrangians. It has been widely used to describe resonances in hadronic physics, combined with chiral perturbation theory, as well as in the strongly interacting symmetry breaking sector. In this work we show how it can be slightly modified to also account for the subthreshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.
International Nuclear Information System (INIS)
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems
Energy Technology Data Exchange (ETDEWEB)
Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)
1996-12-31
A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver
2014-01-06
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg
2014-01-01
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
Energy Technology Data Exchange (ETDEWEB)
Maiz, F., E-mail: fethimaiz@gmail.com [University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413 (Saudi Arabia)
2015-04-15
A novel method to calculate the quantum transmission, resonance and eigenvalue energies forming the sub-bands structure of non-symmetrical, non-periodical semiconducting heterostructure potential has been proposed in this paper. The method can be applied on a multilayer system with varying thickness of the layer and effective mass of electrons and holes. Assuming an approximated effective mass and using Bastard's boundary conditions, Schrödinger equation at each media is solved and then using a confirmed recurrence method, the transmission and reflection coefficients and the energy quantification condition are expressed. They are simple combination of coupled equations. Schrödinger's equation solutions are Airy functions or plane waves, depending on the electrical potential energy slope. To illustrate the feasibility of the proposed method, the N barriers – (N−1) wells structure for N=3, 5, 8, 9, 17 and 35 are studied. All results show very good agreements with previously published results obtained from applying different methods on similar systems.
Preconditioned iterations to calculate extreme eigenvalues
Energy Technology Data Exchange (ETDEWEB)
Brand, C.W.; Petrova, S. [Institut fuer Angewandte Mathematik, Leoben (Austria)
1994-12-31
Common iterative algorithms to calculate a few extreme eigenvalues of a large, sparse matrix are Lanczos methods or power iterations. They converge at a rate proportional to the separation of the extreme eigenvalues from the rest of the spectrum. Appropriate preconditioning improves the separation of the eigenvalues. Davidson`s method and its generalizations exploit this fact. The authors examine a preconditioned iteration that resembles a truncated version of Davidson`s method with a different preconditioning strategy.
1987-06-01
11.55), we get (11.56) 1 bu(u - ZhU)dx < bull - hUi{ !s Ch2V(a), where C = C(aOa 1lbo,blV 0 (a),X). Next we consider I(S-Sh)uIL and Ij(T-Th)uaL2 It is...Math. Ann. 97, 711-736. Courant, R. [1943]: Variational methods for the solution of prob- .-lems of equilibrium and vibrations, Bull . Amer. Math. Soc...fournir des bornes superieures ou inferieures, C.R. Acad. Sci., Paris 235, 995-997. .V Prodi, G. (1962]: Theoremi di tipo locale per il sistema de Navier
Spectral nodal method for one-speed X,Y-geometry Eigenvalue diffusion problems
International Nuclear Information System (INIS)
Dominguez, Dany S.; Lorenzo, Daniel M.; Hernandez, Carlos G.; Barros, Ricardo C.; Silva, Fernando C. da
2001-01-01
Presented here is a new numerical nodal method for steady-state multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the transverse-integrated nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X and Y directions, and then considering flat approximations for the transverse leakage terms. These flat approximations are the only approximations that we consider in this method; as a result the numerical solutions are completely free from truncation errors in slab geometry. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in a heterogeneous medium. (author)
Energy Technology Data Exchange (ETDEWEB)
Maiz, F., E-mail: Fethi_maiz@yahoo.fr [King Khalid University, Faculty of Science, Physics Department, P.O. Box 9004, Abha (Saudi Arabia); University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); Eissa, S.A. [King Khalid University, Faculty of Science, Physics Department, P.O. Box 9004, Abha (Saudi Arabia); AL-AZHAR University, Faculty of Science, Physics Department, Nasr City, Cairo (Egypt); AlFaify, S. [King Khalid University, Faculty of Science, Physics Department, P.O. Box 9004, Abha (Saudi Arabia)
2013-09-15
Assuming an effective mass approximation and using Bastard's boundary conditions, a simple method for simultaneous determination of the energy levels forming the sub-band structure and the transmissions coefficient of non-symmetrical, non-periodical potential semiconducting heterostructure is being proposed. The method can be applied on a multilayer system with varying thickness and effective mass of the layers, and with potential that is neither periodical nor symmetrical. To illustrate the feasibility of the proposed method, cases of symmetrical rectangular triple-barrier structure with constant effective mass, multi-barrier semiconductor heterostructure (nine barriers–eight-wells), and monomer height barrier superlattices (300 barriers) systems have been examined. Findings show very good agreements with previously published results obtained by different methods on similar systems. The proposed method was found to be useful for any number of semiconducting layers arranged in any random way making it more realistic, simple, and applicable to superlattice analysis and for devices design.
A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion
CUI, C.; Hou, W.
2017-12-01
Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.
On quasiclassical approximation in the inverse scattering method
International Nuclear Information System (INIS)
Geogdzhaev, V.V.
1985-01-01
Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem
Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates
Kitahara, M
1985-01-01
The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro
Radiation Source Mapping with Bayesian Inverse Methods
Hykes, Joshua Michael
We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution
A method of the asymmetric Abel's inversion in plasma diagnosis
International Nuclear Information System (INIS)
Matoba, Tohru; Funahashi, Akimasa
1975-09-01
In the case of a noncylindrical plasma, axis symmetric components are drawn from observed projected intensities of physical quantities, assuming an asymmetric form. And the radial intensity distribution is determined by Abel's inversion method. The best fitting curve is obtained analytically from measured values by the least-square estimation of nonlinear parameters. The cylindrical symmetric Abel's inversion code ( ABELIC ) and the asymmetric Abel's inversion code ( ABELILSENP 2 ) are described. (auth.)
Colpitts, Eigenvalues and Chaos
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
It is possible to obtain insight in the chaotic nature of a nonlinear oscillator by means of a study of the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator. The movements of the eigenvalues as functions of time are found. The instantaneous power in t...
International Nuclear Information System (INIS)
Sperotto, Fabiola Aiub; Segatto, Cynthia Feijo; Zabadal, Jorge
2002-01-01
In this work, we determine the dominant eigenvalue of the one-dimensional neutron transport equation in a slab constructing an integral form for the neutron transport equation which is the expressed in terms of fractional derivative of the angular flux. Equating the fractional derivative of the angular flux to the integrate equation, we determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of Riemann-Liouville definition of fractional derivative. Once known the angular flux the dominant eigenvalue is calculated solving a transcendental equation resulting from the application of the boundary conditions. We report the methodology applied, for comparison with available results in literature. (author)
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM
DEFF Research Database (Denmark)
Knudsen, Kim; Lassas, Matti; Mueller, Jennifer
2009-01-01
A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral...... the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel...
Hybrid inverse design method for nonlifting bodies in incompressible flow
CSIR Research Space (South Africa)
Broughton, BA
2006-11-01
Full Text Available A methodology for the inverse design of non-lifting axisymmetric bodies in compressible flow is presented. In this method, an inverse design approach based on conformal mapping is used to design a set of airfoils in isolation. These airfoils...
EISPACK-J: subprogram package for solving eigenvalue problems
International Nuclear Information System (INIS)
Fujimura, Toichiro; Tsutsui, Tsuneo
1979-05-01
EISPACK-J, a subprogram package for solving eigenvalue problems, has been developed and subprograms with a variety of functions have been prepared. These subprograms can solve standard problems of complex matrices, general problems of real matrices and special problems in which only the required eigenvalues and eigenvectors are calculated. They are compared to existing subprograms, showing their features through benchmark tests. Many test problems, including realistic scale problems, are provided for the benchmark tests. Discussions are made on computer core storage and computing time required for each subprogram, and accuracy of the solution. The results show that the subprograms of EISPACK-J, based on Householder, QR and inverse iteration methods, are the best in computing time and accuracy. (author)
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2012-01-01
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when
A two-stage method for inverse medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2013-01-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based
Full Waveform Inversion Using Oriented Time Migration Method
Zhang, Zhendong
2016-04-12
Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I
Spegazzini, Nicolas; Siesler, Heinz W; Ozaki, Yukihiro
2012-08-02
The doublet of the ν(C=O) carbonyl band in isomeric urethane systems has been extensively discussed in qualitative terms on the basis of FT-IR spectroscopy of the macromolecular structures. Recently, a reaction extent model was proposed as an inverse kinetic problem for the synthesis of diphenylurethane for which hydrogen-bonded and non-hydrogen-bonded C=O functionalities were identified. In this article, the heteronuclear C=O···H-N hydrogen bonding in the isomeric structure of diphenylurethane synthesized from phenylisocyanate and phenol was investigated via FT-IR spectroscopy, using a methodology of regularization for the inverse reaction extent model through an eigenvalue problem. The kinetic and thermodynamic parameters of this system were derived directly from the spectroscopic data. The activation and thermodynamic parameters of the isomeric structures of diphenylurethane linked through a hydrogen bonding equilibrium were studied. The study determined the enthalpy (ΔH = 15.25 kJ/mol), entropy (TΔS = 14.61 kJ/mol), and free energy (ΔG = 0.6 kJ/mol) of heteronuclear C=O···H-N hydrogen bonding by FT-IR spectroscopy through direct calculation from the differences in the kinetic parameters (δΔ(‡)H, -TδΔ(‡)S, and δΔ(‡)G) at equilibrium in the chemical reaction system. The parameters obtained in this study may contribute toward a better understanding of the properties of, and interactions in, supramolecular systems, such as the switching behavior of hydrogen bonding.
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
Estimating surface acoustic impedance with the inverse method.
Piechowicz, Janusz
2011-01-01
Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.
Eigenvalue Decomposition-Based Modified Newton Algorithm
Directory of Open Access Journals (Sweden)
Wen-jun Wang
2013-01-01
Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.
Inverse thermal analysis method to study solidification in cast iron
DEFF Research Database (Denmark)
Dioszegi, Atilla; Hattel, Jesper
2004-01-01
Solidification modelling of cast metals is widely used to predict final properties in cast components. Accurate models necessitate good knowledge of the solidification behaviour. The present study includes a re-examination of the Fourier thermal analysis method. This involves an inverse numerical...... solution of a 1-dimensional heat transfer problem connected to solidification of cast alloys. In the analysis, the relation between the thermal state and the fraction solid of the metal is evaluated by a numerical method. This method contains an iteration algorithm controlled by an under relaxation term...... inverse thermal analysis was tested on both experimental and simulated data....
An inverse method for color uniformity in white LED spotlights
Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.
2013-01-01
Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is
An inverse method for color uniformity in white LED spotlights
Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.
2014-01-01
Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is
Uniqueness and numerical methods in inverse obstacle scattering
International Nuclear Information System (INIS)
Kress, Rainer
2007-01-01
The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages
Computation of standard deviations in eigenvalue calculations
International Nuclear Information System (INIS)
Gelbard, E.M.; Prael, R.
1990-01-01
In Brissenden and Garlick (1985), the authors propose a modified Monte Carlo method for eigenvalue calculations, designed to decrease particle transport biases in the flux and eigenvalue estimates, and in corresponding estimates of standard deviations. Apparently a very similar method has been used by Soviet Monte Carlo specialists. The proposed method is based on the generation of ''superhistories'', chains of histories run in sequence without intervening renormalization of the fission source. This method appears to have some disadvantages, discussed elsewhere. Earlier numerical experiments suggest that biases in fluxes and eigenvalues are negligibly small, even for very small numbers of histories per generation. Now more recent experiments, run on the CRAY-XMP, tend to confirm these earlier conclusions. The new experiments, discussed in this paper, involve the solution of one-group 1D diffusion theory eigenvalue problems, in difference form, via Monte Carlo. Experiments covered a range of dominance ratios from ∼0.75 to ∼0.985. In all cases flux and eigenvalue biases were substantially smaller than one standard deviation. The conclusion that, in practice, the eigenvalue bias is negligible has strong theoretical support. (author)
Liu, Tianyu; Du, Xining; Ji, Wei; Xu, X. George; Brown, Forrest B.
2014-06-01
For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed.
International Nuclear Information System (INIS)
Liu, T.; Du, X.; Ji, W.; Xu, G.; Brown, F.B.
2013-01-01
For nuclear reactor analysis such as the neutron eigenvalue calculations, the time consuming Monte Carlo (MC) simulations can be accelerated by using graphics processing units (GPUs). However, traditional MC methods are often history-based, and their performance on GPUs is affected significantly by the thread divergence problem. In this paper we describe the development of a newly designed event-based vectorized MC algorithm for solving the neutron eigenvalue problem. The code was implemented using NVIDIA's Compute Unified Device Architecture (CUDA), and tested on a NVIDIA Tesla M2090 GPU card. We found that although the vectorized MC algorithm greatly reduces the occurrence of thread divergence thus enhancing the warp execution efficiency, the overall simulation speed is roughly ten times slower than the history-based MC code on GPUs. Profiling results suggest that the slow speed is probably due to the memory access latency caused by the large amount of global memory transactions. Possible solutions to improve the code efficiency are discussed. (authors)
On multiple level-set regularization methods for inverse problems
International Nuclear Information System (INIS)
DeCezaro, A; Leitão, A; Tai, X-C
2009-01-01
We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels
Eigenvalue distributions of Wilson loops
International Nuclear Information System (INIS)
Lohmayer, Robert
2010-01-01
In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the modulus square of the characteristic polynomial. Furthermore
Eigenvalue distributions of Wilson loops
Energy Technology Data Exchange (ETDEWEB)
Lohmayer, Robert
2010-07-01
In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the
A high-order SPH method by introducing inverse kernels
Directory of Open Access Journals (Sweden)
Le Fang
2017-02-01
Full Text Available The smoothed particle hydrodynamics (SPH method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS and Moving-Least-Square (MLS methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.
Multi-frequency direct sampling method in inverse scattering problem
Kang, Sangwoo; Lambert, Marc; Park, Won-Kwang
2017-10-01
We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.
Gaining insight into food webs reconstructed by the inverse method
Kones, J.; Soetaert, K.E.R.; Van Oevelen, D.; Owino, J.; Mavuti, K.
2006-01-01
The use of the inverse method to analyze flow patterns of organic components in ecological systems has had wide application in ecological modeling. Through this approach, an infinite number of food web flows describing the food web and satisfying biological constraints are generated, from which one
A variational Bayesian method to inverse problems with impulsive noise
Jin, Bangti
2012-01-01
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve
Gradient-type methods in inverse parabolic problems
International Nuclear Information System (INIS)
Kabanikhin, Sergey; Penenko, Aleksey
2008-01-01
This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.
A method of inversion of satellite magnetic anomaly data
Mayhew, M. A.
1977-01-01
A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.
Indium oxide inverse opal films synthesized by structure replication method
Amrehn, Sabrina; Berghoff, Daniel; Nikitin, Andreas; Reichelt, Matthias; Wu, Xia; Meier, Torsten; Wagner, Thorsten
2016-04-01
We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.
Refractive index inversion based on Mueller matrix method
Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao
2016-03-01
Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.
International Nuclear Information System (INIS)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
A finite-difference contrast source inversion method
International Nuclear Information System (INIS)
Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M
2008-01-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium
Regularization method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
Inverse operator theory method and its applications in nonlinear physics
International Nuclear Information System (INIS)
Fang Jinqing
1993-01-01
Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed
Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition
Energy Technology Data Exchange (ETDEWEB)
Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)
2014-12-15
In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.
Study of inverse methods in remote sensing with laser
International Nuclear Information System (INIS)
Jesus, Wellington Carlos de
2009-01-01
The Laboratory of Environmental Applications of Lasers at IPEN realizes a study about atmospherics properties, such as extinction and backscattering coefficient. These coefficient are estimated by an inverse method, whose estimate quality is difficult to measure. This work presents a method with good statistic approach to retrieval the same coefficients. The new method, however, offers a number of advantages compared to the first method in use, including (1) the ability to incorporate different kinds of information under a common retrieval philosophy and (2) the method provides number of ways for evaluating the quality of the retrieval. Thus we hope improve the accuracy of estimates. (author)
Complexity analysis of accelerated MCMC methods for Bayesian inversion
International Nuclear Information System (INIS)
Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M
2013-01-01
The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
2D Inversion of Transient Electromagnetic Method (TEM)
Bortolozo, Cassiano Antonio; Luís Porsani, Jorge; Acácio Monteiro dos Santos, Fernando
2017-04-01
A new methodology was developed for 2D inversion of Transient Electromagnetic Method (TEM). The methodology consists in the elaboration of a set of routines in Matlab code for modeling and inversion of TEM data and the determination of the most efficient field array for the problem. In this research, the 2D TEM modeling uses the finite differences discretization. To solve the inversion problem, were applied an algorithm based on Marquardt technique, also known as Ridge Regression. The algorithm is stable and efficient and it is widely used in geoelectrical inversion problems. The main advantage of 1D survey is the rapid data acquisition in a large area, but in regions with two-dimensional structures or that need more details, is essential to use two-dimensional interpretation methodologies. For an efficient field acquisition we used in an innovative form the fixed-loop array, with a square transmitter loop (200m x 200m) and 25m spacing between the sounding points. The TEM surveys were conducted only inside the transmitter loop, in order to not deal with negative apparent resistivity values. Although it is possible to model the negative values, it makes the inversion convergence more difficult. Therefore the methodology described above has been developed in order to achieve maximum optimization of data acquisition. Since it is necessary only one transmitter loop disposition in the surface for each series of soundings inside the loop. The algorithms were tested with synthetic data and the results were essential to the interpretation of the results with real data and will be useful in future situations. With the inversion of the real data acquired over the Paraná Sedimentary Basin (PSB) was successful realized a 2D TEM inversion. The results indicate a robust geoelectrical characterization for the sedimentary and crystalline aquifers in the PSB. Therefore, using a new and relevant approach for 2D TEM inversion, this research effectively contributed to map the most
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
Maximum-likelihood method for numerical inversion of Mellin transform
International Nuclear Information System (INIS)
Iqbal, M.
1997-01-01
A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts the Mellin transform to Laplace transform, then the maximum-likelihood regularization method is used to recover the original function of the Mellin transform. The performance of the method is illustrated by the inversion of the test functions available in the literature (J. Inst. Math. Appl., 20 (1977) 73; Math. Comput., 53 (1989) 589). Effectiveness of the method is shown by results obtained through demonstration by means of tables and diagrams
A variational Bayesian method to inverse problems with impulsive noise
Jin, Bangti
2012-01-01
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.
Lag profile inversion method for EISCAT data analysis
Directory of Open Access Journals (Sweden)
I. I. Virtanen
2008-03-01
Full Text Available The present standard EISCAT incoherent scatter experiments are based on alternating codes that are decoded in power domain by simple summation and subtraction operations. The signal is first digitised and then different lagged products are calculated and decoded in real time. Only the decoded lagged products are saved for further analysis so that both the original data samples and the undecoded lagged products are lost. A fit of plasma parameters can be later performed using the recorded lagged products. In this paper we describe a different analysis method, which makes use of statistical inversion in removing range ambiguities from the lag profiles. An analysis program carrying out both the lag profile inversion and the fit of the plasma parameters has been constructed. Because recording the received signal itself instead of the lagged products allows very flexible data analysis, the program is constructed to use raw data, i.e. IQ-sampled signal recorded from an IF stage of the radar. The program is now capable of analysing standard alternating-coded EISCAT experiments as well as experiments with any other kind of radar modulation if raw data is available. The program calculates the ambiguous lag profiles and is capable of inverting them as such but, for analysis in real time, time integration is needed before inversion. We demonstrate the method using alternating code experiments in the EISCAT UHF radar and specific hardware connected to the second IF stage of the receiver. This method produces a data stream of complex samples, which are stored for later processing. The raw data is analysed with lag profile inversion and the results are compared to those given by the standard method.
Quantum method of the inverse scattering problem. Pt. 1
International Nuclear Information System (INIS)
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Inversion methods for analysis of neutron brightness measurements in tokamaks
International Nuclear Information System (INIS)
Gorini, G.; Gottardi, N.
1990-02-01
The problem of determining neutron emissivity from neutron brightness measurements in magnetic fusion plasmas is addressed. In the case of two-dimensional measurements with two orthogonal cameras, a complete, tomographic analysis of the data can in principle be performed. The results depend critically on the accuracy of the measurements and alternative solutions can be sought under the assumption of a known emissivity topology (Generalized Abel Inversion). In this work, neutron brightness data from the JET tokamak have been studied with both methods. We find that with the present experimental uncertainty (levels 10-20%) the Abel inversion method works best, while two-dimensional information cannot in general be deduced. This is confirmed by studies of the error propagation in the inversion using artificial data, which are also presented here. An important application of emissivity profile information is the determination of the plasma deuterium temperature profile, T D (R). Results are presented here from the analysis of JET data and the errors in T D (R) are discussed in some detail. It is found that, for typical JET plasma conditions, the dominant source of uncertainty arises from the high plasma impurity level and the fact that it is poorly known; these problems can be expected to be remedied and neutron brightness measurements would be expected to be very effective (especially in high density plasmas) as a T D (R) diagnostics. (author)
Application of the kernel method to the inverse geosounding problem.
Hidalgo, Hugo; Sosa León, Sonia; Gómez-Treviño, Enrique
2003-01-01
Determining the layered structure of the earth demands the solution of a variety of inverse problems; in the case of electromagnetic soundings at low induction numbers, the problem is linear, for the measurements may be represented as a linear functional of the electrical conductivity distribution. In this paper, an application of the support vector (SV) regression technique to the inversion of electromagnetic data is presented. We take advantage of the regularizing properties of the SV learning algorithm and use it as a modeling technique with synthetic and field data. The SV method presents better recovery of synthetic models than Tikhonov's regularization. As the SV formulation is solved in the space of the data, which has a small dimension in this application, a smaller problem than that considered with Tikhonov's regularization is produced. For field data, the SV formulation develops models similar to those obtained via linear programming techniques, but with the added characteristic of robustness.
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi
2012-01-10
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.
The Adjoint Method for the Inverse Problem of Option Pricing
Directory of Open Access Journals (Sweden)
Shou-Lei Wang
2014-01-01
Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.
Modern algorithms for large sparse eigenvalue problems
International Nuclear Information System (INIS)
Meyer, A.
1987-01-01
The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)
Topological derivatives of eigenvalues and neural networks in identification of imperfections
International Nuclear Information System (INIS)
Grzanek, M; Nowakowski, A; Sokolowski, J
2008-01-01
Numerical method for identification of imperfections is devised for elliptic spectral problems. The neural networks are employed for numerical solution. The topological derivatives of eigenvalues are used in the learning procedure of the neural networks. The topological derivatives of eigenvalues are determined by the methods of asymptotic analysis in singularly perturbed geometrical domains. The convergence of the numerical method in a probabilistic setting is analysed. The method is presented for the identification of small singular perturbations of the boundary of geometrical domain, however the framework is general and can be used for numerical solutions of inverse problems in the presence of small imperfections in the interior of the domain. Some numerical results are given for elliptic spectral problem in two spatial dimensions.
Improved algorithm for three-dimensional inverse method
Qiu, Xuwen
An inverse method, which works for full 3D viscous applications in turbomachinery aerodynamic design, is developed. The method takes pressure loading and thickness distribution as inputs and computes the 3D-blade geometry. The core of the inverse method consists of two closely related steps, which are integrated into a time-marching procedure of a Navier-Stokes solver. First, the pressure loading condition is enforced while flow is allowed to cross the blade surfaces. A permeable blade boundary condition is developed here in order to be consistent with the propagation characteristics of the transient Navier-Stokes equations. In the second step, the blade geometry is adjusted so that the flow-tangency condition is satisfied for the new blade. A Non-Uniform Rational B-Spline (NURBS) model is used to represent the span-wise camber curves. The flow-tangency condition is then transformed into a general linear least squares fitting problem, which is solved by a robust Singular Value Decomposition (SVD) scheme. This blade geometry generation scheme allows the designer to have direct control over the smoothness of the calculated blade, and thus ensures the numerical stability during the iteration process. Numerical experiments show that this method is very accurate, efficient and robust. In target-shooting tests, the program was able to converge to the target blade accurately from a different initial blade. The speed of an inverse run is only about 15% slower than its analysis counterpart, which means a complete 3D viscous inverse design can be done in a matter of hours. The method is also proved to work well with the presence of clearance between the blade and the housing, a key factor to be considered in aerodynamic design. The method is first developed for blades without splitters, and is then extended to provide the capability of analyzing and designing machines with splitters. This gives designers an integrated environment where the aerodynamic design of both full
Numerical computation of FCT equilibria by inverse equilibrium method
International Nuclear Information System (INIS)
Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki
1986-11-01
FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)
International Nuclear Information System (INIS)
Kim, Song Hyun; Song, Myung Sub; Shin, Chang Ho; Noh, Jae Man
2014-01-01
In using the perturbation theory, the uncertainty of the response can be estimated by a single transport simulation, and therefore it requires small computational load. However, it has a disadvantage that the computation methodology must be modified whenever estimating different response type such as multiplication factor, flux, or power distribution. Hence, it is suitable for analyzing few responses with lots of perturbed parameters. Statistical approach is a sampling based method which uses randomly sampled cross sections from covariance data for analyzing the uncertainty of the response. XSUSA is a code based on the statistical approach. The cross sections are only modified with the sampling based method; thus, general transport codes can be directly utilized for the S/U analysis without any code modifications. However, to calculate the uncertainty distribution from the result, code simulation should be enough repeated with randomly sampled cross sections. Therefore, this inefficiency is known as a disadvantage of the stochastic method. In this study, an advanced sampling method of the cross sections is proposed and verified to increase the estimation efficiency of the sampling based method. In this study, to increase the estimation efficiency of the sampling based S/U method, an advanced sampling and estimation method was proposed. The main feature of the proposed method is that the cross section averaged from each single sampled cross section is used. For the use of the proposed method, the validation was performed using the perturbation theory
Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination
Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos
2010-01-01
The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093
Solution of the radiative enclosure with a hybrid inverse method
Energy Technology Data Exchange (ETDEWEB)
Silva, Rogerio Brittes da; Franca, Francis Henrique Ramos [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica], E-mail: frfranca@mecanica.ufrgs.br
2010-07-01
This work applies the inverse analysis to solve a three-dimensional radiative enclosure - which the surfaces are diffuse-grays - filled with transparent medium. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A hybrid solution that couples two methods, the generalized extremal optimization (GEO) and the truncated singular value decomposition (TSVD) is proposed. The determination of the heat sources distribution is treated as an optimization problem, by GEO algorithm , whereas the solution of the system of equation, that embodies the Fredholm equation of first kind and therefore is expected to be ill conditioned, is build up through TSVD regularization method. The results show that the hybrid method can lead to a heat flux on the design surface that satisfies the imposed conditions with maximum error of less than 1,10%. The results illustrated the relevance of a hybrid method as a prediction tool. (author)
On the evolution equations, solvable through the inverse scattering method
International Nuclear Information System (INIS)
Gerdjikov, V.S.; Khristov, E.Kh.
1979-01-01
The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation
GePb Alloy Growth Using Layer Inversion Method
Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.
2018-04-01
Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.
GePb Alloy Growth Using Layer Inversion Method
Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.
2018-07-01
Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.
Sturm--Liouville eigenvalue problem
International Nuclear Information System (INIS)
Bailey, P.B.
1977-01-01
The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular
Eigenvalues of the volume operator in loop quantum gravity
International Nuclear Information System (INIS)
Meissner, Krzysztof A
2006-01-01
We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins, which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity
Energy eigenvalues of helium-like atoms in dense plasmas
International Nuclear Information System (INIS)
Hashino, Tasuke; Nakazaki, Shinobu; Kato, Takako; Kashiwabara, Hiromichi.
1987-04-01
Calculations based on a variational method with wave functions including the correlation of electrons are carried out to obtain energy eigenvalues of Schroedinger's equation for helium-like atoms embedded in dense plasmas, taking the Debye-Hueckel approximation. Energy eigenvalues for the 1 1 S, 2 1 S, and 2 3 S states are obtained as a function of Debye screening length. (author)
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Energy Technology Data Exchange (ETDEWEB)
Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
A two-stage method for inverse medium scattering
Ito, Kazufumi
2013-03-01
We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.
Energy Technology Data Exchange (ETDEWEB)
Labarile, A.; Barrachina, T.; Miró, R.; Verdú, G., E-mail: alabarile@iqn.upv.es, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Institute for Industrial, Radiophysical and Environmental Safety - ISIRYM, Valencia (Spain); Pereira, C., E-mail: claubia@nuclear.ufmg.br [Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG (Brazil). Departamento de Engenharia Nuclear
2017-07-01
The use of Best-Estimate computer codes is one of the greatest concerns in the nuclear industry especially for licensing analysis. Of paramount importance is the estimation of the uncertainties of the whole system to establish the safety margins based on highly reliable results. The estimation of these uncertainties should be performed by applying a methodology to propagate the uncertainties from the input parameters and the models implemented in the code to the output parameters. This study employs two different approaches for the Sensitivity Analysis (SA) and Uncertainty Quantification (UQ), the adjoint-based perturbation theory of TSUNAMI-3D, and the stochastic sampling technique of SAMPLER/KENO. The cases studied are two models of Light Water Reactors in the framework of the OECD/NEA UAM-LWR benchmark, a Boiling Water Reactor (BWR) and a Pressurized Water Reactor (PWR). Both of them at Hot Full Power (HFP) and Hot Zero Power (HZP) conditions, with and without control rod. This work presents the results of k{sub eff} from different simulation, and discuss the comparison of the two methods employed. In particular, a list of the major contributors to the uncertainty of k{sub eff} in terms of microscopic cross sections; their sensitivity coefficients; a comparison between the results of the two modules and with reference values; statistical information from the stochastic approach, and the probability and statistical confidence reached in the simulations. The reader will find all these information discussed in this paper. (author)
Perturbation of eigenvalues of preconditioned Navier-Stokes operators
Energy Technology Data Exchange (ETDEWEB)
Elman, H.C. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.
Perturbation of embedded eigenvalue by a near-lying resonance
Energy Technology Data Exchange (ETDEWEB)
Belyaev, V B; Motovilov, A K
1997-12-31
The case of quantum-mechanical system (including electronic molecules) is considered where Hamiltonian allows a separation, in particular by the Faddeev method, of a weakly coupled channel. Width (i.e. the imaginary part) of the resonance generated by a discrete spectrum eigenvalue of the separated channel is studied in the case where main part of the Hamiltonian gives itself another resonance. It is shown that if real parts of these resonances coincide and, at the same time, a coupling between the separated and main channels is sufficiently small then the width of the resonance generated by the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon being a kind of universal law, may play an important role increasing the `cold fusion` probability in electronic molecules whose nuclear constituents have narrow pre-threshold resonances. 21 refs.
Determination of brazed joint constitutive law by inverse method
International Nuclear Information System (INIS)
Lovato, G.; Moret, F.; Gallo, P. le; Cailletaud, G.; Pilvin, P.
1993-01-01
An important parameter often neglected for the calculation of residual stresses in brazed ceramic/metal assemblies is the joint constitutive law. In situ camber measurements on a model system (axisymmetric TZM/InCuSil ABA/316L samples) performed using a special vertical dilatometer during the whole brazing thermal cycle are compared with results of FEM calculations based on published filler metal constitutive laws. A strong disagreement is observed. Actual constitutive law of the joint is determined from these measurements using a numerical inverse method. Calculated displacements are fully consistent with experimental ones. True solidification temperature of the joint is determined. The identified constitutive law of the joint exhibits a low flow stress from solidification temperature to 320 C. (orig.)
A direct sampling method for inverse electromagnetic medium scattering
Ito, Kazufumi
2013-09-01
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data. © 2013 IOP Publishing Ltd.
Direct sampling methods for inverse elastic scattering problems
Ji, Xia; Liu, Xiaodong; Xi, Yingxia
2018-03-01
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.
Microstrip natural wave spectrum mathematical model using partial inversion method
International Nuclear Information System (INIS)
Pogarsky, S.A.; Litvinenko, L.N.; Prosvirnin, S.L.
1995-01-01
It is generally agreed that both microstrip lines itself and different discontinuities based on microstrips are the most difficult problem for accurate electrodynamic analysis. Over the last years much has been published about principles and accurate (or full wave) methods of microstrip lines investigations. The growing interest for this problem may be explained by the microstrip application in the millimeter-wave range for purpose of realizing interconnects and a variety of passive components. At these higher operating rating frequencies accurate component modeling becomes more critical. A creation, examination and experimental verification of the accurate method for planar electrodynamical structures natural wave spectrum investigations are the objects of this manuscript. The moment method with partial inversion operator method using may be considered as a basical way for solving this problem. This method is outlook for accurate analysis of different planar discontinuities in microstrip: such as step discontinuities, microstrip turns, Y- and X-junctions and etc., substrate space steps dielectric constants and other anisotropy types
Antar, B. N.
1976-01-01
A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Eigenvalue study of a chaotic resonator
Energy Technology Data Exchange (ETDEWEB)
Banova, Todorka [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany); Technische Universitaet Darmstadt, Graduate School of Computational Engineering, Dolivostrasse 15, D-64293 Darmstadt (Germany); Ackermann, Wolfgang; Weiland, Thomas [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)
2013-07-01
The field of quantum chaos comprises the study of the manifestations of classical chaos in the properties of the corresponding quantum systems. Within this work, we compute the eigenfrequencies that are needed for the level spacing analysis of a microwave resonator with chaotic characteristics. The major challenges posed by our work are: first, the ability of the approaches to tackle the large scale eigenvalue problem and second, the capability to extract many, i.e. order of thousands, eigenfrequencies for the considered cavity. The first proposed approach for an accurate eigenfrequency extraction takes into consideration the evaluated electric field computations in time domain of a superconducting cavity and by means of signal-processing techniques extracts the eigenfrequencies. The second approach is based on the finite element method with curvilinear elements, which transforms the continuous eigenvalue problem to a discrete generalized eigenvalue problem. Afterwards, the Lanczos algorithm is used for the solution of the generalized eigenvalue problem. In the poster, a summary of the applied algorithms, as well as, critical implementation details together with the simulation results are provided.
Comparison of optimal design methods in inverse problems
International Nuclear Information System (INIS)
Banks, H T; Holm, K; Kappel, F
2011-01-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst–Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667–77; De Gaetano A and Arino O 2000 J. Math. Biol. 40 136–68; Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979–90)
Comparison of optimal design methods in inverse problems
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Introduction to the mathematics of inversion in remote sensing and indirect measurements
Twomey, S
2013-01-01
Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing m...
Research on inverse methods and optimization in Italy
Larocca, Francesco
1991-01-01
The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).
Level set methods for inverse scattering—some recent developments
International Nuclear Information System (INIS)
Dorn, Oliver; Lesselier, Dominique
2009-01-01
We give an update on recent techniques which use a level set representation of shapes for solving inverse scattering problems, completing in that matter the exposition made in (Dorn and Lesselier 2006 Inverse Problems 22 R67) and (Dorn and Lesselier 2007 Deformable Models (New York: Springer) pp 61–90), and bringing it closer to the current state of the art
Parallel Symmetric Eigenvalue Problem Solvers
2015-05-01
Research” and the use of copyright material. Approved by Major Professor(s): Approved by: Head of the Departmental Graduate Program Date Alicia Marie... matrix . . . . . . . . . . . . . . . . . 106 8.15 Sparsity patterns for the Nastran benchmark of order 1.5 million . . . . 108 8.16 Sparsity patterns...magnitude eigenvalues of a given matrix pencil (A,B) along with their associated eigenvectors. Computing the smallest eigenvalues is more difficult
Centrifugal compressor shape modification using a proposed inverse design method
International Nuclear Information System (INIS)
Niliahmadabadi, Mahdi; Poursadegh, Farzad
2013-01-01
This paper is concerned with a quasi-3D design method for the radial and axial diffusers of a centrifugal compressor on the meridional plane. The method integrates a novel inverse design algorithm, called ball-spine algorithm (BSA), and a quasi-3D analysis code. The Euler equation is solved on the meridional plane for a numerical domain, of which unknown boundaries (hub and shroud) are iteratively modified under the BSA until a prescribed pressure distribution is reached. In BSA, unknown walls are composed of a set of virtual balls that move freely along specified directions called spines. The difference between target and current pressure distributions causes the flexible boundary to deform at each modification step. In validating the quasi-3D analysis code, a full 3D Navier-Stokes code is used to analyze the existing and designed compressors numerically. Comparison of the quasi-3D analysis results with full 3D analysis results shows viable agreement. The 3D numerical analysis of the current compressor shows a huge total pressure loss on the 90 .deg. bend between the radial and axial diffusers. Geometric modification of the meridional plane causes the efficiency to improve by about 10%.
Stress estimation in reservoirs using an integrated inverse method
Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre
2018-05-01
Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.
Centrifugal compressor shape modification using a proposed inverse design method
Energy Technology Data Exchange (ETDEWEB)
Niliahmadabadi, Mahdi [Isfahan University of Technology, Isfahan (Iran, Islamic Republic of); Poursadegh, Farzad [Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2013-03-15
This paper is concerned with a quasi-3D design method for the radial and axial diffusers of a centrifugal compressor on the meridional plane. The method integrates a novel inverse design algorithm, called ball-spine algorithm (BSA), and a quasi-3D analysis code. The Euler equation is solved on the meridional plane for a numerical domain, of which unknown boundaries (hub and shroud) are iteratively modified under the BSA until a prescribed pressure distribution is reached. In BSA, unknown walls are composed of a set of virtual balls that move freely along specified directions called spines. The difference between target and current pressure distributions causes the flexible boundary to deform at each modification step. In validating the quasi-3D analysis code, a full 3D Navier-Stokes code is used to analyze the existing and designed compressors numerically. Comparison of the quasi-3D analysis results with full 3D analysis results shows viable agreement. The 3D numerical analysis of the current compressor shows a huge total pressure loss on the 90 .deg. bend between the radial and axial diffusers. Geometric modification of the meridional plane causes the efficiency to improve by about 10%.
Lagrangian Differentiation, Integration and Eigenvalues Problems
International Nuclear Information System (INIS)
Durand, L.
1983-01-01
Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented. It is then shown that one can 'invert' his differentiation technique to obtain a flexible, factorially convergent Lagrangian integration scheme which should be useful in a variety of problems, e.g. solution of integral equations
New approach to calculate bound state eigenvalues
International Nuclear Information System (INIS)
Gerck, E.; Gallas, J.A.C.
1983-01-01
A method of solving the radial Schrodinger equation for bound states is discussed. The method is based on a new piecewise representation of the second derivative operator on a set of functions that obey the boundary conditions. This representation is trivially diagonalised and leads to closed form expressions of the type E sub(n)=E(ab+b+c/n+...) for the eigenvalues. Examples are given for the power-law and logarithmic potentials. (Author) [pt
International Nuclear Information System (INIS)
Xiaojing Zhu; Predecki, P.; Ballard, B.
1995-01-01
Two different inversion methods, the inverse Laplace method and the linear constrained numerical method, for retrieving the z-profiles of diffraction data from experimentally obtained i-profiles were compared using tests with a known function as the original z-profile. Two different real data situations were simulated to determine the effects of specimen thickness and missing τ-profile data at small τ-values on the retrieved z-profiles. The results indicate that although both methods are able to retrieve the z-profiles in the bulk specimens satisfactorily, the numerical method can be used for thin film samples as well. Missing τ-profile data at small τ values causes error in the retrieved z-profiles with both methods, particularly when the trend of the τ-profile at small τ is significantly changed because of the missing data. 6 refs., 3 figs
Full Waveform Inversion Using Oriented Time Migration Method
Zhang, Zhendong
2016-01-01
Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have
The attitude inversion method of geostationary satellites based on unscented particle filter
Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao
2018-04-01
The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.
Novel inversion method for land mine imaging and detection
Sindoni, Orazio I.; Cohoon, David K.
2000-08-01
We have developed, using both partial differential equation approaches and integral equation formulations, a precise method to invert acoustic or electromagnetic scattering data from macroscopic concealed objects. Our approach makes use of the ideas associated with our exact solution of partial differential equations as described in our paper where we were able to collapse the number of equations by elimination of transcendentals therefore preserving the absolute mathematical precision inherent in the partial differential equation formulation. Our mathematical method, as a consequence, has not encountered the traditional loss of precision when inverting the scattered data. The unrestricted wavelength range allows us to penetrate any material which may surround the object and differentiate between the object and the media. For this reason we have applied our inversion scheme to landmine detection as we can penetrate and differentiate under both wet and dry conditions. Also, we are able to account, under certain conditions, for dielectric nonlinearities of material in the concealed object. Therefore, we are able to build in density dependent false colors a 3D grid representative of both the media and of the embedded object including the internal structure of the object. We have surveyed the literature on the subject of recovery of physical location of concealed objects and we have found that most of the present applications such as land mine detection, and we have found that most of the present applications have shortcomings due to the physical changes that are present in the surrounding media or the discontinuities of physical properties of the media. For all the above reasons we believe that we may have the most versatile and mathematically precise approach to the solution of this problem.
Fourier convergence analysis applied to neutron diffusion Eigenvalue problem
International Nuclear Information System (INIS)
Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook
2004-01-01
Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge
Inverse Scattering Method and Soliton Solution Family for String Effective Action
International Nuclear Information System (INIS)
Ya-Jun, Gao
2009-01-01
A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained
Reconstruction Methods for Inverse Problems with Partial Data
DEFF Research Database (Denmark)
Hoffmann, Kristoffer
This thesis presents a theoretical and numerical analysis of a general mathematical formulation of hybrid inverse problems in impedance tomography. This includes problems from several existing hybrid imaging modalities such as Current Density Impedance Imaging, Magnetic Resonance Electrical...... Impedance Tomography, and Ultrasound Modulated Electrical Impedance Tomography. After giving an introduction to hybrid inverse problems in impedance tomography and the mathematical tools that facilitate the related analysis, we explain in detail the stability properties associated with the classification...... of a linearised hybrid inverse problem. This is done using pseudo-differential calculus and theory for overdetermined boundary value problem. Using microlocal analysis we then present novel results on the propagation of singularities, which give a precise description of the distinct features of solutions...
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...
Generalized Eigenvalues for pairs on heritian matrices
Rublein, George
1988-01-01
A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.
Shakir, Muhammad Zeeshan
2013-03-01
Eigenvalue Ratio (ER) detector based on the two extreme eigenvalues of the received signal covariance matrix is currently one of the most effective solution for spectrum sensing. However, the analytical results of such scheme often depend on asymptotic assumptions since the distribution of the ratio of two extreme eigenvalues is exceptionally complex to compute. In this paper, a non-asymptotic spectrum sensing approach for ER detector is introduced to approximate the marginal and joint distributions of the two extreme eigenvalues. The two extreme eigenvalues are considered as dependent Gaussian random variables such that their joint probability density function (PDF) is approximated by a bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. The PDF approximation approach is based on the moment matching method where we calculate the exact analytical moments of joint and marginal distributions of the two extreme eigenvalues. The decision threshold is calculated by exploiting the statistical mean and the variance of each of the two extreme eigenvalues and the correlation coefficient between them. The performance analysis of our newly proposed approximation approach is compared with the already published asymptotic Tracy-Widom approximation approach. It has been shown that our results are in perfect agreement with the simulation results for any number of secondary users and received samples. © 2002-2012 IEEE.
Bound-state Dirac eigenvalues for scalar potentials
International Nuclear Information System (INIS)
Ram, B.; Arafah, M.
1981-01-01
The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)
Element diameter free stability parameters for stabilized methods applied to fluids
International Nuclear Information System (INIS)
Franca, L.P.; Madureira, A.L.
1992-08-01
Stability parameters for stabilized methods in fluids are suggested. The computation of the largest eigenvalue of a generalized eigenvalue problem replaces controversial definitions of element diameters and inverse estimate constants, used heretofore to compute these stability parameters. The design is employed in the advective-diffusive model, incompressible Navier-Stokes equations and the Stokes problem. (author)
A time domain inverse dynamic method for the end point tracking control of a flexible manipulator
Kwon, Dong-Soo; Book, Wayne J.
1991-01-01
The inverse dynamic equation of a flexible manipulator was solved in the time domain. By dividing the inverse system equation into the causal part and the anticausal part, we calculated the torque and the trajectories of all state variables for a given end point trajectory. The interpretation of this method in the frequency domain was explained in detail using the two-sided Laplace transform and the convolution integral. The open loop control of the inverse dynamic method shows an excellent result in simulation. For real applications, a practical control strategy is proposed by adding a feedback tracking control loop to the inverse dynamic feedforward control, and its good experimental performance is presented.
International Nuclear Information System (INIS)
Menezes, Welton Alves; Alves Filho, Hermes; Barros, Ricardo C.
2009-01-01
In this paper the X,Y-geometry SD-SGF-CN spectral nodal method, cf. spectral diamond-spectral Green's function-constant nodal, is used to determine the one-speed node-edge average angular fluxes in heterogeneous domains. This hybrid spectral nodal method uses the spectral diamond (SD) auxiliary equation for the multiplying regions and the spectral Green's function (SGF) auxiliary equation for the non-multiplying regions of the domain. Moreover, we consider constant approximations for the transverse-leakage terms in the transverse integrated S N nodal equations. We solve the SD-SGF-CN equations using the one-node block inversion (NBI) iterative scheme, which uses the most recent estimates available for the node-entering fluxes to evaluate the node-exiting fluxes in the directions that constitute the incoming fluxes for the adjacent node. Using these results, we offer an algorithm for analytical reconstruction of the coarse-mesh nodal solution within each spatial node, as localized numerical solutions are not generated by usual accurate nodal methods. Numerical results are presented to illustrate the accuracy of the present algorithm. (author)
Evaluation of Inversion Methods Applied to Ionospheric ro Observations
Rios Caceres, Arq. Estela Alejandra; Rios, Victor Hugo; Guyot, Elia
The new technique of radio-occultation can be used to study the Earth's ionosphere. The retrieval processes of ionospheric profiling from radio occultation observations usually assume spherical symmetry of electron density distribution at the locality of occultation and use the Abel integral transform to invert the measured total electron content (TEC) values. This pa-per presents a set of ionospheric profiles obtained from SAC-C satellite with the Abel inversion technique. The effects of the ionosphere on the GPS signal during occultation, such as bending and scintillation, are examined. Electron density profiles are obtained using the Abel inversion technique. Ionospheric radio occultations are validated using vertical profiles of electron con-centration from inverted ionograms , obtained from ionosonde sounding in the vicinity of the occultation. Results indicate that the Abel transform works well in the mid-latitudes during the daytime, but is less accurate during the night-time.
Eigenvalue treatment of cosmological models
International Nuclear Information System (INIS)
Novello, M.; Soares, D.
1976-08-01
From the decomposition of Weyl tensor into its electric and magnetic parts, it is formulated the eigenvalue problem for cosmological models, and is used quasi-maxwellian form of Einstein's equation to propagate it along a time-like congruence. Three related theorems are presented
Inverse mass matrix via the method of localized lagrange multipliers
Czech Academy of Sciences Publication Activity Database
González, José A.; Kolman, Radek; Cho, S.S.; Felippa, C.A.; Park, K.C.
2018-01-01
Roč. 113, č. 2 (2018), s. 277-295 ISSN 0029-5981 R&D Projects: GA MŠk(CZ) EF15_003/0000493; GA ČR GA17-22615S Institutional support: RVO:61388998 Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis Subject RIV: BI - Acoustics OBOR OECD: Applied mechanics Impact factor: 2.162, year: 2016 https://onlinelibrary.wiley.com/doi/10.1002/nme.5613
Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography
DEFF Research Database (Denmark)
Hoffmann, Kristoffer; Knudsen, Kim
2014-01-01
For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...... impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two...
Generalized eigenvalue based spectrum sensing
Shakir, Muhammad
2012-01-01
Spectrum sensing is one of the fundamental components in cognitive radio networks. In this chapter, a generalized spectrum sensing framework which is referred to as Generalized Mean Detector (GMD) has been introduced. In this context, we generalize the detectors based on the eigenvalues of the received signal covariance matrix and transform the eigenvalue based spectrum sensing detectors namely: (i) the Eigenvalue Ratio Detector (ERD) and two newly proposed detectors which are referred to as (ii) the GEometric Mean Detector (GEMD) and (iii) the ARithmetic Mean Detector (ARMD) into an unified framework of generalize spectrum sensing. The foundation of the proposed framework is based on the calculation of exact analytical moments of the random variables of the decision threshold of the respective detectors. The decision threshold has been calculated in a closed form which is based on the approximation of Cumulative Distribution Functions (CDFs) of the respective test statistics. In this context, we exchange the analytical moments of the two random variables of the respective test statistics with the moments of the Gaussian (or Gamma) distribution function. The performance of the eigenvalue based detectors is compared with the several traditional detectors including the energy detector (ED) to validate the importance of the eigenvalue based detectors and the performance of the GEMD and the ARMD particularly in realistic wireless cognitive radio network. Analytical and simulation results show that the newly proposed detectors yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, the presented results based on proposed approximation approaches are in perfect agreement with the empirical results. © 2012 Springer Science+Business Media Dordrecht.
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
statistical distributions; linear stochastic systems. 1. ... dimensional multivariate Gaussian random vector with mean µ ∈ Rm and covariance ... 5, the proposed analytical methods are applied to a three degree-of-freedom system and the ...... The joint pdf ofω1 andω3 is however close to a bivariate Gaussian density function.
Inversion of Density Interfaces Using the Pseudo-Backpropagation Neural Network Method
Chen, Xiaohong; Du, Yukun; Liu, Zhan; Zhao, Wenju; Chen, Xiaocheng
2018-05-01
This paper presents a new pseudo-backpropagation (BP) neural network method that can invert multi-density interfaces at one time. The new method is based on the conventional forward modeling and inverse modeling theories in addition to conventional pseudo-BP neural network arithmetic. A 3D inversion model for gravity anomalies of multi-density interfaces using the pseudo-BP neural network method is constructed after analyzing the structure and function of the artificial neural network. The corresponding iterative inverse formula of the space field is presented at the same time. Based on trials of gravity anomalies and density noise, the influence of the two kinds of noise on the inverse result is discussed and the scale of noise requested for the stability of the arithmetic is analyzed. The effects of the initial model on the reduction of the ambiguity of the result and improvement of the precision of inversion are discussed. The correctness and validity of the method were verified by the 3D model of the three interfaces. 3D inversion was performed on the observed gravity anomaly data of the Okinawa trough using the program presented herein. The Tertiary basement and Moho depth were obtained from the inversion results, which also testify the adaptability of the method. This study has made a useful attempt for the inversion of gravity density interfaces.
International Nuclear Information System (INIS)
Huang, C.-H.; Wu, H.-H.
2006-01-01
In the present study an inverse hyperbolic heat conduction problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary heat flux based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary heat flux. Moreover, the drawbacks of the previous study for this similar inverse problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary heat flux can be estimated in this study
DEFF Research Database (Denmark)
Oh, Geok Lian
properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only...... density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through...... the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem. In this Ph...
Directory of Open Access Journals (Sweden)
J. F. Meirink
2008-11-01
Full Text Available A four-dimensional variational (4D-Var data assimilation system for inverse modelling of atmospheric methane emissions is presented. The system is based on the TM5 atmospheric transport model. It can be used for assimilating large volumes of measurements, in particular satellite observations and quasi-continuous in-situ observations, and at the same time it enables the optimization of a large number of model parameters, specifically grid-scale emission rates. Furthermore, the variational method allows to estimate uncertainties in posterior emissions. Here, the system is applied to optimize monthly methane emissions over a 1-year time window on the basis of surface observations from the NOAA-ESRL network. The results are rigorously compared with an analogous inversion by Bergamaschi et al. (2007, which was based on the traditional synthesis approach. The posterior emissions as well as their uncertainties obtained in both inversions show a high degree of consistency. At the same time we illustrate the advantage of 4D-Var in reducing aggregation errors by optimizing emissions at the grid scale of the transport model. The full potential of the assimilation system is exploited in Meirink et al. (2008, who use satellite observations of column-averaged methane mixing ratios to optimize emissions at high spatial resolution, taking advantage of the zooming capability of the TM5 model.
An adjoint-based scheme for eigenvalue error improvement
International Nuclear Information System (INIS)
Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.
2011-01-01
A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)
Zhang, Zhendong
2017-07-11
Full waveform inversion for reection events is limited by its linearized update re-quirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model, and thus, use a gradient given by the oriented time-domain imaging method. Specifically, we apply the oriented time-domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to 2D or 3D velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reection response. To eliminate the cross-talk artifacts between different parameters, we utilize what we consider being an optimal parametrization for this step. To do so, we extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high-wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.
Method for the preparation of metal colloids in inverse micelles and product preferred by the method
Wilcoxon, Jess P.
1992-01-01
A method is provided for preparing catalytic elemental metal colloidal particles (e.g. gold, palladium, silver, rhodium, iridium, nickel, iron, platinum, molybdenum) or colloidal alloy particles (silver/iridium or platinum/gold). A homogeneous inverse micelle solution of a metal salt is first formed in a metal-salt solvent comprised of a surfactant (e.g. a nonionic or cationic surfactant) and an organic solvent. The size and number of inverse micelles is controlled by the proportions of the surfactant and the solvent. Then, the metal salt is reduced (by chemical reduction or by a pulsed or continuous wave UV laser) to colloidal particles of elemental metal. After their formation, the colloidal metal particles can be stabilized by reaction with materials that permanently add surface stabilizing groups to the surface of the colloidal metal particles. The sizes of the colloidal elemental metal particles and their size distribution is determined by the size and number of the inverse micelles. A second salt can be added with further reduction to form the colloidal alloy particles. After the colloidal elemental metal particles are formed, the homogeneous solution distributes to two phases, one phase rich in colloidal elemental metal particles and the other phase rich in surfactant. The colloidal elemental metal particles from one phase can be dried to form a powder useful as a catalyst. Surfactant can be recovered and recycled from the phase rich in surfactant.
The inverse method parametric verification of real-time embedded systems
André , Etienne
2013-01-01
This book introduces state-of-the-art verification techniques for real-time embedded systems, based on the inverse method for parametric timed automata. It reviews popular formalisms for the specification and verification of timed concurrent systems and, in particular, timed automata as well as several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata.The inverse method is introduced, and its benefits for guaranteeing robustness in real-time systems are shown. Then, it is shown how an iteration of the inverse method can solv
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
Optimization method for an evolutional type inverse heat conduction problem
International Nuclear Information System (INIS)
Deng Zuicha; Yu Jianning; Yang Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u t -u xx +q(x,t)u=0, with initial and boundary conditions u(x,0)=u 0 (x), u x vertical bar x=0 =u x vertical bar x=1 =0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced
Optimization method for an evolutional type inverse heat conduction problem
Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.
An Optimal Lower Eigenvalue System
Directory of Open Access Journals (Sweden)
Yingfan Liu
2011-01-01
Full Text Available An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.
Eigenvalue pinching on spinc manifolds
Roos, Saskia
2017-02-01
We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.
Effect of templates on inverse opals fabricated through annular self-assembly/sol-gel method
International Nuclear Information System (INIS)
Ge Dengteng; Yang Lili; Fan Zeng; Zhao Jiupeng; Li Yao
2011-01-01
Highlights: → Flexible inverse opals could be facilely prepared through annular growth method. → The infiltrated materials are highly densified due to the existence of templates. → The crystalline grains are refined due to the the existence of templates. - Abstract: There is a strong interest in simple preparation of flexible inverse opals for applications. In this article, indium tin oxides (ITO) flexible inverse opals were prepared through annular growth of templates and sol-gel process. It is shown that this method provides a facile route for large scale flexible inverse opals with excellent ordered structures. ITO materials are found much denser in inverse opals, which is due to the increased capillary force during drying process and enhanced shrinkage during annealing process. It is also found that the crystalline grains are refined and the photoluminescence performance is strengthened in low frequency.
Solving the RPA eigenvalue equation in real-space
Muta, A; Hashimoto, Y; Yabana, K
2002-01-01
We present a computational method to solve the RPA eigenvalue equation employing a uniform grid representation in three-dimensional Cartesian coordinates. The conjugate gradient method is used for this purpose as an interactive method for a generalized eigenvalue problem. No construction of unoccupied orbitals is required in the procedure. We expect this method to be useful for systems lacking spatial symmetry to calculate accurate eigenvalues and transition matrix elements of a few low-lying excitations. Some applications are presented to demonstrate the feasibility of the method, considering the simplified mean-field model as an example of a nuclear physics system and the electronic excitations in molecules with time-dependent density functional theory as an example of an electronic system. (author)
Highly indefinite multigrid for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Borges, L.; Oliveira, S.
1996-12-31
Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen; Alkhalifah, Tariq Ali
2018-01-01
hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI
DEFF Research Database (Denmark)
Lange, Katrine; Frydendall, Jan; Cordua, Knud Skou
2012-01-01
The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account...... arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori...... solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem....
Resampling: An optimization method for inverse planning in robotic radiosurgery
International Nuclear Information System (INIS)
Schweikard, Achim; Schlaefer, Alexander; Adler, John R. Jr.
2006-01-01
By design, the range of beam directions in conventional radiosurgery are constrained to an isocentric array. However, the recent introduction of robotic radiosurgery dramatically increases the flexibility of targeting, and as a consequence, beams need be neither coplanar nor isocentric. Such a nonisocentric design permits a large number of distinct beam directions to be used in one single treatment. These major technical differences provide an opportunity to improve upon the well-established principles for treatment planning used with GammaKnife or LINAC radiosurgery. With this objective in mind, our group has developed over the past decade an inverse planning tool for robotic radiosurgery. This system first computes a set of beam directions, and then during an optimization step, weights each individual beam. Optimization begins with a feasibility query, the answer to which is derived through linear programming. This approach offers the advantage of completeness and avoids local optima. Final beam selection is based on heuristics. In this report we present and evaluate a new strategy for utilizing the advantages of linear programming to improve beam selection. Starting from an initial solution, a heuristically determined set of beams is added to the optimization problem, while beams with zero weight are removed. This process is repeated to sample a set of beams much larger compared with typical optimization. Experimental results indicate that the planning approach efficiently finds acceptable plans and that resampling can further improve its efficiency
Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method
Sun, Yong; Meng, Zhaohai; Li, Fengting
2018-03-01
Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.
An algebraic substructuring using multiple shifts for eigenvalue computations
International Nuclear Information System (INIS)
Ko, Jin Hwan; Jung, Sung Nam; Byun, Do Young; Bai, Zhaojun
2008-01-01
Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large-sized problems, but originally it was designed to calculate only the smallest eigenvalues. Recently, an updated version of AS has been introduced to calculate the interior eigenvalues over a specified range by using a shift concept that is referred to as the shifted AS. In this work, we propose a combined method of both AS and the shifted AS by using multiple shifts for solving a considerable number of eigensolutions in a large-sized problem, which is an emerging computational issue of noise or vibration analysis in vehicle design. In addition, we investigated the accuracy of the shifted AS by presenting an error criterion. The proposed method has been applied to the FE model of an automobile body. The combined method yielded a higher efficiency without loss of accuracy in comparison to the original AS
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem
Directory of Open Access Journals (Sweden)
Baiyu Wang
2014-01-01
Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.
Optimization method for identifying the source term in an inverse wave equation
Directory of Open Access Journals (Sweden)
Arumugam Deiveegan
2017-08-01
Full Text Available In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.
Metamodel-based inverse method for parameter identification: elastic-plastic damage model
Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb
2017-04-01
This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.
A simple method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Melnikov, V.N.; Rudyak, B.V.; Zakhariev, V.N.
1977-01-01
A new method is proposed for approximate reconstruction of a potential as a step function from scattering data using the completeness relation of solutions of the Schroedinger equation. The suggested method allows one to take into account exactly the additional centrifugal barrier for partial waves with angular momentum l>0, and also the Coulomb potential. The method admits different generalizations. Numerical calculations for checking the method have been performed
Assessment of Groundwater Chemical Quality, Using Inverse Distance Weighted Method
Directory of Open Access Journals (Sweden)
Sh. Ashraf
2013-04-01
Full Text Available An interpolation technique, ordinary Inverse Distance Weighted (IDW, was used to obtain the spatial distribution of groundwater quality parameters in Damghan plain of Iran. According to Scofield guidelines for TDS value, 60% of the water samples were harmful for irrigation purposes. Regarding to EC parameter, more than 60% of studied area was laid in bad range for irrigation purposes. The most dominant anion was Cl- and 10% of water samples showed a very hazardous class. According to Doneen guidelines for chloride value, 100% of collected water from the aquifer had slight to moderate problems for irrigation water purposes. The predominant cations in Damghan plain aquifer were according to Na+> Ca++> Mg++> K+. Sodium ion was the dominant cation and regarding to Na+ content guidelines, almost all groundwater samples had problem for foliar application. Calcium ion distribution was within usual range. The magnesium ion concentration is generally lower than sodium and calcium. The majority of the samples showed Mg++amount within usual range. Also K+ value ranged from 0.1 to 0.23 meq/L and all the water samples had potassium values within the permissible limit. Based on SAR criterion 80 % of collected water had slight to moderate problems. The SSP values were found from 2.87 to 6.87%. According to SAR value, thirty percent of ground water samples were doubtful class. The estimated amounts of RSC were ranged from 0.4-2 and based on RSC criterion, twenty percent of groundwater samples had slight to moderate problems.
FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems
Vourc'h, Eric; Rodet, Thomas
2015-11-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods
FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)
2014-10-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the
Assessment of Groundwater Chemical Quality, Using Inverse Distance Weighted Method
Directory of Open Access Journals (Sweden)
Sh. Ashraf
2014-02-01
Full Text Available An interpolation technique, ordinary Inverse Distance Weighted (IDW, was used to obtain the spatial distribution of groundwater quality parameters in Damghan plain of Iran. According to Scofield guidelines for TDS value, 60% of the water samples were harmful for irrigation purposes. Regarding to EC parameter, more than 60% of studied area was laid in bad range for irrigation purposes. The most dominant anion was Cl- and 10% of water samples showed a very hazardous class. According to Doneen guidelines for chloride value, 100% of collected water from the aquifer had slight to moderate problems for irrigation water purposes. The predominant cations in Damghan plain aquifer were according to Na+> Ca++> Mg++> K+. Sodium ion was the dominant cation and regarding to Na+ content guidelines, almost all groundwater samples had problem for foliar application. Calcium ion distribution was within usual range. The magnesium ion concentration is generally lower than sodium and calcium. The majority of the samples showed Mg++amount within usual range. Also K+ value ranged from 0.1 to 0.23 meq/L and all the water samples had potassium values within the permissible limit. Based on SAR criterion 80 % of collected water had slight to moderate problems. The SSP values were found from 2.87 to 6.87%. According to SAR value, thirty percent of ground water samples were doubtful class. The estimated amounts of RSC were ranged from 0.4-2 and based on RSC criterion, twenty percent of groundwater samples had slight to moderate problems Normal 0 false false false EN-US X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font
a method of gravity and seismic sequential inversion and its GPU implementation
Liu, G.; Meng, X.
2011-12-01
In this abstract, we introduce a gravity and seismic sequential inversion method to invert for density and velocity together. For the gravity inversion, we use an iterative method based on correlation imaging algorithm; for the seismic inversion, we use the full waveform inversion. The link between the density and velocity is an empirical formula called Gardner equation, for large volumes of data, we use the GPU to accelerate the computation. For the gravity inversion method , we introduce a method based on correlation imaging algorithm,it is also a interative method, first we calculate the correlation imaging of the observed gravity anomaly, it is some value between -1 and +1, then we multiply this value with a little density ,this value become the initial density model. We get a forward reuslt with this initial model and also calculate the correaltion imaging of the misfit of observed data and the forward data, also multiply the correaltion imaging result a little density and add it to the initial model, then do the same procedure above , at last ,we can get a inversion density model. For the seismic inveron method ,we use a mothod base on the linearity of acoustic wave equation written in the frequency domain,with a intial velociy model, we can get a good velocity result. In the sequential inversion of gravity and seismic , we need a link formula to convert between density and velocity ,in our method , we use the Gardner equation. Driven by the insatiable market demand for real time, high-definition 3D images, the programmable NVIDIA Graphic Processing Unit (GPU) as co-processor of CPU has been developed for high performance computing. Compute Unified Device Architecture (CUDA) is a parallel programming model and software environment provided by NVIDIA designed to overcome the challenge of using traditional general purpose GPU while maintaining a low learn curve for programmers familiar with standard programming languages such as C. In our inversion processing
Hessian eigenvalue distribution in a random Gaussian landscape
Yamada, Masaki; Vilenkin, Alexander
2018-03-01
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.
Instructions for applying inverse method for reactivity measurement
International Nuclear Information System (INIS)
Milosevic, M.
1988-11-01
This report is a brief description of the completed method for reactivity measurement. It contains description of the experimental procedure needed instrumentation and computer code IM for determining reactivity. The objective of this instructions manual is to enable experiments and reactivity measurement on any critical system according to the methods adopted at the RB reactor
International Nuclear Information System (INIS)
Azimi, A.; Hannani, S.K.; Farhanieh, B.
2005-01-01
In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)
A fully general and adaptive inverse analysis method for cementitious materials
DEFF Research Database (Denmark)
Jepsen, Michael S.; Damkilde, Lars; Lövgren, Ingemar
2016-01-01
The paper presents an adaptive method for inverse determination of the tensile σ - w relationship, direct tensile strength and Young’s modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear σ - w function. Usually, simple bi- or tri-linear functions...... are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear σ - w functions. The proposed method is fully general in the sense that it relies...... of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the σ - w function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased...
Intelligent inversion method for pre-stack seismic big data based on MapReduce
Yan, Xuesong; Zhu, Zhixin; Wu, Qinghua
2018-01-01
Seismic exploration is a method of oil exploration that uses seismic information; that is, according to the inversion of seismic information, the useful information of the reservoir parameters can be obtained to carry out exploration effectively. Pre-stack data are characterised by a large amount of data, abundant information, and so on, and according to its inversion, the abundant information of the reservoir parameters can be obtained. Owing to the large amount of pre-stack seismic data, existing single-machine environments have not been able to meet the computational needs of the huge amount of data; thus, the development of a method with a high efficiency and the speed to solve the inversion problem of pre-stack seismic data is urgently needed. The optimisation of the elastic parameters by using a genetic algorithm easily falls into a local optimum, which results in a non-obvious inversion effect, especially for the optimisation effect of the density. Therefore, an intelligent optimisation algorithm is proposed in this paper and used for the elastic parameter inversion of pre-stack seismic data. This algorithm improves the population initialisation strategy by using the Gardner formula and the genetic operation of the algorithm, and the improved algorithm obtains better inversion results when carrying out a model test with logging data. All of the elastic parameters obtained by inversion and the logging curve of theoretical model are fitted well, which effectively improves the inversion precision of the density. This algorithm was implemented with a MapReduce model to solve the seismic big data inversion problem. The experimental results show that the parallel model can effectively reduce the running time of the algorithm.
EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations
International Nuclear Information System (INIS)
Garbow, Burton S.; Cline, A.K.; Meyering, J.
1993-01-01
: Driver subroutine for a nonsym. tridiag. matrix; SVD: Singular value decomposition of rectangular matrix; TINVIT: Find some vectors of sym. tridiag. matrix; TQLRAT: Find all values of sym. tridiag. matrix; TQL1: Find all values of sym. tridiag. matrix; TQL2: Find all values/vectors of sym. tridiag. matrix; TRBAK1: Back transform vectors of matrix formed by TRED1; TRBAK3: Back transform vectors of matrix formed by TRED3; TRED1: Reduce sym. matrix to sym. tridiag. matrix; TRED2: Reduce sym. matrix to sym. tridiag. matrix; TRED3: Reduce sym. packed matrix to sym. tridiag. matrix; TRIDIB: Find some values of sym. tridiag. matrix; TSTURM: Find some values/vectors of sym. tridiag. matrix. 2 - Method of solution: Almost all the algorithms used in EISPACK are based on similarity transformations. Similarity transformations based on orthogonal and unitary matrices are particularly attractive from a numerical point of view because they do not magnify any errors present in the input data or introduced during the computation. Most of the techniques employed are constructive realizations of variants of Schur's theorem, 'Any matrix can be triangularized by a unitary similarity transformation'. It is usually not possible to compute Schur's transformation with a finite number of rational arithmetic operations. Instead, the algorithms employ a potentially infinite sequence of similarity transformations in which the resultant matrix approaches an upper triangular matrix. The sequence is terminated when all of the sub-diagonal elements of the resulting matrix are less than the roundoff errors involved in the computation. The diagonal elements are then the desired approximations to the eigenvalues of the original matrix and the corresponding eigenvectors can be calculated. Special algorithms deal with symmetric matrices. QR, LR, QL, rational QR, bisection QZ, and inverse iteration methods are used
A scheme for the evaluation of dominant time-eigenvalues of a nuclear reactor
International Nuclear Information System (INIS)
Modak, R.S.; Gupta, Anurag
2007-01-01
This paper presents a scheme to obtain the fundamental and few dominant solutions of the prompt time eigenvalue problem (referred to as α-eigenvalue problem) for a nuclear reactor using multi-group neutron diffusion theory. The scheme is based on the use of an algorithm called Orthomin(1). This algorithm was originally proposed by Suetomi and Sekimoto [Suetomi, E., Sekimoto, H., 1991. Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations. Ann. Nucl. Energy 18 (4), 205-227] to obtain the fundamental K-eigenvalue (K-effective) of nuclear reactors. Recently, it has been shown that the algorithm can be used to obtain the further dominant K-modes also. Since α-eigenvalue problem is usually more difficult to solve than the K-eigenvalue problem, an attempt has been made here to use Orthomin(1) for its solution. Numerical results are given for realistic 3-D test case
Joint density of eigenvalues in spiked multivariate models.
Dharmawansa, Prathapasinghe; Johnstone, Iain M
2014-01-01
The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative hypotheses which are a low rank departure from the null hypothesis. For rank one alternatives, this note provides a representation for the joint eigenvalue density in terms of a single contour integral. This will be of use for deriving approximate distributions for likelihood ratios and 'linear' statistics used in testing.
Solving inverse problems for biological models using the collage method for differential equations.
Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R
2013-07-01
In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.
A general method for closed-loop inverse simulation of helicopter maneuver flight
Wei WU
2017-01-01
Maneuverability is a key factor to determine whether a helicopter could finish certain flight missions successfully or not. Inverse simulation is commonly used to calculate the pilot controls of a helicopter to complete a certain kind of maneuver flight and to assess its maneuverability. A general method for inverse simulation of maneuver flight for helicopters with the flight control system online is developed in this paper. A general mathematical describing function is established to provid...
Constructing inverse probability weights for continuous exposures: a comparison of methods.
Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S
2014-03-01
Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
An interpretation of signature inversion
International Nuclear Information System (INIS)
Onishi, Naoki; Tajima, Naoki
1988-01-01
An interpretation in terms of the cranking model is presented to explain why signature inversion occurs for positive γ of the axially asymmetric deformation parameter and emerges into specific orbitals. By introducing a continuous variable, the eigenvalue equation can be reduced to a one dimensional Schroedinger equation by means of which one can easily understand the cause of signature inversion. (author)
Inverse analysis of a rectangular fin using the lattice Boltzmann method
International Nuclear Information System (INIS)
Bamdad, Keivan; Ashorynejad, Hamid Reza
2015-01-01
Highlights: • Lattice Boltzmann method is used to study a transient conductive-convective fin. • LBM and Conjugate Gradient Method (CGM) are used to solve an inverse problem in fins. • LBM–ACGM estimates the unknown boundary conditions of fins accurately. • The accuracy and CPU time of LBM–ACGM are compared to IFDM–ACGM. • LBM–ACGM could be a good alternative for the conventional inverse methods. - Abstract: Inverse methods have many applications in determining unknown variables in heat transfer problems when direct measurements are impossible. As most common inverse methods are iterative and time consuming especially for complex geometries, developing more efficient methods seems necessary. In this paper, a direct transient conduction–convection heat transfer problem (fin) under several boundary conditions was solved by using lattice Boltzmann method (LBM), and then the results were successfully validated against both the finite difference method and analytical solution. Then, in the inverse problem both unknown base temperatures and heat fluxes in the rectangular fin were estimated by combining the adjoint conjugate gradient method (ACGM) and LBM. A close agreement between the exact values and estimated results confirmed the validity and accuracy of the ACGM–LBM. To compare the calculation time of ACGM–LBM, the inverse problem was solved by implicit finite difference methods as well. This comparison proved that the ACGM–LBM was an accurate and fast method to determine unknown thermal boundary conditions in transient conduction–convection heat transfer problems. The findings can efficiently determine the unknown variables in fins when a desired temperature distribution is available
An inverse method for the design of TIR collimators to achieve a uniform color light beam
Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.
2012-01-01
Color over Angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the
An inverse method for the design of TIR collimators to achieve a uniform color light beam
Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.
2013-01-01
Color-over-angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Active Subspace Methods for Data-Intensive Inverse Problems
Energy Technology Data Exchange (ETDEWEB)
Wang, Qiqi [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2017-04-27
The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.
Periodic Solutions, Eigenvalue Curves, and Degeneracy of the Fractional Mathieu Equation
International Nuclear Information System (INIS)
Parra-Hinojosa, A; Gutiérrez-Vega, J C
2016-01-01
We investigate the eigenvalue curves, the behavior of the periodic solutions, and the orthogonality properties of the Mathieu equation with an additional fractional derivative term using the method of harmonic balance. The addition of the fractional derivative term breaks the hermiticity of the equation in such a way that its eigenvalues need not be real nor its eigenfunctions orthogonal. We show that for a certain choice of parameters the eigenvalue curves reveal the appearance of degenerate eigenvalues. We offer a detailed discussion of the matrix representation of the differential operator corresponding to the fractional Mathieu equation, as well as some numerical examples of its periodic solutions. (paper)
Spatial homogenization method based on the inverse problem
International Nuclear Information System (INIS)
Tóta, Ádám; Makai, Mihály
2015-01-01
Highlights: • We derive a spatial homogenization method in slab and cylindrical geometries. • The fluxes and the currents on the boundary are preserved. • The reaction rates and the integral of the fluxes are preserved. • We present verification computations utilizing two- and four-energy groups. - Abstract: We present a method for deriving homogeneous multi-group cross sections to replace a heterogeneous region’s multi-group cross sections; providing that the fluxes, the currents on the external boundary, the reaction rates and the integral of the fluxes are preserved. We consider one-dimensional geometries: a symmetric slab and a homogeneous cylinder. Assuming that the boundary fluxes are given, two response matrices (RMs) can be defined concerning the current and the flux integral. The first one derives the boundary currents from the boundary fluxes, while the second one derives the flux integrals from the boundary fluxes. Further RMs can be defined that connects reaction rates to the boundary fluxes. Assuming that these matrices are known, we present formulae that reconstruct the multi-group diffusion cross-section matrix, the diffusion coefficients and the reaction cross sections in case of one-dimensional (1D) homogeneous regions. We apply these formulae to 1D heterogeneous regions and thus obtain a homogenization method. This method produces such an equivalent homogeneous material, that the fluxes and the currents on the external boundary, the reaction rates and the integral of the fluxes are preserved for any boundary fluxes. We carry out the exact derivations in 1D slab and cylindrical geometries. Verification computations for the presented homogenization method were performed using two- and four-group material cross sections, both in a slab and in a cylindrical geometry
3D CSEM inversion based on goal-oriented adaptive finite element method
Zhang, Y.; Key, K.
2016-12-01
We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with
Interior transmission eigenvalues of a rectangle
International Nuclear Information System (INIS)
Sleeman, B D; Stocks, D C
2016-01-01
The problem of scattering of acoustic waves by an inhomogeneous medium is intimately connected with so called inside–outside duality, in which the interior transmission eigenvalue problem plays a fundamental role. Here a study of the interior transmission eigenvalues for rectangular domains of constant refractive index is made. By making a nonstandard use of the classical separation of variables technique both real and complex eigenvalues are determined. (paper)
Numerical Methods for Forward and Inverse Problems in Discontinuous Media
Energy Technology Data Exchange (ETDEWEB)
Chartier, Timothy P.
2011-03-08
The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.
Novel TMS coils designed using an inverse boundary element method
Cobos Sánchez, Clemente; María Guerrero Rodriguez, Jose; Quirós Olozábal, Ángel; Blanco-Navarro, David
2017-01-01
In this work, a new method to design TMS coils is presented. It is based on the inclusion of the concept of stream function of a quasi-static electric current into a boundary element method. The proposed TMS coil design approach is a powerful technique to produce stimulators of arbitrary shape, and remarkably versatile as it permits the prototyping of many different performance requirements and constraints. To illustrate the power of this approach, it has been used for the design of TMS coils wound on rectangular flat, spherical and hemispherical surfaces, subjected to different constraints, such as minimum stored magnetic energy or power dissipation. The performances of such coils have been additionally described; and the torque experienced by each stimulator in the presence of a main magnetic static field have theoretically found in order to study the prospect of using them to perform TMS and fMRI concurrently. The obtained results show that described method is an efficient tool for the design of TMS stimulators, which can be applied to a wide range of coil geometries and performance requirements.
A Decoupling Control Method for Shunt Hybrid Active Power Filter Based on Generalized Inverse System
Directory of Open Access Journals (Sweden)
Xin Li
2017-01-01
Full Text Available In this paper, a novel decoupling control method based on generalized inverse system is presented to solve the problem of SHAPF (Shunt Hybrid Active Power Filter possessing the characteristics of 2-input-2-output nonlinearity and strong coupling. Based on the analysis of operation principle, the mathematical model of SHAPF is firstly built, which is verified to be invertible using interactor algorithm; then the generalized inverse system of SHAPF is obtained to connect in series with the original system so that the composite system is decoupled under the generalized inverse system theory. The PI additional controller is finally designed to control the decoupled 1-order pseudolinear system to make it possible to adjust the performance of the subsystem. The simulation results demonstrated by MATLAB show that the presented generalized inverse system strategy can realise the dynamic decoupling of SHAPF. And the control system has fine dynamic and static performance.
On the feasibility of inversion methods based on models of urban sky glow
International Nuclear Information System (INIS)
Kolláth, Z.; Kránicz, B.
2014-01-01
Multi-wavelength imaging luminance photometry of sky glow provides a huge amount of information on light pollution. However, the understanding of the measured data involves the combination of different processes and data of radiation transfer, atmospheric physics and atmospheric constitution. State-of-the-art numerical radiation transfer models provide the possibility to define an inverse problem to obtain information on the emission intensity distribution of a city and perhaps the physical properties of the atmosphere. We provide numerical tests on the solvability and feasibility of such procedures. - Highlights: • A method of urban sky glow inversion is introduced based on Monte-Carlo calculations. • Imaging photometry can provide enough information for basic inversions. • The inversion technique can be used to construct maps of light pollution. • The inclusion of multiple scattering in the models plays an important role
Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method
Directory of Open Access Journals (Sweden)
Huan Ma
2015-01-01
Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.
Treating experimental data of inverse kinetic method by unitary linear regression analysis
International Nuclear Information System (INIS)
Zhao Yusen; Chen Xiaoliang
2009-01-01
The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)
Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.
Zhou, S.; Huang, Q.
2017-12-01
Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti
2012-05-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
On rational approximation methods for inverse source problems
Rundell, William
2011-02-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
On rational approximation methods for inverse source problems
Rundell, William; Hanke, Martin
2011-01-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla
2014-07-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Statistical method for resolving the photon-photoelectron-counting inversion problem
International Nuclear Information System (INIS)
Wu Jinlong; Li Tiejun; Peng, Xiang; Guo Hong
2011-01-01
A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Inverse problem theory methods for data fitting and model parameter estimation
Tarantola, A
2002-01-01
Inverse Problem Theory is written for physicists, geophysicists and all scientists facing the problem of quantitative interpretation of experimental data. Although it contains a lot of mathematics, it is not intended as a mathematical book, but rather tries to explain how a method of acquisition of information can be applied to the actual world.The book provides a comprehensive, up-to-date description of the methods to be used for fitting experimental data, or to estimate model parameters, and to unify these methods into the Inverse Problem Theory. The first part of the book deals wi
Energy Technology Data Exchange (ETDEWEB)
Krukovsky, P G [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)
1998-12-31
The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.
Energy Technology Data Exchange (ETDEWEB)
Krukovsky, P.G. [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)
1997-12-31
The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.
A subspace preconditioning algorithm for eigenvector/eigenvalue computation
Energy Technology Data Exchange (ETDEWEB)
Bramble, J.H.; Knyazev, A.V.; Pasciak, J.E.
1996-12-31
We consider the problem of computing a modest number of the smallest eigenvalues along with orthogonal bases for the corresponding eigen-spaces of a symmetric positive definite matrix. In our applications, the dimension of a matrix is large and the cost of its inverting is prohibitive. In this paper, we shall develop an effective parallelizable technique for computing these eigenvalues and eigenvectors utilizing subspace iteration and preconditioning. Estimates will be provided which show that the preconditioned method converges linearly and uniformly in the matrix dimension when used with a uniform preconditioner under the assumption that the approximating subspace is close enough to the span of desired eigenvectors.
Elastic frequency-domain finite-difference contrast source inversion method
International Nuclear Information System (INIS)
He, Qinglong; Chen, Yong; Han, Bo; Li, Yang
2016-01-01
In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)
Critical eigenvalue in LMFBRs: a physics assessment
International Nuclear Information System (INIS)
McKnight, R.D.; Collins, P.J.; Olsen, D.N.
1984-01-01
This paper summarizes recent work to put the analysis of past critical eigenvalue measurements from the US critical experiments program on a consistent basis. The integral data base includes 53 configurations built in 11 ZPPR assemblies which simulate mixed oxide LMFBRs. Both conventional and heterogeneous designs representing 350, 700, and 900 MWe sizes and with and without simulated control rods and/or control rod positions have been studied. The review of the integral data base includes quantitative assessment of experimental uncertainties in the measured excess reactivity. Analyses have been done with design level and higher-order methods using ENDF/B-IV data. Comparisons of these analyses with the experiments are used to generate recommended bias factors for criticality predictions. Recommended methods for analysis of LMFBR fast critical assemblies and LMFBR design calculations are presented. Unresolved issues and areas which require additional experimental or analytical study are identified
Efficient generalized Golub-Kahan based methods for dynamic inverse problems
Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik
2018-02-01
We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.
Method of T2 spectrum inversion with conjugate gradient algorithm from NMR data
International Nuclear Information System (INIS)
Li Pengju; Shi Shangming; Song Yanjie
2010-01-01
Based on the optimization techniques, the T 2 spectrum inversion method of conjugate gradient that is easy to realize non-negativity constraint of T2 spectrum is proposed. The method transforms the linear mixed-determined problem of T2 spectrum inversion into the typical optimization problem of searching the minimum of objective function by building up the objective function according to the basic idea of geophysics modeling. The optimization problem above is solved with the conjugate gradient algorithm that has quick convergence rate and quadratic termination. The method has been applied to the inversion of noise free echo train generated from artificial spectrum, artificial echo train with signal-to-noise ratio (SNR)=25 and NMR experimental data of drilling core. The comparison between the inversion results of this paper and artificial spectrum or the result of software imported in NMR laboratory shows that the method can correctly invert T 2 spectrum from artificial NMR relaxation data even though SNR=25 and that inversion T 2 spectrum with good continuity and smoothness from core NMR experimental data accords perfectly with that of laboratory software imported, and moreover,the absolute error between the NMR porosity computed from T 2 spectrum and helium (He) porosity in laboratory is 0.65%. (authors)
Solving eigenvalue response matrix equations with nonlinear techniques
International Nuclear Information System (INIS)
Roberts, Jeremy A.; Forget, Benoit
2014-01-01
Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness
Variational principles for Ginzburg-Landau equation by He's semi-inverse method
International Nuclear Information System (INIS)
Liu, W.Y.; Yu, Y.J.; Chen, L.D.
2007-01-01
Via the semi-inverse method of establishing variational principles proposed by He, a generalized variational principle is established for Ginzburg-Landau equation. The present theory provides a quite straightforward tool to the search for various variational principles for physical problems. This paper aims at providing a more complete theoretical basis for applications using finite element and other direct variational methods
Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy
International Nuclear Information System (INIS)
Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos
2008-01-01
Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events
Inversion methods for fast-ion velocity-space tomography in fusion plasmas
DEFF Research Database (Denmark)
Jacobsen, Asger Schou; Stagner, L.; Salewski, Mirko
2016-01-01
Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zeroth and first-order Tikhonov...... regularization. The inversion methods are applied to fast-ion Dα measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing...... entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high...
Some technical details concerning a new method of gravimetric-seismic inversion
DEFF Research Database (Denmark)
Strykowski, Gabriel
1999-01-01
In this paper a number of technical details related to a new method of gravimetric-seismic inversion, which is still under development, are explained. Although the present contribution aims on providing general statements on how to formulate and solve complex gravimetric-seismic modeling; problems......, the inspiration comes from the practical modeling problems in the area of Jutland peninsula (Denmark). More specifically, the methodological aspects of the proposed inversion method are illustrated on a problem of 3D modeling of the intra crustal intrusion associated with the Silkeborg Gravity High. The existing...... refraction seismic profile locates the source of the anomaly in depths 10 km - 18 km. In an earlier publication, (Strykowski, 1998), and for the same test area, a method of complex geological stripping is described. The present contribution is a continuation of this paper in the direction of inversion...
The θ-term, CPN-1 model and the inversion approach in the imaginary θ method
International Nuclear Information System (INIS)
Imachi, Masahiro; Kambayashi, Hitoshi; Shinno, Yasuhiko; Yoneyama, Hiroshi
2006-01-01
The weak coupling region of CP N-1 lattice field theory with the θ-term is investigated. Both the usual real theta method can the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of h=-Imθ is studied, where θ denotes the magnitude of the topological term. Step-like behavior in the x-h relation (where x=Q/V, Q is the topological charge, and V is the two-dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions. (author)
International Nuclear Information System (INIS)
Ye, Yong-jun; Wang, Li-heng; Ding, De-xin; Zhao, Ya-li; Fan, Nan-bin
2014-01-01
The radon diffusion coefficient and the free radon production rate are important parameters for describing radon migration in the fragmented uranium ore. In order to determine the two parameters, the pure diffusion migration equation for radon was firstly established and its analytic solution with the two parameters to be determined was derived. Then, a self manufactured experimental column was used to simulate the pure diffusion of the radon, the improved scintillation cell method was used to measure the pore radon concentrations at different depths of the column loaded with the fragmented uranium ore, and the nonlinear least square algorithm was used to inversely determine the radon diffusion coefficient and the free radon production rate. Finally, the solution with the two inversely determined parameters was used to predict the pore radon concentrations at some depths of the column, and the predicted results were compared with the measured results. The results show that the predicted results are in good agreement with the measured results and the numerical inverse method is applicable to the determination of the radon diffusion coefficient and the free radon production rate for the fragmented uranium ore. - Highlights: • Inverse method for determining two transport parameters of radon is proposed. • A self-made experimental apparatus is used to simulate radon diffusion process. • Sampling volume and position for measuring radon concentration are optimized. • The inverse results of an experimental sample are verified
A general method for closed-loop inverse simulation of helicopter maneuver flight
Directory of Open Access Journals (Sweden)
Wei WU
2017-12-01
Full Text Available Maneuverability is a key factor to determine whether a helicopter could finish certain flight missions successfully or not. Inverse simulation is commonly used to calculate the pilot controls of a helicopter to complete a certain kind of maneuver flight and to assess its maneuverability. A general method for inverse simulation of maneuver flight for helicopters with the flight control system online is developed in this paper. A general mathematical describing function is established to provide mathematical descriptions of different kinds of maneuvers. A comprehensive control solver based on the optimal linear quadratic regulator theory is developed to calculate the pilot controls of different maneuvers. The coupling problem between pilot controls and flight control system outputs is well solved by taking the flight control system model into the control solver. Inverse simulation of three different kinds of maneuvers with different agility requirements defined in the ADS-33E-PRF is implemented based on the developed method for a UH-60 helicopter. The results show that the method developed in this paper can solve the closed-loop inverse simulation problem of helicopter maneuver flight with high reliability as well as efficiency. Keywords: Closed-loop, Flying quality, Helicopters, Inverse simulation, Maneuver flight
On two-spectra inverse problems
Guliyev, Namig J.
2018-01-01
We consider a two-spectra inverse problem for the one-dimensional Schr\\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this problem.
Two numerical methods for an inverse problem for the 2-D Helmholtz equation
Gryazin, Y A; Lucas, T R
2003-01-01
Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.
A Universal Quantum Circuit Scheme For Finding Complex Eigenvalues
Daskin, Anmer; Grama, Ananth; Kais, Sabre
2013-01-01
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of resonance states for quantum systems.
Escape rate from strange sets as an eigenvalue
International Nuclear Information System (INIS)
Tel, T.
1986-06-01
A new method is applied for calculating the escape rate from chaotic repellers or semi-attractors, based on the eigenvalue problem of the master equation of discrete dynamical systems. The corresponding eigenfunction is found to be smooth along unstable directions and to be, in general, a fractal measure. Examples of one and two dimensional maps are investigated. (author)
New algorithms for the symmetric tridiagonal eigenvalue computation
Energy Technology Data Exchange (ETDEWEB)
Pan, V. [City Univ. of New York, Bronx, NY (United States)]|[International Computer Sciences Institute, Berkeley, CA (United States)
1994-12-31
The author presents new algorithms that accelerate the bisection method for the symmetric eigenvalue problem. The algorithms rely on some new techniques, which include acceleration of Newton`s iteration and can also be further applied to acceleration of some other iterative processes, in particular, of iterative algorithms for approximating polynomial zeros.
Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies
Institute of Scientific and Technical Information of China (English)
Tang Wen-Lin; Tian Gui-Hua
2011-01-01
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes
International Nuclear Information System (INIS)
Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.
2005-01-01
An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)
On the nonnegative inverse eigenvalue problem of traditional matrices
Directory of Open Access Journals (Sweden)
Alimohammad Nazari
2014-07-01
Full Text Available In this paper, at first for a given set of real or complex numbers $\\sigma$ with nonnegativesummation, we introduce some special conditions that with them there is no nonnegativetridiagonal matrix in which $\\sigma$ is its spectrum. In continue we present some conditions forexistence such nonnegative tridiagonal matrices.
Efficient solutions to the NDA-NCA low-order eigenvalue problem
International Nuclear Information System (INIS)
Willert, J. A.; Kelley, C. T.
2013-01-01
Recent algorithmic advances combine moment-based acceleration and Jacobian-Free Newton-Krylov (JFNK) methods to accelerate the computation of the dominant eigenvalue in a k-eigenvalue calculation. In particular, NDA-NCA [1], builds a sequence of low-order (LO) diffusion-based eigenvalue problems in which the solution converges to the true eigenvalue solution. Within NDA-NCA, the solution to the LO k-eigenvalue problem is computed by solving a system of nonlinear equation using some variant of Newton's method. We show that we can speed up the solution to the LO problem dramatically by abandoning the JFNK method and exploiting the structure of the Jacobian matrix. (authors)
Phonon spectrum of YBCO obtained by specific heat inversion method for real data
Tao Wen; Dai Xian Xi; Dai Ji Xin; Evenson, W E
2003-01-01
In this paper, the phonon spectrum of YBCO is obtained from experimental specific heat data by an exact inversion formula with a parameter for eliminating divergences. The results can be compared to those of neutron inelastic scattering, which can only be carried out in a few laboratories. Some key points of specific heat-phonon spectrum inversion (SPI) theory and a method of asymptotic behaviour control are discussed. An improved unique existence theorem is presented, and a universal function set for numerical calculation of SPI is calculated with high accuracy, which makes the inversion method applicable and convenient in practice. This is the first time specific heat-phonon SPI has been realized for a concrete system.
Covariance expressions for eigenvalue and eigenvector problems
Liounis, Andrew J.
There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.
Energy Technology Data Exchange (ETDEWEB)
Goetze, Dirk
2011-07-01
Mobility is one of the key factors of our society. The consequences for the environment and mankind can be seen every day. For example in 2009, about 35,500 people involved in traffic accidents in Europe died. The ambitious objective of the European Union, the reduction of the total number of road casualties in 2010, to 27,000 which is half of the road casualties in 2001, was not obtained. The enormous number of fatalities shows, that road safety will be an important issue in the future. Upcoming initiatives of the European Union will focus on accidents outside the city limits where about 60% of all road fatalities occur but also on vulnerable road users (such as children, pedestrians, cyclists and the elderly). The automotive industry has to assure that the vehicle structures are able to reduce the severity of injuries not only for vehicle occupants but also for the other people who are involved in an accident. This can be reached with active and passive safety systems. In this work an alternative design process for passive safety structures is introduced, which is based on the vehicle requirements. The so-called inverse design method is demonstrated for the design of energy absorbers in frontend systems used for pedestrian protection. It is based on a multi-stage optimization process. Compared to the classic design process, where the crash-pulse is usually based on vehicle stiffness and the deformation length, the inverse method focuses on the structural design based on a desired crash-pulse. Using virtual absorbers, which are not limited by any material behavior or geometry, legform to bumper testes can be simulated. Thus, the desired legform deceleration can be generated. The data obtained is used for the second step of the inverse design method, the generation of a ''real'' absorber. For the design of the ''real'' absorber small drop-tower simulations are sufficient. A parameterized finite element model is used. Both the
Testing an inversion method for estimating electron energy fluxes from all-sky camera images
Directory of Open Access Journals (Sweden)
N. Partamies
2004-06-01
Full Text Available An inversion method for reconstructing the precipitating electron energy flux from a set of multi-wavelength digital all-sky camera (ASC images has recently been developed by tomografia. Preliminary tests suggested that the inversion is able to reconstruct the position and energy characteristics of the aurora with reasonable accuracy. This study carries out a thorough testing of the method and a few improvements for its emission physics equations. We compared the precipitating electron energy fluxes as estimated by the inversion method to the energy flux data recorded by the Defense Meteorological Satellite Program (DMSP satellites during four passes over auroral structures. When the aurorae appear very close to the local zenith, the fluxes inverted from the blue (427.8nm filtered ASC images or blue and green line (557.7nm images together give the best agreement with the measured flux values. The fluxes inverted from green line images alone are clearly larger than the measured ones. Closer to the horizon the quality of the inversion results from blue images deteriorate to the level of the ones from green images. In addition to the satellite data, the precipitating electron energy fluxes were estimated from the electron density measurements by the EISCAT Svalbard Radar (ESR. These energy flux values were compared to the ones of the inversion method applied to over 100 ASC images recorded at the nearby ASC station in Longyearbyen. The energy fluxes deduced from these two types of data are in general of the same order of magnitude. In 35% of all of the blue and green image inversions the relative errors were less than 50% and in 90% of the blue and green image inversions less than 100%. This kind of systematic testing of the inversion method is the first step toward using all-sky camera images in the way in which global UV images have recently been used to estimate the energy fluxes. The advantages of ASCs, compared to the space-born imagers, are
Performance of some numerical Laplace inversion methods on American put option formula
Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.
2018-03-01
Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.
Study of Tip-loss Using an Inverse 3D Navier-Stokes Method
DEFF Research Database (Denmark)
Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong
2003-01-01
the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....
Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method
International Nuclear Information System (INIS)
Urazboev, Gayrat
2012-01-01
In this work, there is shown that the solutions of Toda lattice with self-consistent source can be found by the inverse scattering method for the discrete Sturm-Liuville operator. For the considered problem the one-soliton solution is obtained.
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation
Micro-seismic Imaging Using a Source Independent Waveform Inversion Method
Wang, Hanchen
2016-01-01
waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking
International Nuclear Information System (INIS)
Chaichian, M.; Kulish, P. P.
1978-04-01
Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)
Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation
International Nuclear Information System (INIS)
Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.
1989-01-01
The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs
The black-body radiation inversion problem, its instability and a new universal function set method
International Nuclear Information System (INIS)
Ye, JiPing; Ji, FengMin; Wen, Tao; Dai, Xian-Xi; Dai, Ji-Xin; Evenson, William E.
2006-01-01
The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS
An Analytical Method for the Abel Inversion of Asymmetrical Gaussian Profiles
International Nuclear Information System (INIS)
Xu Guosheng; Wan Baonian
2007-01-01
An analytical algorithm for fast calculation of the Abel inversion for density profile measurement in tokamak is developed. Based upon the assumptions that the particle source is negligibly small in the plasma core region, density profiles can be approximated by an asymmetrical Gaussian distribution controlled only by one parameter V 0 /D and V 0 /D is constant along the radial direction, the analytical algorithm is presented and examined against a testing profile. The validity is confirmed by benchmark with the standard Abel inversion method and the theoretical profile. The scope of application as well as the error analysis is also discussed in detail
Multiple estimation channel decoupling and optimization method based on inverse system
Wu, Peng; Mu, Rongjun; Zhang, Xin; Deng, Yanpeng
2018-03-01
This paper addressed the intelligent autonomous navigation request of intelligent deformation missile, based on the intelligent deformation missile dynamics and kinematics modeling, navigation subsystem solution method and error modeling, and then focuses on the corresponding data fusion and decision fusion technology, decouples the sensitive channel of the filter input through the inverse system of design dynamics to reduce the influence of sudden change of the measurement information on the filter input. Then carrying out a series of simulation experiments, which verified the feasibility of the inverse system decoupling algorithm effectiveness.
A STUDY ON DYNAMIC LOAD HISTORY RECONSTRUCTION USING PSEUDO-INVERSE METHODS
Santos, Ariane Rebelato Silva dos; Marczak, Rogério José
2017-01-01
Considering that the vibratory forces generally cannot be measured directly at the interface of two bodies, an inverse method is studied in the present work to recover the load history in such cases. The proposed technique attempts to reconstruct the dynamic loads history by using a frequency domain analysis and Moore-Penrose pseudo-inverses of the frequency response function (FRF) of the system. The methodology consists in applying discrete dynamic loads on a finite element model in the time...
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
Directory of Open Access Journals (Sweden)
Herb E. Kunze
2014-01-01
Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.
The algebraic method of the scattering inverse problem solution under untraditional statements
Popushnoj, M N
2001-01-01
The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated
Cycle-Based Cluster Variational Method for Direct and Inverse Inference
Furtlehner, Cyril; Decelle, Aurélien
2016-08-01
Large scale inference problems of practical interest can often be addressed with help of Markov random fields. This requires to solve in principle two related problems: the first one is to find offline the parameters of the MRF from empirical data (inverse problem); the second one (direct problem) is to set up the inference algorithm to make it as precise, robust and efficient as possible. In this work we address both the direct and inverse problem with mean-field methods of statistical physics, going beyond the Bethe approximation and associated belief propagation algorithm. We elaborate on the idea that loop corrections to belief propagation can be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define regions in a generalized belief propagation setting. For the direct problem, the region graph is specified in such a way as to avoid feed-back loops as much as possible by selecting a minimal cycle basis. Following this line we are led to propose a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. Next we observe that the inverse problem can be addressed region by region independently, with one small inverse problem per region to be solved. It turns out that each elementary inverse problem on the loop geometry can be solved efficiently. In particular in the random Ising context we propose two complementary methods based respectively on fixed point equations and on a one-parameter log likelihood function minimization. Numerical experiments confirm the effectiveness of this approach both for the direct and inverse MRF inference. Heterogeneous problems of size up to 10^5 are addressed in a reasonable computational time, notably with better convergence properties than ordinary belief propagation.
Finite-fault source inversion using adjoint methods in 3D heterogeneous media
Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia
2018-04-01
Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect
Inverse problems for ODEs using contraction maps and suboptimality of the 'collage method'
Kunze, H. E.; Hicken, J. E.; Vrscay, E. R.
2004-06-01
Broad classes of inverse problems in differential and integral equations can be cast in the following framework: the optimal approximation of a target x of a suitable metric space X by the fixed point \\bar x of a contraction map T on X. The 'collage method' attempts to solve such inverse problems by finding an operator Tc that maps the target x as close as possible to itself. In the case of ODEs, the appropriate contraction maps are integral Picard operators. In practice, the target solutions possibly arise from an interpolation of experimental data points. In this paper, we investigate the suboptimality of the collage method. A simple inequality that provides upper bounds on the improvement over collage coding is presented and some examples are studied. We conclude that, at worst, the collage method provides an excellent starting point for further optimization, in contrast to more traditional searching methods that must first select a good starting point.
Sliding mode control of photoelectric tracking platform based on the inverse system method
Directory of Open Access Journals (Sweden)
Yao Zong Chen
2016-01-01
Full Text Available In order to improve the photoelectric tracking platform tracking performance, an integral sliding mode control strategy based on inverse system decoupling method is proposed. The electromechanical dynamic model is established based on multi-body system theory and Newton-Euler method. The coupled multi-input multi-output (MIMO nonlinear system is transformed into two pseudo-linear single-input single-output (SISO subsystems based on the inverse system method. An integral sliding mode control scheme is designed for the decoupled pseudo-linear system. In order to eliminate system chattering phenomenon caused by traditional sign function in sliding-mode controller, the sign function is replaced by the Sigmoid function. Simulation results show that the proposed decoupling method and the control strategy can restrain the influences of internal coupling and disturbance effectively, and has better robustness and higher tracking accuracy.
An inverse method for non linear ablative thermics with experimentation of automatic differentiation
Energy Technology Data Exchange (ETDEWEB)
Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr
2008-11-01
Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.
Shigetoh, Keisuke; Horibuchi, Kayo; Nakamura, Daisuke
2017-11-01
Owing to the large differences in the chemical properties between Al and N polarities in aluminum nitride (AlN), the choice of the polar direction for crystal growth strongly affects not only the quality but also the shape (facet formation) of the grown crystal. In particular, N-polar (0 0 0 -1) has been considered to be a more preferable direction than Al-polar (0 0 0 1) for sublimation growth because compared to Al-polar (0 0 0 1), N-polar (0 0 0 -1) exhibits better stability at high growth rate (high supersaturation) conditions and enables easier lateral enlargement of the crystal. However, some critical growth conditions induce polarity inversion and hinder stable N-polar growth. Furthermore, the origin of the polarity inversion in AlN growth by the sublimation method is still unclear. To ensure stable N-polar growth without polarity inversion, the formation mechanism of the inversion domain during AlN sublimation growth must be elucidated. Therefore, herein, we demonstrate homoepitaxial growth on an N-polar seed and carefully investigate the obtained crystal that shows polarity inversion. Annular bright-field scanning transmission electron microscopy reveals that polarity is completely converted to the Al polarity via the formation of a 30 nm thick mixed polar layer (MPL) just above the seed. Moreover, three-dimensional atom probe tomography shows the segregation of the oxygen impurities in the MPL with a high concentration of about 3 atom%. Finally, by avoiding the incorporation of oxygen impurity into the crystal at the initial stage of the growth, we demonstrate an effective reduction (seven orders of magnitude) of the inversion domain boundary formation.
A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization
Liu, Shuang; Hu, Xiangyun; Liu, Tianyou
2014-07-01
Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.
On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations
Directory of Open Access Journals (Sweden)
Heinrich Voss
2016-06-01
Full Text Available Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.
Complex energy eigenvalues of a linear potential with a parabolical barrier
International Nuclear Information System (INIS)
Malherbe, J.B.
1978-01-01
The physical meaning and restrictions of complex energy eigenvalues are briefly discussed. It is indicated that a quasi-stationary phase describes an idealised disintegration system. Approximate resonance-eigenvalues of the one dimensional Schrodinger equation with a linear potential and parabolic barrier are calculated by means of Connor's semiclassical method. This method is based on the generalized WKB-method of Miller and Good. The results obtained confirm the correctness of a model representation which explains the unusual distribution of eigenvalues by certain other linear potentials in a complex energy level [af
Directory of Open Access Journals (Sweden)
Jing Wang
2013-01-01
Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.
Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods
Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco
2015-04-01
The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface
Photonic band structure calculations using nonlinear eigenvalue techniques
International Nuclear Information System (INIS)
Spence, Alastair; Poulton, Chris
2005-01-01
This paper considers the numerical computation of the photonic band structure of periodic materials such as photonic crystals. This calculation involves the solution of a Hermitian nonlinear eigenvalue problem. Numerical methods for nonlinear eigenvalue problems are usually based on Newton's method or are extensions of techniques for the standard eigenvalue problem. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. This new approach has several advantages over the current methods. First, in our numerical calculations the new variation is more robust than existing techniques, having a larger domain of convergence. Second, the linear systems remain Hermitian and are nonsingular as the method converges. Third, the approach provides an elegant and efficient way of both thinking about the problem and organising the computer solution so that only one linear system needs to be factorised at each stage in the solution process. Finally, first- and higher-order derivatives are calculated as a natural extension of the basic method, and this has advantages in the electromagnetic problem discussed here, where the band structure is plotted as a set of paths in the (ω,k) plane
International Nuclear Information System (INIS)
Yang Deshan; Li Hua; Low, Daniel A; Deasy, Joseph O; Naqa, Issam El
2008-01-01
Deformable image registration is widely used in various radiation therapy applications including daily treatment planning adaptation to map planned tissue or dose to changing anatomy. In this work, a simple and efficient inverse consistency deformable registration method is proposed with aims of higher registration accuracy and faster convergence speed. Instead of registering image I to a second image J, the two images are symmetrically deformed toward one another in multiple passes, until both deformed images are matched and correct registration is therefore achieved. In each pass, a delta motion field is computed by minimizing a symmetric optical flow system cost function using modified optical flow algorithms. The images are then further deformed with the delta motion field in the positive and negative directions respectively, and then used for the next pass. The magnitude of the delta motion field is forced to be less than 0.4 voxel for every pass in order to guarantee smoothness and invertibility for the two overall motion fields that are accumulating the delta motion fields in both positive and negative directions, respectively. The final motion fields to register the original images I and J, in either direction, are calculated by inverting one overall motion field and combining the inversion result with the other overall motion field. The final motion fields are inversely consistent and this is ensured by the symmetric way that registration is carried out. The proposed method is demonstrated with phantom images, artificially deformed patient images and 4D-CT images. Our results suggest that the proposed method is able to improve the overall accuracy (reducing registration error by 30% or more, compared to the original and inversely inconsistent optical flow algorithms), reduce the inverse consistency error (by 95% or more) and increase the convergence rate (by 100% or more). The overall computation speed may slightly decrease, or increase in most cases
Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H
2016-05-01
The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.
3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method
Directory of Open Access Journals (Sweden)
Jian-ke Qiang
2013-01-01
Full Text Available During the past decades, we observed a strong interest in 3D DC resistivity inversion and imaging with complex topography. In this paper, we implemented 3D DC resistivity inversion based on regularized conjugate gradient method with FEM. The Fréchet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth’s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. The synthetic model study shows that this optimized weighting function is helpful to improve the resolution of deep anomaly. By incorporating topography into inversion, the artificial anomaly which is actually caused by topography can be eliminated. As a result, this algorithm potentially can be applied to process the DC resistivity data collected in mountain area. Our synthetic model study also shows that the convergence and computation speed are very stable and fast.
Energy Technology Data Exchange (ETDEWEB)
Wang, Kun, E-mail: wangkun@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); Lappeenranta University of Technology, Lappeenranta (Finland); University of Science and Technology of China, Hefei (China); Song, Yuntao [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); University of Science and Technology of China, Hefei (China); Wu, Huapeng [Lappeenranta University of Technology, Lappeenranta (Finland); Wei, Xiaoyang; Khan, Shahab Ud-Din; Cheng, Yong [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China)
2017-06-15
Highlights: • An Obstacle Topology Partition Projection (OTPP) method of tokamak-like vessel for collision detection. • Median values preferentially of depth-first search algorithm for solving redundant inverse kinematics based on OTPP. • Application of RIK in grasping target objects. - Abstract: This paper proposed a new method for solving inverse kinematics (IK) of a redundant manipulator called EAST Articulated Maintenance Arm (EAMA), which is applied in the fusion reactor EAST (Experimental Advanced Superconducting Tokamak) and used to complete some maintenance tasks in the complex areas. However, it is difficult to realize remote control due to its redundancy, coupling structure and the complex operational environment. The IK research of the robot played a vital role to the manipulator’s motion control algorithm of remote handling (RH) technology. An Obstacle Topology Partition Projection (OTPP) approach integrated with Modified Inverse Depth First Search (MIDFS) method was presented. This is a kind of new geometric algorithm in order to solve the problem of IK for a high-redundancy manipulator. It can also be used to find a solution satisfying collision avoidance with optimal safety distance between the manipulator and obstacles. Simulations and experiments were conducted to demonstrate the efficiency and accuracy of the proposed method.
International Nuclear Information System (INIS)
Wang, Kun; Song, Yuntao; Wu, Huapeng; Wei, Xiaoyang; Khan, Shahab Ud-Din; Cheng, Yong
2017-01-01
Highlights: • An Obstacle Topology Partition Projection (OTPP) method of tokamak-like vessel for collision detection. • Median values preferentially of depth-first search algorithm for solving redundant inverse kinematics based on OTPP. • Application of RIK in grasping target objects. - Abstract: This paper proposed a new method for solving inverse kinematics (IK) of a redundant manipulator called EAST Articulated Maintenance Arm (EAMA), which is applied in the fusion reactor EAST (Experimental Advanced Superconducting Tokamak) and used to complete some maintenance tasks in the complex areas. However, it is difficult to realize remote control due to its redundancy, coupling structure and the complex operational environment. The IK research of the robot played a vital role to the manipulator’s motion control algorithm of remote handling (RH) technology. An Obstacle Topology Partition Projection (OTPP) approach integrated with Modified Inverse Depth First Search (MIDFS) method was presented. This is a kind of new geometric algorithm in order to solve the problem of IK for a high-redundancy manipulator. It can also be used to find a solution satisfying collision avoidance with optimal safety distance between the manipulator and obstacles. Simulations and experiments were conducted to demonstrate the efficiency and accuracy of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Garreta, Vincent; Guiot, Joel; Hely, Christelle [CEREGE, UMR 6635, CNRS, Universite Aix-Marseille, Europole de l' Arbois, Aix-en-Provence (France); Miller, Paul A.; Sykes, Martin T. [Lund University, Department of Physical Geography and Ecosystems Analysis, Geobiosphere Science Centre, Lund (Sweden); Brewer, Simon [Universite de Liege, Institut d' Astrophysique et de Geophysique, Liege (Belgium); Litt, Thomas [University of Bonn, Paleontological Institute, Bonn (Germany)
2010-08-15
Climate reconstructions from data sensitive to past climates provide estimates of what these climates were like. Comparing these reconstructions with simulations from climate models allows to validate the models used for future climate prediction. It has been shown that for fossil pollen data, gaining estimates by inverting a vegetation model allows inclusion of past changes in carbon dioxide values. As a new generation of dynamic vegetation model is available we have developed an inversion method for one model, LPJ-GUESS. When this novel method is used with high-resolution sediment it allows us to bypass the classic assumptions of (1) climate and pollen independence between samples and (2) equilibrium between the vegetation, represented as pollen, and climate. Our dynamic inversion method is based on a statistical model to describe the links among climate, simulated vegetation and pollen samples. The inversion is realised thanks to a particle filter algorithm. We perform a validation on 30 modern European sites and then apply the method to the sediment core of Meerfelder Maar (Germany), which covers the Holocene at a temporal resolution of approximately one sample per 30 years. We demonstrate that reconstructed temperatures are constrained. The reconstructed precipitation is less well constrained, due to the dimension considered (one precipitation by season), and the low sensitivity of LPJ-GUESS to precipitation changes. (orig.)
The generalised Marchenko equation and the canonical structure of the A.K.N.S.-Z.S. inverse method
International Nuclear Information System (INIS)
Dodd, R.K.; Bullough, R.K.
1979-01-01
A generalised Marchenko equation is derived for a 2 X 2 matrix inverse method and it is used to show that, for the subset of equations solvable by the method which can be constructed as defining the flows of Hamiltonians, the inverse transform is a canonical (homogeneous contact) transformation. Baecklund transformations are re-examined from this point of view. (Auth.)
International Nuclear Information System (INIS)
Kim, Yeung Chan
2016-01-01
A study on the measurement of critical heat flux using the transient inverse heat conduction method in spray cooling was performed. The inverse heat conduction method estimates the surface heat flux or temperature using a measured interior temperature history. The effects of the measuring time interval and location of temperature measurement on the measurement of critical heat flux were primarily investigated. The following results were obtained. The estimated critical heat flux decreased as the time interval of temperature measurement increased. Meanwhile, the effect of measurement location on critical heat flux was not significant. It was also found, from the experimental results, that the critical superheat increased as the measurement location of thermocouple neared the heat transfer surface.
Energy Technology Data Exchange (ETDEWEB)
Kim, Yeung Chan [Andong Nat’l Univ., Andong (Korea, Republic of)
2016-10-15
A study on the measurement of critical heat flux using the transient inverse heat conduction method in spray cooling was performed. The inverse heat conduction method estimates the surface heat flux or temperature using a measured interior temperature history. The effects of the measuring time interval and location of temperature measurement on the measurement of critical heat flux were primarily investigated. The following results were obtained. The estimated critical heat flux decreased as the time interval of temperature measurement increased. Meanwhile, the effect of measurement location on critical heat flux was not significant. It was also found, from the experimental results, that the critical superheat increased as the measurement location of thermocouple neared the heat transfer surface.
International Nuclear Information System (INIS)
Choi, C. Y.
1997-01-01
A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
International Nuclear Information System (INIS)
Le Louër, Frédérique
2015-01-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)
Inverse method for temperature and stress monitoring in complex-shaped bodies
International Nuclear Information System (INIS)
Duda, Piotr; Taler, Jan E- mail: aler@ss5.mech.pk.edu.pl; Roos, Eberhard
2004-01-01
The purpose of this work is to formulate a space marching method, which an be used to solve inverse multidimensional heat conduction problems. The method is designed to reconstruct the transient temperature distribution in a hole construction element based on measured temperatures taken at selected points on the outer surface of the construction element. Next, the Finite element Method is used to calculate thermal stresses and stresses caused by other loads such as, for instance, internal pressure. The developed method or solving temperature and total stress distribution is tested using the measured temperatures generated from a direct solution. Transient temperature nd total stress distributions obtained from the method presented below are compared with the values obtained from the direct solution. Finally, the resented method is experimentally verified during the cooling of a hick-walled cylindrical element. The model of a pressure vessel was reheated at 300 deg.C and then cooled by cold water injection. The comparison of results obtained from the inverse method with experimental data hows the high accuracy of the developed method. The presented method allows o optimize the power block's start-up and shut-down operations, contributes o the reduction of heat loss during these operations and to the extension of power block's life. The fatigue and creep usage factor can be computed in an n-line mode. The presented method herein can be applied to monitoring systems that work in conventional as well as in nuclear power plants
New exact approaches to the nuclear eigenvalue problem
International Nuclear Information System (INIS)
Andreozzi, F.; Lo Iudice, N.; Porrino, A.; Knapp, F.; Kvasil, J.
2005-01-01
In a recent past some of us have developed a new algorithm for diagonalizing the shell model Hamiltonian which consists of an iterative sequence of diagonalization of sub-matrices of small dimensions. The method, apart from being easy to implement, is robust, yielding always stable numerical solutions, and free of ghost eigenvalues. Subsequently, we have endowed the algorithm with an importance sampling, which leads to a drastic truncation of the shell model space, while keeping the accuracy of the solutions under control. Applications to typical nuclei show that the sampling yields also an extrapolation law to the exact eigenvalues. Complementary to the shell model algorithm is a method we are developing for studying collective and non collective excitations. To this purpose we solve the nuclear eigenvalue problem in a space which is the direct sum of Tamm-Dancoff n-phonon subspaces (n=0,1, ...N). The multiphonon basis is constructed by an iterative equation of motion method, which generates an over complete set of n-phonon states from the (n-1)-phonon basis. The redundancy is removed completely and exactly by a method based on the Choleski decomposition. The full Hamiltonian matrix comes out to have a simple structure and, therefore, can be drastically truncated before diagonalization by the mentioned importance sampling method. The phonon composition of the basis states allows removing naturally and maximally the spurious admixtures induced by the centre of mass motion. An application of the method to 16 O will be given for illustrative purposes. (authors)
The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization
Directory of Open Access Journals (Sweden)
Yang Yu
2015-01-01
Full Text Available The two-phase Stefan problem is widely used in industrial field. This paper focuses on solving the two-phase inverse Stefan problem when the interface moving is unknown, which is more realistic from the practical point of view. With the help of optimization method, the paper presents a hybrid method which combines the homotopy perturbation method with the improved Adomian decomposition method to solve this problem. Simulation experiment demonstrates the validity of this method. Optimization method plays a very important role in this paper, so we propose a modified spectral DY conjugate gradient method. And the convergence of this method is given. Simulation experiment illustrates the effectiveness of this modified spectral DY conjugate gradient method.
An improved method of inverse kinematics calculation for a six-link manipulator
International Nuclear Information System (INIS)
Sasaki, Shinobu
1987-07-01
As one method of solving the inverse problem related to a six-link manipulator, an improvement was made of previously proposed calculation algorithm based on a solution of an algebraic equation of the 24-th order. In this paper, the same type of a polynomial was derived in the form of the equation of 16-th order, i.e., the order reduced by 8, as compared to previous algorithm. The accuracy of solutions was identified to be much refined. (author)
Heat flux estimation in an infrared experimental furnace using an inverse method
International Nuclear Information System (INIS)
Le Bideau, P.; Ploteau, J.P.; Glouannec, P.
2009-01-01
Infrared emitters are widely used in industrial furnaces for thermal treatment. In these processes, the knowledge of the incident heat flux on the surface of the product is a primary step to optimise the command emitters and for maintenance shift. For these reasons, it is necessary to develop autonomous flux meters that could provide an answer to these requirements. These sensors must give an in-line distribution of infrared irradiation in the tunnel furnace and must be able to measure high heat flux in severe thermal environments. In this paper we present a method for in-line assessments solving an inverse heat conduction problem. A metallic mass is instrumented by thermocouples and an inverse method allows the incident heat flux to be estimated. In the first part, attention is focused on a new design tool, which is a numerical code, for the evaluation of potential options during captor conception. In the second part we present the realization and the test of this 'indirect' flux meter and its associated inverse problem. 'Direct' detectors based on thermoelectric devices are compared with this new flux meter in the same conditions in the same furnace. Results prove that this technique is a reliable method, appropriate for high temperature ambiances. This technique can be applied to furnaces where the heat flux is inaccessible to 'direct' measurements.
International Nuclear Information System (INIS)
Ma Xiang; Zabaras, Nicholas
2009-01-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media
Optical coherence tomography signal analysis: LIDAR like equation and inverse methods
International Nuclear Information System (INIS)
Amaral, Marcello Magri
2012-01-01
Optical Coherence Tomography (OCT) is based on the media backscattering properties in order to obtain tomographic images. In a similar way, LIDAR (Light Detection and Range) technique uses these properties to determine atmospheric characteristics, specially the signal extinction coefficient. Exploring this similarity allowed the application of signal inversion methods to the OCT images, allowing to construct images based in the extinction coefficient, original result until now. The goal of this work was to study, propose, develop and implement algorithms based on OCT signal inversion methodologies with the aim of determine the extinction coefficient as a function of depth. Three inversion methods were used and implemented in LABView R : slope, boundary point and optical depth. Associated errors were studied and real samples (homogeneous and stratified) were used for two and three dimension analysis. The extinction coefficient images obtained from the optical depth method were capable to differentiate air from the sample. The images were studied applying PCA and cluster analysis that established the methodology strength in determining the sample's extinction coefficient value. Moreover, the optical depth methodology was applied to study the hypothesis that there is some correlation between signal extinction coefficient and the enamel teeth demineralization during a cariogenic process. By applying this methodology, it was possible to observe the variation of the extinction coefficient as depth function and its correlation with microhardness variation, showing that in deeper layers its values tends to a healthy tooth values, behaving as the same way that the microhardness. (author)
Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.
2017-10-01
This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution
Directory of Open Access Journals (Sweden)
S.N. Nnamchi
2010-01-01
Full Text Available Determination of the thermal conductivity and the specific heat capacity of neem seeds (Azadirachta indica A. Juss usingthe inverse method is the main subject of this work. One-dimensional formulation of heat conduction problem in a spherewas used. Finite difference method was adopted for the solution of the heat conduction problem. The thermal conductivityand the specific heat capacity were determined by least square method in conjunction with Levenberg-Marquardt algorithm.The results obtained compare favourably with those obtained experimentally. These results are useful in the analysis ofneem seeds drying and leaching processes.
3D CSEM data inversion using Newton and Halley class methods
Amaya, M.; Hansen, K. R.; Morten, J. P.
2016-05-01
For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those
International Nuclear Information System (INIS)
Qi, Zhipeng; Li, Xiu; Lu, Xushan; Zhang, Yingying; Yao, Weihua
2015-01-01
We introduce a new and potentially useful method for wave field inverse transformation and its application in transient electromagnetic method (TEM) 3D interpretation. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave field that satisfies a wave equation. The continuous imaging of TEM can be accomplished using the imaging methods in seismic interpretation after the diffusion equation is transformed into a fictitious wave equation. The interpretation method based on the imaging of a fictitious wave field could be used as a fast 3D inversion method. Moreover, the fictitious wave field possesses some wave field features making it possible for the application of a wave field interpretation method in TEM to improve the prospecting resolution.Wave field transformation is a key issue in the migration imaging of a fictitious wave field. The equation in the wave field transformation belongs to the first class Fredholm integration equation, which is a typical ill-posed equation. Additionally, TEM has a large dynamic time range, which also facilitates the weakness of this ill-posed problem. The wave field transformation is implemented by using pre-conditioned regularized conjugate gradient method. The continuous imaging of a fictitious wave field is implemented by using Kirchhoff integration. A synthetic aperture and deconvolution algorithm is also introduced to improve the interpretation resolution. We interpreted field data by the method proposed in this paper, and obtained a satisfying interpretation result. (paper)
Eigenvalues calculation algorithms for {lambda}-modes determination. Parallelization approach
Energy Technology Data Exchange (ETDEWEB)
Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Ginestart, D. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada
1997-03-01
In this paper, we review two methods to obtain the {lambda}-modes of a nuclear reactor, Subspace Iteration method and Arnoldi`s method, which are popular methods to solve the partial eigenvalue problem for a given matrix. In the developed application for the neutron diffusion equation we include improved acceleration techniques for both methods. Also, we propose two parallelization approaches for these methods, a coarse grain parallelization and a fine grain one. We have tested the developed algorithms with two realistic problems, focusing on the efficiency of the methods according to the CPU times. (author).
DEFF Research Database (Denmark)
Liu, Yuanrong; Chen, Weimin; Zhong, Jing
2017-01-01
The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....
Estimation of oil reservoir thermal properties through temperature log data using inversion method
International Nuclear Information System (INIS)
Cheng, Wen-Long; Nian, Yong-Le; Li, Tong-Tong; Wang, Chang-Long
2013-01-01
Oil reservoir thermal properties not only play an important role in steam injection well heat transfer, but also are the basic parameters for evaluating the oil saturation in reservoir. In this study, for estimating reservoir thermal properties, a novel heat and mass transfer model of steam injection well was established at first, this model made full analysis on the wellbore-reservoir heat and mass transfer as well as the wellbore-formation, and the simulated results by the model were quite consistent with the log data. Then this study presented an effective inversion method for estimating the reservoir thermal properties through temperature log data. This method is based on the heat transfer model in steam injection wells, and can be used to predict the thermal properties as a stochastic approximation method. The inversion method was applied to estimate the reservoir thermal properties of two steam injection wells, it was found that the relative error of thermal conductivity for the two wells were 2.9% and 6.5%, and the relative error of volumetric specific heat capacity were 6.7% and 7.0%,which demonstrated the feasibility of the proposed method for estimating the reservoir thermal properties. - Highlights: • An effective inversion method for predicting the oil reservoir thermal properties was presented. • A novel model for steam injection well made full study on the wellbore-reservoir heat and mass transfer. • The wellbore temperature field and steam parameters can be simulated by the model efficiently. • Both reservoirs and formation thermal properties could be estimated simultaneously by the proposed method. • The estimated steam temperature was quite consistent with the field data
International Nuclear Information System (INIS)
Friedman, R.S.; Jamieson, M.J.; Preston, S.C.
1990-01-01
A method for solving coupled eigenvalue differential equations is given and its relation to an existing technique is shown. Use of the Gram-Schmidt process to overcome the severe instabilities arising in molecular problems is described in detail. (orig.)
Inversion of Gravity Anomalies Using Primal-Dual Interior Point Methods
Directory of Open Access Journals (Sweden)
Aaron A. Velasco
2016-06-01
Full Text Available Structural inversion of gravity datasets based on the use of density anomalies to derive robust images of the subsurface (delineating lithologies and their boundaries constitutes a fundamental non-invasive tool for geological exploration. The use of experimental techniques in geophysics to estimate and interpret di erences in the substructure based on its density properties have proven e cient; however, the inherent non-uniqueness associated with most geophysical datasets make this the ideal scenario for the use of recently developed robust constrained optimization techniques. We present a constrained optimization approach for a least squares inversion problem aimed to characterize 2-Dimensional Earth density structure models based on Bouguer gravity anomalies. The proposed formulation is solved with a Primal-Dual Interior-Point method including equality and inequality physical and structural constraints. We validate our results using synthetic density crustal structure models with varying complexity and illustrate the behavior of the algorithm using di erent initial density structure models and increasing noise levels in the observations. Based on these implementations, we conclude that the algorithm using Primal-Dual Interior-Point methods is robust, and its results always honor the geophysical constraints. Some of the advantages of using this approach for structural inversion of gravity data are the incorporation of a priori information related to the model parameters (coming from actual physical properties of the subsurface and the reduction of the solution space contingent on these boundary conditions.
Direct inversion of circulation and mixing from tracer measurements – Part 1: Method
Directory of Open Access Journals (Sweden)
T. von Clarmann
2016-11-01
Full Text Available From a series of zonal mean global stratospheric tracer measurements sampled in altitude vs. latitude, circulation and mixing patterns are inferred by the inverse solution of the continuity equation. As a first step, the continuity equation is written as a tendency equation, which is numerically integrated over time to predict a later atmospheric state, i.e., mixing ratio and air density. The integration is formally performed by the multiplication of the initially measured atmospheric state vector by a linear prediction operator. Further, the derivative of the predicted atmospheric state with respect to the wind vector components and mixing coefficients is used to find the most likely wind vector components and mixing coefficients which minimize the residual between the predicted atmospheric state and the later measurement of the atmospheric state. Unless multiple tracers are used, this inversion problem is under-determined, and dispersive behavior of the prediction further destabilizes the inversion. Both these problems are addressed by regularization. For this purpose, a first-order smoothness constraint has been chosen. The usefulness of this method is demonstrated by application to various tracer measurements recorded with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS. This method aims at a diagnosis of the Brewer–Dobson circulation without involving the concept of the mean age of stratospheric air, and related problems like the stratospheric tape recorder, or intrusions of mesospheric air into the stratosphere.
Sorting waves and associated eigenvalues
Carbonari, Costanza; Colombini, Marco; Solari, Luca
2017-04-01
The presence of mixed sediment always characterizes gravel bed rivers. Sorting processes take place during bed load transport of heterogeneous sediment mixtures. The two main elements necessary to the occurrence of sorting are the heterogeneous character of sediments and the presence of an active sediment transport. When these two key ingredients are simultaneously present, the segregation of bed material is consistently detected both in the field [7] and in laboratory [3] observations. In heterogeneous sediment transport, bed altimetric variations and sorting always coexist and both mechanisms are independently capable of driving the formation of morphological patterns. Indeed, consistent patterns of longitudinal and transverse sorting are identified almost ubiquitously. In some cases, such as bar formation [2] and channel bends [5], sorting acts as a stabilizing effect and therefore the dominant mechanism driving pattern formation is associated with bed altimetric variations. In other cases, such as longitudinal streaks, sorting enhances system instability and can therefore be considered the prevailing mechanism. Bedload sheets, first observed by Khunle and Southard [1], represent another classic example of a morphological pattern essentially triggered by sorting, as theoretical [4] and experimental [3] results suggested. These sorting waves cause strong spatial and temporal fluctuations of bedload transport rate typical observed in gravel bed rivers. The problem of bed load transport of a sediment mixture is formulated in the framework of a 1D linear stability analysis. The base state consists of a uniform flow in an infinitely wide channel with active bed load transport. The behaviour of the eigenvalues associated with fluid motion, bed evolution and sorting processes in the space of the significant flow and sediment parameters is analysed. A comparison is attempted with the results of the theoretical analysis of Seminara Colombini and Parker [4] and Stecca
A method to estimate the height of temperature inversion layer and the effective mixing depht
International Nuclear Information System (INIS)
Nicolli, D.
1978-05-01
A review of the concept PBL or turbulent boundary layer is made as it is understood in meteorology. Some features of the PBL parameterization are also discussed, as well as the methods used to estimate the temperature inversion heights during morning and afternoon hours. The study bases on the assumption of the dry adiabatic lapse rate in the mixing layer that is, water vapor and airborne material are supposed to be homogeneously mixed below the inversion layer or in the effective mixing depth. The mean mixing heights over Rio de Janeiro area respectively about 500m and 1000m at morning and afternoon hours. For Sao Paulo these values are respectively 400m and 1300m at morning and afternoon hours [pt
Liu, Long; Liu, Wei
2018-04-01
A forward modeling and inversion algorithm is adopted in order to determine the water injection plan in the oilfield water injection network. The main idea of the algorithm is shown as follows: firstly, the oilfield water injection network is inversely calculated. The pumping station demand flow is calculated. Then, forward modeling calculation is carried out for judging whether all water injection wells meet the requirements of injection allocation or not. If all water injection wells meet the requirements of injection allocation, calculation is stopped, otherwise the demand injection allocation flow rate of certain step size is reduced aiming at water injection wells which do not meet requirements, and next iterative operation is started. It is not necessary to list the algorithm into water injection network system algorithm, which can be realized easily. Iterative method is used, which is suitable for computer programming. Experimental result shows that the algorithm is fast and accurate.
Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A
2017-08-21
In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.
Application of homotopy analysis method and inverse solution of a rectangular wet fin
International Nuclear Information System (INIS)
Panda, Srikumar; Bhowmik, Arka; Das, Ranjan; Repaka, Ramjee; Martha, Subash C.
2014-01-01
Highlights: • Solution of a wet fin with is obtained by homotopy analysis method (HAM). • Present HAM results have been well-validated with literature results. • Inverse analysis is done using genetic algorithm. • Measurement error of ±10–12% (approx.) is found to yield satisfactory reconstructions. - Abstract: This paper presents the analytical solution of a rectangular fin under the simultaneous heat and mass transfer across the fin surface and the fin tip, and estimates the unknown thermal and geometrical configurations of the fin using inverse heat transfer analysis. The local temperature field is obtained by using homotopy analysis method for insulated and convective fin tip boundary conditions. Using genetic algorithm, the thermal and geometrical parameters, viz., thermal conductivity of the material, surface heat transfer coefficient and dimensions of the fin have been simultaneously estimated for the prescribed temperature field. Earlier inverse studies on wet fin have been restricted to the analysis of nonlinear governing equation with either insulated tip condition or finite tip temperature only. The present study developed a closed-form solution with the consideration of nonlinearity effects in both governing equation and boundary condition. The study on inverse optimization leads to many feasible combination of fin materials, thermal conditions and fin dimensions. Thus allows the flexibility for designing a fin under wet conditions, based on multiple combinations of fin materials, fin dimensions and thermal configurations to achieve the required heat transfer duty. It is further determined that the allowable measurement error should be limited to ±10–12% in order to achieve satisfactory reconstruction
Yong, Peng; Liao, Wenyuan; Huang, Jianping; Li, Zhenchuan
2018-04-01
Full waveform inversion is an effective tool for recovering the properties of the Earth from seismograms. However, it suffers from local minima caused mainly by the limited accuracy of the starting model and the lack of a low-frequency component in the seismic data. Because of the high velocity contrast between salt and sediment, the relation between the waveform and velocity perturbation is strongly nonlinear. Therefore, salt inversion can easily get trapped in the local minima. Since the velocity of salt is nearly constant, we can make the most of this characteristic with total variation regularization to mitigate the local minima. In this paper, we develop an adaptive primal dual hybrid gradient method to implement total variation regularization by projecting the solution onto a total variation norm constrained convex set, through which the total variation norm constraint is satisfied at every model iteration. The smooth background velocities are first inverted and the perturbations are gradually obtained by successively relaxing the total variation norm constraints. Numerical experiment of the projection of the BP model onto the intersection of the total variation norm and box constraints has demonstrated the accuracy and efficiency of our adaptive primal dual hybrid gradient method. A workflow is designed to recover complex salt structures in the BP 2004 model and the 2D SEG/EAGE salt model, starting from a linear gradient model without using low-frequency data below 3 Hz. The salt inversion processes demonstrate that wavefield reconstruction inversion with a total variation norm and box constraints is able to overcome local minima and inverts the complex salt velocity layer by layer.
Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations
Aldoghaither, Abeer
2015-11-12
Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final
The eigenvalues of the SN transport matrix
International Nuclear Information System (INIS)
Ourique, L.E.; Vilhena, M.T. de
2005-01-01
In a recent paper, we analyze the dependence of the eigenvalues of the S N matrix transport, associated with the system of linear differential equations that corresponds to the S N approximations of the transport equation [1]. By considering a control parameter, we have shown that there exist some bifurcation points. This means that the solutions of S N approximations change from oscillatory to non-oscillatory behavior, a different approach of the study by [2]. Nowadays, the one-dimensional transport equation and related problems have been a source of new techniques for solving particular cases as well the development of analytical methods that search aspects of existence and uniqueness of the solutions [3], [4]. In this work, we generalize the results shown in [1], searching for a model of the distribution of the bifurcation points of the S N matrix transport, studying the one-dimensional case in a slab, with anisotropic differential cross section of order 3. The result indicates that the bifurcation points obey a certain rule of distribution. Beside that, the condition number of the matrix transport increases too much in the neighborhood of these points, as we have seen in [1]. (author)
Wielandt acceleration for MCNP5 Monte Carlo eigenvalue calculations
International Nuclear Information System (INIS)
Brown, F.
2007-01-01
Monte Carlo criticality calculations use the power iteration method to determine the eigenvalue (k eff ) and eigenfunction (fission source distribution) of the fundamental mode. A recently proposed method for accelerating convergence of the Monte Carlo power iteration using Wielandt's method has been implemented in a test version of MCNP5. The method is shown to provide dramatic improvements in convergence rates and to greatly reduce the possibility of false convergence assessment. The method is effective and efficient, improving the Monte Carlo figure-of-merit for many problems. In addition, the method should eliminate most of the underprediction bias in confidence intervals for Monte Carlo criticality calculations. (authors)
Parallelization of mathematical library for generalized eigenvalue problem for real band matrices
International Nuclear Information System (INIS)
Tanaka, Yasuhisa.
1997-05-01
This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)
International Nuclear Information System (INIS)
Melchert, O; Scheid, W; Apagyi, B
2006-01-01
The Cox-Thompson inverse scattering method at fixed energy has been generalized to treat complex phase shifts derived from experiments. New formulae for relating phase shifts to shifted angular momenta are derived. The method is applied to phase shifts of known potentials in order to test its quality and stability and, further, it is used to invert experimental n-α and n- 12 C phase shifts
Iterative and range test methods for an inverse source problem for acoustic waves
International Nuclear Information System (INIS)
Alves, Carlos; Kress, Rainer; Serranho, Pedro
2009-01-01
We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples
Remarks on a financial inverse problem by means of Monte Carlo Methods
Cuomo, Salvatore; Di Somma, Vittorio; Sica, Federica
2017-10-01
Estimating the price of a barrier option is a typical inverse problem. In this paper we present a numerical and statistical framework for a market with risk-free interest rate and a risk asset, described by a Geometric Brownian Motion (GBM). After approximating the risk asset with a numerical method, we find the final option price by following an approach based on sequential Monte Carlo methods. All theoretical results are applied to the case of an option whose underlying is a real stock.
International Nuclear Information System (INIS)
Garratt, T.J.
1989-05-01
Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)
A comparison of inverse boundary element method and near-field acoustical holography
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Saemann, E.-U.
1999-01-01
An inverse boundary element method (IBEM) is used to estimate the surface velocity of a rolling tyre from measurements of the near-field pressure. Subsequently, the sound pressure is calculated over a finite plane surface next to the tyre from the reconstructed velocity field on the tyre surface........ In order to verify the reconstruction process, part of the measurement data is used together with Near-Field Acoustical Holography (NAH). Estimated distributions of sound pressure and particle velocity over a plane surface obtained from the two methods are compared....
The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws
Institute of Scientific and Technical Information of China (English)
DonghaiLI; XuezhiJIANG; 等
1997-01-01
The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.
A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.
Directory of Open Access Journals (Sweden)
Kai Zhang
Full Text Available In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method, for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.
Directory of Open Access Journals (Sweden)
Wei Gao
2016-01-01
Full Text Available According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV method and the L-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.
Practical use of control rod calibration system with the inverse kinetics method
International Nuclear Information System (INIS)
Yamanaka, Haruhiko; Hayashi, Kazuhiko; Motohashi, Jun; Kawashima, Kazuhito; Ichimura, Toshiyuki; Tamai, Kazuo; Takeuti, Mitsuo
2002-01-01
The control rod calibration results in the JRR-3 are used as a reactivity standard to measure and manage the reactivity change in the core. The total travel of all six control rods has been calibrated by an inverse kinetics method (IK method) during an annual maintenance period. The IK method has the great merit in saving measuring time compared with the conventional positive period method (PP method). The JRR-3 control rod calibration system was renovated and put into practical use in order to improve reliability and function by accumulating 10-year experience with the IK method in the JRR-3. The report shows the function, the performance and results of verification of the JRR-3 control rod calibration system. (author)
EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.
Tal-Ezer, Hillel
2016-05-19
Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.
6th International Workshop on New Computational Methods for Inverse Problems
International Nuclear Information System (INIS)
2016-01-01
Foreword This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 6 th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2016 (http://complement.farman.ens-cachan.fr/NCMIP 2016.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 20, 2016. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013, May 2014 and May 2015. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists in estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one- day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel
Inverse airfoil design method for low-speed straight-bladed Darrieus-type VAWT applications
Energy Technology Data Exchange (ETDEWEB)
Saeed, F. [King Fahd Univ. of Petroleum and Minerals, Dhahran (Saudi Arabia); Paraschivoiu, I.; Trifu, O. [Ecole Polytechnique, Montreal, PQ (Canada); Hess, M.; Gabrys, C. [Mariah Power Inc., Reno, NV (United States)
2008-07-01
Inverse airfoil design of a low-speed straight-bladed Darrieus-type vertical axis wind turbine (VAWT) can help improve aerodynamic performance and power output by eliminating undesirable flow field characteristics at very low Reynolds number. This study used an interactive inverse airfoil design method (PROFOIL) that allows specification of velocity and boundary-layer characteristics over different segments of the airfoil subject to constraints on the geometry (closure) and the flow field (far field boundary). Additional constraints were also considered to address pitching moment coefficient, thickness and the power output for a given tip-speed ratio. Performance analyses of the airfoil and the VAWT were carried out using state-of-the-art analyses codes XFOIL and CARDAAV, respectively. XFOIL is a panel method with a coupled boundary-layer scheme and is used to obtain the aerodynamic characteristics of resulting airfoil shapes. The final airfoil geometry is obtained through a multi-dimensional Newton iteration. The study showed that the strength of the method lies in the inverse design methodology whereas its weaknesses is in reliably predicting aerodynamic characteristics of airfoils at low Reynolds numbers and high angles of attack. A 10-15 per cent increase in the relative performance of the VAWT was achieved with this method. Although the results of the study showed that the method has great application potential for VAWTs in general, there is much room for improvement in flow analysis capabilities for low Re flows in reliably predicting post-stall aerodynamic characteristics. In the absence of such analysis capabilities, the authors suggested that the results should be viewed qualitatively and not quantitatively. 36 refs., 1 tab., 4 figs.
Application of decomposition method and inverse prediction of parameters in a moving fin
International Nuclear Information System (INIS)
Singla, Rohit K.; Das, Ranjan
2014-01-01
Highlights: • Adomian decomposition is used to study a moving fin. • Effects of different parameters on the temperature and efficiency are studied. • Binary-coded GA is used to solve an inverse problem. • Sensitivity analyses of important parameters are carried out. • Measurement error up to 8% is found to be tolerable. - Abstract: The application of the Adomian decomposition method (ADM) is extended to study a conductive–convective and radiating moving fin having variable thermal conductivity. Next, through an inverse approach, ADM in conjunction with a binary-coded genetic algorithm (GA) is also applied for estimation of unknown properties in order to satisfy a given temperature distribution. ADM being one of the widely-used numerical methods for solving non-linear equations, the required temperature field has been obtained using a forward method involving ADM. In the forward problem, the temperature field and efficiency are investigated for various parameters such as convection–conduction parameter, radiation–conduction parameter, Peclet number, convection sink temperature, radiation sink temperature, and dimensionless thermal conductivity. Additionally, in the inverse problem, the effect of random measurement errors, iterative variation of parameters, sensitivity coefficients of unknown parameters are investigated. The performance of GA is compared with few other optimization methods as well as with different temperature measurement points. It is found from the present study that the results obtained from ADM are in good agreement with the results of the differential transformation method available in the literature. It is also observed that for satisfactory reconstruction of the temperature field, the measurement error should be within 8% and the temperature field is strongly dependent on the speed than thermal parameters of the moving fin
Multi-parameter Analysis and Inversion for Anisotropic Media Using the Scattering Integral Method
Djebbi, Ramzi
2017-10-24
The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth\\'s subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the
A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography
Sun, S.; Chen, C.; WANG, H.; Wang, Q.
2014-12-01
The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M
Method for the disposal of laundry drain by inverse osmosis method
International Nuclear Information System (INIS)
Sugimoto, Yoshikazu; Yusa, Hideo; Kamiya, Kunio; Ebara, Katsuya.
1976-01-01
Purpose: To effectively obtain clean water of high purity from laundry waste from work clothes or the like worn in the atomic power plant and to increase the concentration factor of the impurities. Constitution: The laundry drain is supplied to a forestage condensation tank through a supply pipe, via a control valve controlled by a level gage so as to always maintain the liquid level constant, and the liquid within the tank is increased in pressure by the fore-stage high pressure pump and supplied to the fore-stage inverse osmosis module. There occurs a phenomenon of inverse osmosis so that water in disposed liquid is urged through a film and discharged from a osmosed water discharge pipe. In this case, the concentration of a surface active agent in the disposed liquid is detected by a flow meter depending on the quantity of osmosed water, and when the concentration exceeds a predetermined level to decrease the quantity of osmosed water, the opening of the control valve is increased and the liquid is discharged from the discharge pipe into the final tank for disposal in substantially similar manner. (Yoshihara, H.)
Inverse methods for 3D quantitative optical coherence elasticity imaging (Conference Presentation)
Dong, Li; Wijesinghe, Philip; Hugenberg, Nicholas; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.
2017-02-01
In elastography, quantitative elastograms are desirable as they are system and operator independent. Such quantification also facilitates more accurate diagnosis, longitudinal studies and studies performed across multiple sites. In optical elastography (compression, surface-wave or shear-wave), quantitative elastograms are typically obtained by assuming some form of homogeneity. This simplifies data processing at the expense of smearing sharp transitions in elastic properties, and/or introducing artifacts in these regions. Recently, we proposed an inverse problem-based approach to compression OCE that does not assume homogeneity, and overcomes the drawbacks described above. In this approach, the difference between the measured and predicted displacement field is minimized by seeking the optimal distribution of elastic parameters. The predicted displacements and recovered elastic parameters together satisfy the constraint of the equations of equilibrium. This approach, which has been applied in two spatial dimensions assuming plane strain, has yielded accurate material property distributions. Here, we describe the extension of the inverse problem approach to three dimensions. In addition to the advantage of visualizing elastic properties in three dimensions, this extension eliminates the plane strain assumption and is therefore closer to the true physical state. It does, however, incur greater computational costs. We address this challenge through a modified adjoint problem, spatially adaptive grid resolution, and three-dimensional decomposition techniques. Through these techniques the inverse problem is solved on a typical desktop machine within a wall clock time of 20 hours. We present the details of the method and quantitative elasticity images of phantoms and tissue samples.
Modified Bateman solution for identical eigenvalues
International Nuclear Information System (INIS)
Dreher, Raymond
2013-01-01
Highlights: ► Solving indeterminacies due to identical eigenvalues in Bateman’s solution. ► Exact analytical solution of Bateman’s equations for identical eigenvalues. ► Algorithm calculating higher order derivatives appearing in this solution. ► Alternative evaluation of the derivatives through the Taylor polynomial. ► Implementation of an example program demonstrating the developed solution. - Abstract: In this paper we develop a general solution to the Bateman equations taking into account the special case of identical eigenvalues. A characteristic of this new solution is the presence of higher order derivatives. It is shown that the derivatives can be obtained analytically and also computed in an efficient manner
The eigenvalue problem in phase space.
Cohen, Leon
2018-06-30
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Wang, Wenyan; Han, Bo; Yamamoto, Masahiro
2013-01-01
We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)
Directory of Open Access Journals (Sweden)
P. Li
2015-01-01
Full Text Available Composite material is widely used in the conformal load-bearing antenna structure (CLAS, and the manufacturing flaws in the packaging process of the CLAS will lead to the degradation of its wave-transparent property. For this problem, a novel inverse method of the flaw’s dimension by antenna-radome system’s far field data has been proposed. Two steps are included in the inversion: the first one is the inversion from the far filed data to the transmission coefficient of the CLAS’s radome; the second one is the inversion from the transmission coefficient to the flaw’s dimension. The inversion also has a good potential for the separable multilayer composite material radome. A 12.5 GHz CLAS with microstrip antenna array is used in the simulation, which indicates the effectiveness of the novel inversion method. Finally, the error analysis of the inversion method is presented by numerical simulation; the results is that the inversed error could be less than 10%, if the measurement error of far field data is less than 0.45 dB in amplitude and ±5° in phase.
Ab initio nuclear structure - the large sparse matrix eigenvalue problem
Energy Technology Data Exchange (ETDEWEB)
Vary, James P; Maris, Pieter [Department of Physics, Iowa State University, Ames, IA, 50011 (United States); Ng, Esmond; Yang, Chao [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sosonkina, Masha, E-mail: jvary@iastate.ed [Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Ames, IA, 50011 (United States)
2009-07-01
The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10{sup 10} and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.
Ab initio nuclear structure - the large sparse matrix eigenvalue problem
International Nuclear Information System (INIS)
Vary, James P; Maris, Pieter; Ng, Esmond; Yang, Chao; Sosonkina, Masha
2009-01-01
The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10 10 and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.
Avdyushev, Victor A.
2017-12-01
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the
A matrix-inversion method for gamma-source mapping from gamma-count data - 59082
International Nuclear Information System (INIS)
Bull, Richard K.; Adsley, Ian; Burgess, Claire
2012-01-01
Gamma ray counting is often used to survey the distribution of active waste material in various locations. Ideally the output from such surveys would be a map of the activity of the waste. In this paper a simple matrix-inversion method is presented. This allows an array of gamma-count data to be converted to an array of source activities. For each survey area the response matrix is computed using the gamma-shielding code Microshield [1]. This matrix links the activity array to the count array. The activity array is then obtained via matrix inversion. The method was tested on artificially-created arrays of count-data onto which statistical noise had been added. The method was able to reproduce, quite faithfully, the original activity distribution used to generate the dataset. The method has been applied to a number of practical cases, including the distribution of activated objects in a hot cell and to activated Nimonic springs amongst fuel-element debris in vaults at a nuclear plant. (authors)
Directory of Open Access Journals (Sweden)
Jun Wang
2015-01-01
Full Text Available The aim of this paper is to develop a new frequency response function- (FRF- based indirect inverse substructuring method without measuring system-level FRFs in the coupling DOFs for the analysis of the dynamic characteristics of a three-substructure coupled product transport system with rigid and flexible coupling. By enforcing the dynamic equilibrium conditions at the coupling coordinates and the displacement compatibility conditions, a closed-form analytical solution to inverse substructuring analysis of multisubstructure coupled product transport system is derived based on the relationship of easy-to-monitor component-level FRFs and the system-level FRFs at the coupling coordinates. The proposed method is validated by a lumped mass-spring-damper model, and the predicted coupling dynamic stiffness is compared with the direct computation, showing exact agreement. The method developed offers an approach to predict the unknown coupling dynamic stiffness from measured FRFs purely. The suggested method may help to obtain the main controlling factors and contributions from the various structure-borne paths for product transport system.
FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2012-09-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finance. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition
FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)
Blanc-Féraud, Laure; Joubert, Pierre-Yves
2013-10-01
Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen; Alkhalifah, Tariq
2018-03-01
At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen
2018-03-26
At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.
Directory of Open Access Journals (Sweden)
Shoubin Wang
2017-01-01
Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.
Preconditioned alternating direction method of multipliers for inverse problems with constraints
International Nuclear Information System (INIS)
Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie
2017-01-01
We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method. (paper)
Demonstration of improved seismic source inversion method of tele-seismic body wave
Yagi, Y.; Okuwaki, R.
2017-12-01
Seismic rupture inversion of tele-seismic body wave has been widely applied to studies of large earthquakes. In general, tele-seismic body wave contains information of overall rupture process of large earthquake, while the tele-seismic body wave is inappropriate for analyzing a detailed rupture process of M6 7 class earthquake. Recently, the quality and quantity of tele-seismic data and the inversion method has been greatly improved. Improved data and method enable us to study a detailed rupture process of M6 7 class earthquake even if we use only tele-seismic body wave. In this study, we demonstrate the ability of the improved data and method through analyses of the 2016 Rieti, Italy earthquake (Mw 6.2) and the 2016 Kumamoto, Japan earthquake (Mw 7.0) that have been well investigated by using the InSAR data set and the field observations. We assumed the rupture occurring on a single fault plane model inferred from the moment tensor solutions and the aftershock distribution. We constructed spatiotemporal discretized slip-rate functions with patches arranged as closely as possible. We performed inversions using several fault models and found that the spatiotemporal location of large slip-rate area was robust. In the 2016 Kumamoto, Japan earthquake, the slip-rate distribution shows that the rupture propagated to southwest during the first 5 s. At 5 s after the origin time, the main rupture started to propagate toward northeast. First episode and second episode correspond to rupture propagation along the Hinagu fault and the Futagawa fault, respectively. In the 2016 Rieti, Italy earthquake, the slip-rate distribution shows that the rupture propagated to up-dip direction during the first 2 s, and then rupture propagated toward northwest. From both analyses, we propose that the spatiotemporal slip-rate distribution estimated by improved inversion method of tele-seismic body wave has enough information to study a detailed rupture process of M6 7 class earthquake.
Non-local currents in 2D QFT: an alternative To - the quantum inverse scattering method
International Nuclear Information System (INIS)
Bernard, D.; Leclair, A.; Cornell Univ., Ithaca, NY
1990-01-01
The formalism based on non-local charges that we propose provides an alternative to the quantum inverse scattering method for solving integrable quantum field theories in 2D. The content of the paper is: 1. Introduction: historical background. 2. The NLC approach to 2D QFT: a summary. 3 Exchange algebras and on-shell conservation laws: why non-local charges are useful. 4. The lattice construction: the geometrical origin of non-local conserved currents. 5. The continuum construction: how to deal with non-local conserved currents. 6. Examples: Yangian and quantum group currents. 7 Conclusions: open problems. 22 refs., 4 figs
A NEW METHOD OF CHANNEL FRICTION INVERSION BASED ON KALMAN FILTER WITH UNKNOWN PARAMETER VECTOR
Institute of Scientific and Technical Information of China (English)
CHENG Wei-ping; MAO Gen-hai; LIU Guo-hua
2005-01-01
Channel friction is an important parameter in hydraulic analysis.A channel friction parameter inversion method based on Kalman Filter with unknown parameter vector is proposed.Numerical simulations indicate that when the number of monitoring stations exceeds a critical value, the solution is hardly affected.In addition, Kalman Filter with unknown parameter vector is effective only at unsteady state.For the nonlinear equations, computations of sensitivity matrices are time-costly.Two simplified measures can reduce computing time, but not influence the results.One is to reduce sensitivity matrix analysis time, the other is to substitute for sensitivity matrix.
Inverse Heat Conduction Methods in the CHAR Code for Aerothermal Flight Data Reconstruction
Oliver, A. Brandon; Amar, Adam J.
2016-01-01
Reconstruction of flight aerothermal environments often requires the solution of an inverse heat transfer problem, which is an ill-posed problem of determining boundary conditions from discrete measurements in the interior of the domain. This paper will present the algorithms implemented in the CHAR code for use in reconstruction of EFT-1 flight data and future testing activities. Implementation details will be discussed, and alternative hybrid-methods that are permitted by the implementation will be described. Results will be presented for a number of problems.
Design of a new urban wind turbine airfoil using a pressure-load inverse method
Energy Technology Data Exchange (ETDEWEB)
Henriques, J.C.C.; Gato, L.M.C. [IDMEC, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Marques da Silva, F. [LNEC - Laboratorio Nacional de Engenharia Civil, Av. Brasil, 101, 1700-066 Lisboa (Portugal); Estanqueiro, A.I. [INETI - Instituto Nacional de Engenharia, Tecnologia e Inovacao Estrada do Paco do Lumiar, 1649-038 Lisboa (Portugal)
2009-12-15
This paper presents the design methodology of a new wind turbine airfoil that achieves high performance in urban environment by increasing the maximum lift. For this purpose, an inverse method was applied to obtain a new wind turbine blade section with constant pressure-load along the chord, at the design inlet angle. In comparison with conventional blade section designs, the new airfoil has increased maximum lift, reduced leading edge suction peak and controlled soft-stall behaviour, due to a reduction of the adverse pressure gradient on the suction side. Wind tunnel experimental results confirmed the computational results. (author)
Shakir, Muhammad
2011-12-01
In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. The largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results. © 2011 IEEE.
Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues
Shakir, Muhammad; Tang, Wuchen; Rao, Anlei; Imran, Muhammad Ali; Alouini, Mohamed-Slim
2011-01-01
Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach. © 2011 ICST.
A comparison of two methods for earthquake source inversion using strong motion seismograms
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G. C. Beroza
1994-06-01
Full Text Available In this paper we compare two time-domain inversion methods that have been widely applied to the problem of modeling earthquake rupture using strong-motion seismograms. In the multi-window method, each point on the fault is allowed to rupture multiple times. This allows flexibility in the rupture time and hence the rupture velocity. Variations in the slip-velocity function are accommodated by variations in the slip amplitude in each time-window. The single-window method assumes that each point on the fault ruptures only once, when the rupture front passes. Variations in slip amplitude are allowed and variations in rupture velocity are accommodated by allowing the rupture time to vary. Because the multi-window method allows greater flexibility, it has the potential to describe a wider range of faulting behavior; however, with this increased flexibility comes an increase in the degrees of freedom and the solutions are comparatively less stable. We demonstrate this effect using synthetic data for a test model of the Mw 7.3 1992 Landers, California earthquake, and then apply both inversion methods to the actual recordings. The two approaches yield similar fits to the strong-motion data with different seismic moments indicating that the moment is not well constrained by strong-motion data alone. The slip amplitude distribution is similar using either approach, but important differences exist in the rupture propagation models. The single-window method does a better job of recovering the true seismic moment and the average rupture velocity. The multi-window method is preferable when rise time is strongly variable, but tends to overestimate the seismic moment. Both methods work well when the rise time is constant or short compared to the periods modeled. Neither approach can recover the temporal details of rupture propagation unless the distribution of slip amplitude is constrained by independent data.
On a minimization of the eigenvalues of Schroedinger operator relatively domains
International Nuclear Information System (INIS)
Gasymov, Yu.S.; Niftiev, A.A.
2001-01-01
Minimization of the eigenvalues plays an important role in the operators spectral theory. The problem on the minimization of the eigenvalues of the Schroedinger operator by areas is considered in this work. The algorithm, analogous to the conditional gradient method, is proposed for the numerical solution of this problem in the common case. The result is generalized for the case of the positively determined completely continuous operator [ru
Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.
2016-12-01
Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.
A penalty method for PDE-constrained optimization in inverse problems
International Nuclear Information System (INIS)
Leeuwen, T van; Herrmann, F J
2016-01-01
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate. (paper)
Stratified source-sampling techniques for Monte Carlo eigenvalue analysis
International Nuclear Information System (INIS)
Mohamed, A.
1998-01-01
In 1995, at a conference on criticality safety, a special session was devoted to the Monte Carlo ''Eigenvalue of the World'' problem. Argonne presented a paper, at that session, in which the anomalies originally observed in that problem were reproduced in a much simplified model-problem configuration, and removed by a version of stratified source-sampling. In this paper, stratified source-sampling techniques are generalized and applied to three different Eigenvalue of the World configurations which take into account real-world statistical noise sources not included in the model problem, but which differ in the amount of neutronic coupling among the constituents of each configuration. It is concluded that, in Monte Carlo eigenvalue analysis of loosely-coupled arrays, the use of stratified source-sampling reduces the probability of encountering an anomalous result over that if conventional source-sampling methods are used. However, this gain in reliability is substantially less than that observed in the model-problem results
Directory of Open Access Journals (Sweden)
Andre Lamert
2018-03-01
Full Text Available We present and compare two flexible and effective methodologies to predict disturbance zones ahead of underground tunnels by using elastic full-waveform inversion. One methodology uses a linearized, iterative approach based on misfit gradients computed with the adjoint method while the other uses iterative, gradient-free unscented Kalman filtering in conjunction with a level-set representation. Whereas the former does not involve a priori assumptions on the distribution of elastic properties ahead of the tunnel, the latter introduces a massive reduction in the number of explicit model parameters to be inverted for by focusing on the geometric form of potential disturbances and their average elastic properties. Both imaging methodologies are validated through successful reconstructions of simple disturbances. As an application, we consider an elastic multiple disturbance scenario. By using identical synthetic time-domain seismograms as test data, we obtain satisfactory, albeit different, reconstruction results from the two inversion methodologies. The computational costs of both approaches are of the same order of magnitude, with the gradient-based approach showing a slight advantage. The model parameter space reduction approach compensates for this by additionally providing a posteriori estimates of model parameter uncertainty. Keywords: Tunnel seismics, Full waveform inversion, Seismic waves, Level-set method, Adjoint method, Kalman filter
Distribution functions of magnetic nanoparticles determined by a numerical inversion method
International Nuclear Information System (INIS)
Bender, P; Balceris, C; Ludwig, F; Posth, O; Bogart, L K; Szczerba, W; Castro, A; Nilsson, L; Costo, R; Gavilán, H; González-Alonso, D; Pedro, I de; Barquín, L Fernández; Johansson, C
2017-01-01
In the present study, we applied a regularized inversion method to extract the particle size, magnetic moment and relaxation-time distribution of magnetic nanoparticles from small-angle x-ray scattering (SAXS), DC magnetization (DCM) and AC susceptibility (ACS) measurements. For the measurements the particles were colloidally dispersed in water. At first approximation the particles could be assumed to be spherically shaped and homogeneously magnetized single-domain particles. As model functions for the inversion, we used the particle form factor of a sphere (SAXS), the Langevin function (DCM) and the Debye model (ACS). The extracted distributions exhibited features/peaks that could be distinctly attributed to the individually dispersed and non-interacting nanoparticles. Further analysis of these peaks enabled, in combination with a prior characterization of the particle ensemble by electron microscopy and dynamic light scattering, a detailed structural and magnetic characterization of the particles. Additionally, all three extracted distributions featured peaks, which indicated deviations of the scattering (SAXS), magnetization (DCM) or relaxation (ACS) behavior from the one expected for individually dispersed, homogeneously magnetized nanoparticles. These deviations could be mainly attributed to partial agglomeration (SAXS, DCM, ACS), uncorrelated surface spins (DCM) and/or intra-well relaxation processes (ACS). The main advantage of the numerical inversion method is that no ad hoc assumptions regarding the line shape of the extracted distribution functions are required, which enabled the detection of these contributions. We highlighted this by comparing the results with the results obtained by standard model fits, where the functional form of the distributions was a priori assumed to be log-normal shaped. (paper)
Inverse design-momentum, a method for the preliminary design of horizontal axis wind turbines
International Nuclear Information System (INIS)
Battisti, L; Soraperra, G; Fedrizzi, R; Zanne, L
2007-01-01
Wind turbine rotor prediction methods based on generalized momentum theory BEM routinely used in industry and vortex wake methods demand the use of airfoil tabulated data and geometrical specifications such as the blade spanwise chord distribution. They belong to the category of 'direct design' methods. When, on the other hand, the geometry is deduced from some design objective, we refer to 'inverse design' methods. This paper presents a method for the preliminary design of wind turbine rotors based on an inverse design approach. For this purpose, a generalized theory was developed without using classical tools such as BEM. Instead, it uses a simplified meridional flow analysis of axial turbomachines and is based on the assumption that knowing the vortex distribution and appropriate boundary conditions is tantamount to knowing the velocity distribution. The simple conservation properties of the vortex components consistently cope with the forces and specific work exchange expressions through the rotor. The method allows for rotor arbitrarily radial load distribution and includes the wake rotation and expansion. Radial pressure gradient is considered in the wake. The capability of the model is demonstrated first by a comparison with the classical actuator disk theory in investigating the consistency of the flow field, then the model is used to predict the blade planform of a commercial wind turbine. Based on these validations, the authors postulate the use of a different vortex distribution (i.e. not-uniform loading) for blade design and discuss the effect of such choices on blade chord and twist, force distribution and power coefficient. In addition to the method's straightforward application to the pre-design phase, the model clearly shows the link between blade geometry and performance allowing quick preliminary evaluation of non uniform loading on blade structural characteristics
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Rao, M.M.M.; Sadhuram, Y.
. The data are revisited for objective mapping of the temperature fields using Stochastic Inverse Method. Hourly reciprocal transmissions were carried with time lag of 30 minutes between each direction. From the multipath arrival patterns, significant peaks...
The eigenvalue problem for a singular quasilinear elliptic equation
Directory of Open Access Journals (Sweden)
Benjin Xuan
2004-02-01
Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.
Han, Jijun; Yang, Deqiang; Sun, Houjun; Xin, Sherman Xuegang
2017-01-01
Inverse method is inherently suitable for calculating the distribution of source current density related with an irregularly structured electromagnetic target field. However, the present form of inverse method cannot calculate complex field-tissue interactions. A novel hybrid inverse/finite-difference time domain (FDTD) method that can calculate the complex field-tissue interactions for the inverse design of source current density related with an irregularly structured electromagnetic target field is proposed. A Huygens' equivalent surface is established as a bridge to combine the inverse and FDTD method. Distribution of the radiofrequency (RF) magnetic field on the Huygens' equivalent surface is obtained using the FDTD method by considering the complex field-tissue interactions within the human body model. The obtained magnetic field distributed on the Huygens' equivalent surface is regarded as the next target. The current density on the designated source surface is derived using the inverse method. The homogeneity of target magnetic field and specific energy absorption rate are calculated to verify the proposed method.
Directory of Open Access Journals (Sweden)
В С Корнилов
2016-12-01
Full Text Available The article presents scientific and methodical aspects of forming the content of education inverse problems for differential equations for students of higher educational institutions of physical, mathematical and natural science training areas. The goals are formulated and the principles of training are the content of learning inverse problems for differential equations. Attention is drawn to the particular issues of teaching courses inverse problems. Describes the classification criteria and target modules that play the role of tools to create and analyze the model and curriculum, forming learning content inverse problems for differential equations. The content classification features and target modules. Formulate conclusions that learning the inverse problems for differential equations has scientific, educational and humanitarian potential of students and as a result of this training they gain the fundamental knowledge in the applied and computational mathematics, and also develop scientific worldview, applied, environmental, information thinking.
Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method
Alekseev, G.; Tokhtina, A.; Soboleva, O.
2017-10-01
Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.
Inverse operator method for solutions of nonlinear dynamical equations and some typical applications
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields
International Nuclear Information System (INIS)
Chen, Xudong
2010-01-01
This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging
An analytical method for the inverse Cauchy problem of Lame equation in a rectangle
Grigor’ev, Yu
2018-04-01
In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.
Eigenvalues and expansion of bipartite graphs
DEFF Research Database (Denmark)
Høholdt, Tom; Janwa, Heeralal
2012-01-01
We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...
Analysis of eigenvalue correction applied to biometrics
Hendrikse, A.J.; Veldhuis, Raymond N.J.; Spreeuwers, Lieuwe Jan; Bazen, A.M.
Eigenvalue estimation plays an important role in biometrics. However, if the number of samples is limited, estimates are significantly biased. In this article we analyse the influence of this bias on the error rates of PCA/LDA based verification systems, using both synthetic data with realistic
A note on quasilinear elliptic eigenvalue problems
Directory of Open Access Journals (Sweden)
Gianni Arioli
1999-11-01
Full Text Available We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.
Eigenvalues of the -Laplacian and disconjugacy criteria
Directory of Open Access Journals (Sweden)
Pinasco Juan P
2006-01-01
Full Text Available We derive oscillation and nonoscillation criteria for the one-dimensional -Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.
A new localization set for generalized eigenvalues
Directory of Open Access Journals (Sweden)
Jing Gao
2017-05-01
Full Text Available Abstract A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16:883-898, 2009. Numerical examples are given to verify the corresponding results.
TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.
Proximal methods for the resolution of inverse problems: application to positron emission tomography
International Nuclear Information System (INIS)
Pustelnik, N.
2010-12-01
The objective of this work is to propose reliable, efficient and fast methods for minimizing convex criteria, that are found in inverse problems for imagery. We focus on restoration/reconstruction problems when data is degraded with both a linear operator and noise, where the latter is not assumed to be necessarily additive.The reliability of the method is ensured through the use of proximal algorithms, the convergence of which is guaranteed when a convex criterion is considered. Efficiency is sought through the choice of criteria adapted to the noise characteristics, the linear operators and the image specificities. Of particular interest are regularization terms based on total variation and/or sparsity of signal frame coefficients. As a consequence of the use of frames, two approaches are investigated, depending on whether the analysis or the synthesis formulation is chosen. Fast processing requirements lead us to consider proximal algorithms with a parallel structure. Theoretical results are illustrated on several large size inverse problems arising in image restoration, stereoscopy, multi-spectral imagery and decomposition into texture and geometry components. We focus on a particular application, namely Positron Emission Tomography (PET), which is particularly difficult because of the presence of a projection operator combined with Poisson noise, leading to highly corrupted data. To optimize the quality of the reconstruction, we make use of the spatio-temporal characteristics of brain tissue activity. (author)
An inverse method for crack characterization from ultrasonic B-Scan images
International Nuclear Information System (INIS)
Faur, M.; Roy, O.; Benoist, PH.; Morisseau, PH.
1996-01-01
Concern has been expressed about the capabilities of performing non destructive evaluation (NDE) of flaws located near to the outer surface in nuclear pressurized water reactor (PWR) vessels. The ultrasonic examination of PWR is accomplished from the inside with ultrasonic focused transducers working in the pulse echo mode. By recording the echoes as a function of time, the Ascan representation may be obtained. Many ultrasonic flaw detectors used for NDE are based on the simple Ascan concept involving measuring a time interval called 'time of flight'. By combining the Ascan concept synchronized transducer scanning, one can produce Bscan images that are two dimensional descriptions of the flaw interaction with the ultrasonic field. In the following, the flaw is assumed to be an axially oriented crack (the most serious flaw to be found in a pressurized component). In the case of the outer surface cracks (OSC's), analyzing and interpreting ultrasonic Ascan images become difficult because of the various reflections of the ultrasonic beam on the crack and on the outer surface (the so-called corner effect). Methods for automatic interpretation of ultrasonic experimental data are currently under investigation. In this paper, we present an inverse method for determining the geometrical characteristics of OSC's from ultrasonic Bscan images. The direct model used for the inversion procedure predicts synthetic Bscan images of ultrasonic examination of blocks containing planar defects interrogated by focused probes. (authors)
Microseismic imaging using a source-independent full-waveform inversion method
Wang, Hanchen
2016-09-06
Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.
Microseismic imaging using a source-independent full-waveform inversion method
Wang, Hanchen
2016-01-01
Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.
A robust multilevel simultaneous eigenvalue solver
Costiner, Sorin; Taasan, Shlomo
1993-01-01
Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti; Rundell, William
2012-01-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical
IMPACT OF MATRIX INVERSION ON THE COMPLEXITY OF THE FINITE ELEMENT METHOD
Directory of Open Access Journals (Sweden)
M. Sybis
2016-04-01
Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.
Inverse methods for estimating primary input signals from time-averaged isotope profiles
Passey, Benjamin H.; Cerling, Thure E.; Schuster, Gerard T.; Robinson, Todd F.; Roeder, Beverly L.; Krueger, Stephen K.
2005-08-01
Mammalian teeth are invaluable archives of ancient seasonality because they record along their growth axes an isotopic record of temporal change in environment, plant diet, and animal behavior. A major problem with the intra-tooth method is that intra-tooth isotope profiles can be extremely time-averaged compared to the actual pattern of isotopic variation experienced by the animal during tooth formation. This time-averaging is a result of the temporal and spatial characteristics of amelogenesis (tooth enamel formation), and also results from laboratory sampling. This paper develops and evaluates an inverse method for reconstructing original input signals from time-averaged intra-tooth isotope profiles. The method requires that the temporal and spatial patterns of amelogenesis are known for the specific tooth and uses a minimum length solution of the linear system Am = d, where d is the measured isotopic profile, A is a matrix describing temporal and spatial averaging during amelogenesis and sampling, and m is the input vector that is sought. Accuracy is dependent on several factors, including the total measurement error and the isotopic structure of the measured profile. The method is shown to accurately reconstruct known input signals for synthetic tooth enamel profiles and the known input signal for a rabbit that underwent controlled dietary changes. Application to carbon isotope profiles of modern hippopotamus canines reveals detailed dietary histories that are not apparent from the measured data alone. Inverse methods show promise as an effective means of dealing with the time-averaging problem in studies of intra-tooth isotopic variation.
The boundary element method for the solution of the multidimensional inverse heat conduction problem
International Nuclear Information System (INIS)
Lagier, Guy-Laurent
1999-01-01
This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr
Inverse method for stress monitoring in pressure components of steam generators
International Nuclear Information System (INIS)
Duda, P.
2003-01-01
The purpose of this work is to formulate a space marching method, which can be used to solve inverse multidimensional heat conduction problems. The method is designed to reconstruct the transient temperature distribution in a whole construction element based on measured temperatures taken at selected points inside or on the outer surface of the construction element. Next, the Finite Element Method is used to calculate thermal stresses and stresses caused by other loads such as, for instance, internal pressure. The developed method for solving temperature and total stress distribution will be tested using the measured temperatures generated from a direct solution. Transient temperature and total stress distribution obtained from method presented below will be compared with the values obtained from the direct solution. Finally, the presented method will be applied in order to monitor temperature and stress distribution in an outlet header using the real measured temperature values at seven points on the header's outer surface during the power boiler's shut down operation. The presented method allows to optimize the power block's start-up and shut-down operations, contributes to the reduction of heat loss during these operations and to the extension of power block's life. The fatigue and creep usage factor can be computed in an on-line mode. The presented method herein can be applied to monitoring systems that work in conventional as well as in nuclear power plants. (author)
International Nuclear Information System (INIS)
Shimazu, Yoichiro; Tashiro, Shoichi; Tojo, Masayuki
2017-01-01
The performance of two digital reactivity meters, one based on the conventional inverse kinetic method and the other one based on simple feedback theory, are compared analytically using their respective transfer functions. The latter one is proposed by one of the authors. It has been shown that the performance of the two reactivity meters become almost identical when proper system parameters are selected for each reactivity meter. A new correlation between the system parameters of the two reactivity meters is found. With this correlation, filter designers can easily determine the system parameters for the respective reactivity meters to obtain identical performance. (author)
International Nuclear Information System (INIS)
Garratt, T.J.
1989-05-01
Safety assessments of radioactive waste disposal require efficient computer models for the important processes. The present paper is based on an efficient computational technique which can be used to solve a wide variety of safety assessment models. It involves the numerical inversion of analytical solutions to the Laplace-transformed differential equations using a method proposed by Talbot. This method has been implemented on a personal computer in a user-friendly manner. The steps required to implement a particular transform and run the program are outlined. Four examples are described which illustrate the flexibility, accuracy and efficiency of the program. The improvements in computational efficiency described in this paper have application to the probabilistic safety assessment codes ESCORT and MASCOT which are currently under development. Also, it is hoped that the present work will form the basis of software for personal computers which could be used to demonstrate safety assessment procedures to a wide audience. (author)
International Nuclear Information System (INIS)
Lachheb, Mohamed; Karkri, Mustapha; Albouchi, Fethi; Mzali, Foued; Nasrallah, Sassi Ben
2014-01-01
Highlights: • Preparation of paraffin/graphite composites by uni-axial compression technique. • Measurement of thermophysical properties of paraffin/graphite using the periodic method. • Measurement of the experimental densities of paraffin/graphite composites. • Prediction of the effective thermal conductivity using analytical models. - Abstract: In this paper, two types of graphite were combined with paraffin in an attempt to improve thermal conductivity of paraffin phase change material (PCM): Synthetic graphite (Timrex SFG75) and graphite waste obtained from damaged Tubular graphite Heat Exchangers. These paraffin/graphite phase change material (PCM) composites are prepared by the cold uniaxial compression technique and the thermophysical properties were estimated using a periodic temperature method and an inverse technique. Results showed that the thermal conductivity and thermal diffusivity are greatly influenced by the graphite addition
Geometric shapes inversion method of space targets by ISAR image segmentation
Huo, Chao-ying; Xing, Xiao-yu; Yin, Hong-cheng; Li, Chen-guang; Zeng, Xiang-yun; Xu, Gao-gui
2017-11-01
The geometric shape of target is an effective characteristic in the process of space targets recognition. This paper proposed a method of shape inversion of space target based on components segmentation from ISAR image. The Radon transformation, Hough transformation, K-means clustering, triangulation will be introduced into ISAR image processing. Firstly, we use Radon transformation and edge detection to extract space target's main body spindle and solar panel spindle from ISAR image. Then the targets' main body, solar panel, rectangular and circular antenna are segmented from ISAR image based on image detection theory. Finally, the sizes of every structural component are computed. The effectiveness of this method is verified using typical targets' simulation data.
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
International Nuclear Information System (INIS)
Haber, E; Horesh, L; Tenorio, L
2010-01-01
Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data
Identification of strain-rate and thermal sensitive material model with an inverse method
Peroni, L; Peroni, M
2010-01-01
This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strain-rates and temperatures. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields) or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena). Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work. The method presented requires strong effort both from experimental and numerical point of view, an...
Joining direct and indirect inverse calibration methods to characterize karst, coastal aquifers
De Filippis, Giovanna; Foglia, Laura; Giudici, Mauro; Mehl, Steffen; Margiotta, Stefano; Negri, Sergio
2016-04-01
Parameter estimation is extremely relevant for accurate simulation of groundwater flow. Parameter values for models of large-scale catchments are usually derived from a limited set of field observations, which can rarely be obtained in a straightforward way from field tests or laboratory measurements on samples, due to a number of factors, including measurement errors and inadequate sampling density. Indeed, a wide gap exists between the local scale, at which most of the observations are taken, and the regional or basin scale, at which the planning and management decisions are usually made. For this reason, the use of geologic information and field data is generally made by zoning the parameter fields. However, pure zoning does not perform well in the case of fairly complex aquifers and this is particularly true for karst aquifers. In fact, the support of the hydraulic conductivity measured in the field is normally much smaller than the cell size of the numerical model, so it should be upscaled to a scale consistent with that of the numerical model discretization. Automatic inverse calibration is a valuable procedure to identify model parameter values by conditioning on observed, available data, limiting the subjective evaluations introduced with the trial-and-error technique. Many approaches have been proposed to solve the inverse problem. Generally speaking, inverse methods fall into two groups: direct and indirect methods. Direct methods allow determination of hydraulic conductivities from the groundwater flow equations which relate the conductivity and head fields. Indirect methods, instead, can handle any type of parameters, independently from the mathematical equations that govern the process, and condition parameter values and model construction on measurements of model output quantities, compared with the available observation data, through the minimization of an objective function. Both approaches have pros and cons, depending also on model complexity. For
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
An inverse method to estimate the flow through a levee breach
D'Oria, Marco; Mignosa, Paolo; Tanda, Maria Giovanna
2015-08-01
We propose a procedure to estimate the flow through a levee breach based on water levels recorded in river stations downstream and/or upstream of the failure site. The inverse problem is solved using a Bayesian approach and requires the execution of several forward unsteady flow simulations. For this purpose, we have used the well-known 1-D HEC-RAS model, but any unsteady flow model could be adopted in the same way. The procedure has been tested using four synthetic examples. Levee breaches with different characteristics (free flow, flow with tailwater effects, etc.) have been simulated to collect the synthetic level data used at a later stage in the inverse procedure. The method was able to accurately reproduce the flow through the breach in all cases. The practicability of the procedure was then confirmed applying it to the inundation of the Polesine Region (Northern Italy) which occurred in 1951 and was caused by three contiguous and almost simultaneous breaches on the left embankment of the Po River.
Characterization of a Method for Inverse Heat Conduction Using Real and Simulated Thermocouple Data
Pizzo, Michelle E.; Glass, David E.
2017-01-01
It is often impractical to instrument the external surface of high-speed vehicles due to the aerothermodynamic heating. Temperatures can instead be measured internal to the structure using embedded thermocouples, and direct and inverse methods can then be used to estimate temperature and heat flux on the external surface. Two thermocouples embedded at different depths are required to solve direct and inverse problems, and filtering schemes are used to reduce noise in the measured data. Accuracy in the estimated surface temperature and heat flux is dependent on several factors. Factors include the thermocouple location through the thickness of a material, the sensitivity of the surface solution to the error in the specified location of the embedded thermocouples, and the sensitivity to the error in thermocouple data. The effect of these factors on solution accuracy is studied using the methodology discussed in the work of Pizzo, et. al.1 A numerical study is performed to determine if there is an optimal depth at which to embed one thermocouple through the thickness of a material assuming that a second thermocouple is installed on the back face. Solution accuracy will be discussed for a range of embedded thermocouple depths. Moreover, the sensitivity of the surface solution to (a) the error in the specified location of the embedded thermocouple and to (b) the error in the thermocouple data are quantified using numerical simulation, and the results are discussed.
Generalization of Samuelson's inequality and location of eigenvalues
Indian Academy of Sciences (India)
We prove a generalization of Samuelson's inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex × matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.
A parallel algorithm for the non-symmetric eigenvalue problem
International Nuclear Information System (INIS)
Sidani, M.M.
1991-01-01
An algorithm is presented for the solution of the non-symmetric eigenvalue problem. The algorithm is based on a divide-and-conquer procedure that provides initial approximations to the eigenpairs, which are then refined using Newton iterations. Since the smaller subproblems can be solved independently, and since Newton iterations with different initial guesses can be started simultaneously, the algorithm - unlike the standard QR method - is ideal for parallel computers. The author also reports on his investigation of deflation methods designed to obtain further eigenpairs if needed. Numerical results from implementations on a host of parallel machines (distributed and shared-memory) are presented
van der Hilst, R. D.; de Hoop, M. V.; Shim, S. H.; Shang, X.; Wang, P.; Cao, Q.
2012-04-01
Over the past three decades, tremendous progress has been made with the mapping of mantle heterogeneity and with the understanding of these structures in terms of, for instance, the evolution of Earth's crust, continental lithosphere, and thermo-chemical mantle convection. Converted wave imaging (e.g., receiver functions) and reflection seismology (e.g. SS stacks) have helped constrain interfaces in crust and mantle; surface wave dispersion (from earthquake or ambient noise signals) characterizes wavespeed variations in continental and oceanic lithosphere, and body wave and multi-mode surface wave data have been used to map trajectories of mantle convection and delineate mantle regions of anomalous elastic properties. Collectively, these studies have revealed substantial ocean-continent differences and suggest that convective flow is strongly influenced by but permitted to cross the upper mantle transition zone. Many questions have remained unanswered, however, and further advances in understanding require more accurate depictions of Earth's heterogeneity at a wider range of length scales. To meet this challenge we need new observations—more, better, and different types of data—and methods that help us extract and interpret more information from the rapidly growing volumes of broadband data. The huge data volumes and the desire to extract more signal from them means that we have to go beyond 'business as usual' (that is, simplified theory, manual inspection of seismograms, …). Indeed, it inspires the development of automated full wave methods, both for tomographic delineation of smooth wavespeed variations and the imaging (for instance through inverse scattering) of medium contrasts. Adjoint tomography and reverse time migration, which are closely related wave equation methods, have begun to revolutionize seismic inversion of global and regional waveform data. In this presentation we will illustrate this development - and its promise - drawing from our work
An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.
Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P
2012-01-01
The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example
Lippman, Sheri A.; Shade, Starley B.; Hubbard, Alan E.
2011-01-01
Background Intervention effects estimated from non-randomized intervention studies are plagued by biases, yet social or structural intervention studies are rarely randomized. There are underutilized statistical methods available to mitigate biases due to self-selection, missing data, and confounding in longitudinal, observational data permitting estimation of causal effects. We demonstrate the use of Inverse Probability Weighting (IPW) to evaluate the effect of participating in a combined clinical and social STI/HIV prevention intervention on reduction of incident chlamydia and gonorrhea infections among sex workers in Brazil. Methods We demonstrate the step-by-step use of IPW, including presentation of the theoretical background, data set up, model selection for weighting, application of weights, estimation of effects using varied modeling procedures, and discussion of assumptions for use of IPW. Results 420 sex workers contributed data on 840 incident chlamydia and gonorrhea infections. Participators were compared to non-participators following application of inverse probability weights to correct for differences in covariate patterns between exposed and unexposed participants and between those who remained in the intervention and those who were lost-to-follow-up. Estimators using four model selection procedures provided estimates of intervention effect between odds ratio (OR) .43 (95% CI:.22-.85) and .53 (95% CI:.26-1.1). Conclusions After correcting for selection bias, loss-to-follow-up, and confounding, our analysis suggests a protective effect of participating in the Encontros intervention. Evaluations of behavioral, social, and multi-level interventions to prevent STI can benefit by introduction of weighting methods such as IPW. PMID:20375927
Directory of Open Access Journals (Sweden)
Cleather Daniel J
2010-11-01
Full Text Available Abstract Background A vast number of biomechanical studies have employed inverse dynamics methods to calculate inter-segmental moments during movement. Although all inverse dynamics methods are rooted in classical mechanics and thus theoretically the same, there exist a number of distinct computational methods. Recent research has demonstrated a key influence of the dynamics computation of the inverse dynamics method on the calculated moments, despite the theoretical equivalence of the methods. The purpose of this study was therefore to explore the influence of the choice of inverse dynamics on the calculation of inter-segmental moments. Methods An inverse dynamics analysis was performed to analyse vertical jumping and weightlifting movements using two distinct methods. The first method was the traditional inverse dynamics approach, in this study characterized as the 3 step method, where inter-segmental moments were calculated in the local coordinate system of each segment, thus requiring multiple coordinate system transformations. The second method (the 1 step method was the recently proposed approach based on wrench notation that allows all calculations to be performed in the global coordinate system. In order to best compare the effect of the inverse dynamics computation a number of the key assumptions and methods were harmonized, in particular unit quaternions were used to parameterize rotation in both methods in order to standardize the kinematics. Results Mean peak inter-segmental moments calculated by the two methods were found to agree to 2 decimal places in all cases and were not significantly different (p > 0.05. Equally the normalized dispersions of the two methods were small. Conclusions In contrast to previously documented research the difference between the two methods was found to be negligible. This study demonstrates that the 1 and 3 step method are computationally equivalent and can thus be used interchangeably in
International Nuclear Information System (INIS)
Kishimoto, M.; Sakasai, K.; Ara, K.
1994-01-01
In this paper, the new type of non-invasive beam profile monitor for intense ion accelerator using high-temperature superconductor. We regard the inverse estimation problem of beam profile as the optimum allocation problem of the currents into the cross-section of the beam vacuum pipe and applied genetic algorithm to solve this optimization problem. And we carried out the computer simulation to verify the effectiveness of this inverse estimation method of beam profile. (author)
Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues
García Planas, María Isabel; Tarragona Romero, Sonia
2014-01-01
The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family
Frequency response as a surrogate eigenvalue problem in topology optimization
DEFF Research Database (Denmark)
Andreassen, Erik; Ferrari, Federico; Sigmund, Ole
2018-01-01
This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...
Computing the eigenvalues and eigenvectors of a fuzzy matrix
Directory of Open Access Journals (Sweden)
A. Kumar
2012-08-01
Full Text Available Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.$
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Fymat, A. L.
1976-01-01
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
Directory of Open Access Journals (Sweden)
J. Szymszal
2009-01-01
Full Text Available The study discusses application of computer simulation based on the method of inverse cumulative distribution function. The simulationrefers to an elementary static case, which can also be solved by physical experiment, consisting mainly in observations of foundryproduction in a selected foundry plant. For the simulation and forecasting of foundry production quality in selected cast iron grade, arandom number generator of Excel calculation sheet was chosen. Very wide potentials of this type of simulation when applied to theevaluation of foundry production quality were demonstrated, using a number generator of even distribution for generation of a variable ofan arbitrary distribution, especially of a preset empirical distribution, without any need of adjusting to this variable the smooth theoreticaldistributions.
An alternative 3D inversion method for magnetic anomalies with depth resolution
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M. Chiappini
2006-06-01
Full Text Available This paper presents a new method to invert magnetic anomaly data in a variety of non-complex contexts when a priori information about the sources is not available. The region containing magnetic sources is discretized into a set of homogeneously magnetized rectangular prisms, polarized along a common direction. The magnetization distribution is calculated by solving an underdetermined linear system, and is accomplished through the simultaneous minimization of the norm of the solution and the misfit between the observed and the calculated field. Our algorithm makes use of a dipolar approximation to compute the magnetic field of the rectangular blocks. We show how this approximation, in conjunction with other correction factors, presents numerous advantages in terms of computing speed and depth resolution, and does not affect significantly the success of the inversion. The algorithm is tested on both synthetic and real magnetic datasets.
Nuclear lifetime measurements with the DSA coincidence method in inverse reactions
International Nuclear Information System (INIS)
Hermans, J.A.J.
1977-01-01
This thesis describes lifetime measurements with the DSA coincidence method in inverse reactions. Bombardment of 2 H and 3 H targets with heavy ions of energies up to 50 MeV produces nuclei recoiling at initial velocities of v(0) approximately equal to 0.05 c. Heavy-ion beams of 11 B, 12 C, 14 N, 16 O, 18 O, 19 F, 27 A1, 28 Si, 30 Si, 31 P, 32 S, 35 Cl and 37 Cl are at present available from the Utrecht 6 MV EN tandem accelerator. The recoil nuclei are slowed down in Mg, Al, Cu, Ag or Au and the γ-ray Doppler pattern is observed with a large Ge(Li) detector in coincidence with protons
Variational methods for direct/inverse problems of atmospheric dynamics and chemistry
Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena
2013-04-01
We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the
Thermo-mechanical model identification of a strengthened copper with an inverse method
Peroni, M; Dallocchio, A
2009-01-01
This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strain-rates. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields) or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena). Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work.
Desmal, Abdulla
2014-07-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
Directory of Open Access Journals (Sweden)
C. Eva
1994-06-01
Full Text Available In this paper we apply various inversion methods to a set of teleseismic data collected by a network operating along the Ligurian Belt in the transition region between Alps and Apennines. In particular, we consider the regularization method, the truncated singular value decomposition, the Landweber method (with the Related Simultaneous Iterative Reconstruction Technique and the conjugate gradient method. All the methods provide rather similar velocity models which are well approximated by that provided by back-projection (used with an appropriate normalization constant. A drawback of these models seems to be the large discrepancy (of the order of 40% between the observed time residuals and those computed from the model itself. However, for each station of the network, the azimuth dependence of the computed time residuals reproduces rather well the observed one so that it is believable that the most significant information contained in the data has been expIoited. The computed velocity models indicate strong heterogeneities in the first 200 km below the Apennines.
International Nuclear Information System (INIS)
Perotin, L.; Granger, S.
1997-01-01
In order to improve the prediction of wear problems due to flow-induced vibration in PWR components, an inverse method for identifying a distributed random excitation acting on a dynamical system has been developed at EDF. This method, whose applications go far beyond the flow-induced vibration field, has been implemented into the MEIDEE software. This method is presented. (author)
Monotonicity of energy eigenvalues for Coulomb systems
International Nuclear Information System (INIS)
Englisch, R.
1983-01-01
Generalising results by earlier workers for a large class of Hamiltonians (among others, Hamiltonians of Coulomb systems) which can be written in the form H(α) = H 0 + αH' the present works shows that their eigenvalues decrease with increasing α. This result is applied to Coulomb systems in which the distances between the infinitely heavy particles are varying and also is used to obtain a completion and simplification of proof for the stability of the biexciton. (author)
Recurrence quantity analysis based on matrix eigenvalues
Yang, Pengbo; Shang, Pengjian
2018-06-01
Recurrence plots is a powerful tool for visualization and analysis of dynamical systems. Recurrence quantification analysis (RQA), based on point density and diagonal and vertical line structures in the recurrence plots, is considered to be alternative measures to quantify the complexity of dynamical systems. In this paper, we present a new measure based on recurrence matrix to quantify the dynamical properties of a given system. Matrix eigenvalues can reflect the basic characteristics of the complex systems, so we show the properties of the system by exploring the eigenvalues of the recurrence matrix. Considering that Shannon entropy has been defined as a complexity measure, we propose the definition of entropy of matrix eigenvalues (EOME) as a new RQA measure. We confirm that EOME can be used as a metric to quantify the behavior changes of the system. As a given dynamical system changes from a non-chaotic to a chaotic regime, the EOME will increase as well. The bigger EOME values imply higher complexity and lower predictability. We also study the effect of some factors on EOME,including data length, recurrence threshold, the embedding dimension, and additional noise. Finally, we demonstrate an application in physiology. The advantage of this measure lies in a high sensitivity and simple computation.
Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
Chu, W. P.
1985-01-01
The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.
A survey of direct inversion methods having possible application to tunnel detection
International Nuclear Information System (INIS)
Mager, R.D.
1985-01-01
Within recent years there has been considerable interest in the development of geophysical methods for the location of hidden underground tunnels and cavities. Consideration of this problem has been motivated by military applications, such as the detection of shallow man-made tunnels and arm caches, as well as civilian applications such as detection of limestone cavities in karst terrain and the mapping of abandoned mine workings. There are also applications for in-situ coal gasification and for the monitoring of nuclear waste disposal sites. The most reliable method presently used to map these underground anomalies has been direct detection by closely spaced drilling. However, the high cost of drilling renders this method impractical except for detailed and localized mapping, and certainly unfeasible for any type of broad-scale reconnaissance activity. Largely motivated by petroleum and mineral exploration needs, however, the seismic industry has seen a virtual revolution in acquisition and processing techniques within the past ten years. Paralleling these developments have been corresponding developments in acoustical imaging and non-destructive testing. Researchers in the field of inverse scattering have produced a number of new methods for target imaging from backscattered reflection data
An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems
International Nuclear Information System (INIS)
Zhang Jianzhong; Zhang Liwei
2010-01-01
We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.
Inversion of potential field data using the finite element method on parallel computers
Gross, L.; Altinay, C.; Shaw, S.
2015-11-01
In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media
Directory of Open Access Journals (Sweden)
Vicenţiu RăDulescu
2005-06-01
Full Text Available We study nonlinear eigenvalue problems of the type Ã¢ÂˆÂ’div(a(xÃ¢ÂˆÂ‡u=g(ÃŽÂ»,x,u in Ã¢Â„ÂN, where a(x is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.
Dimensionality of social networks using motifs and eigenvalues.
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Anthony Bonato
Full Text Available We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.
Dynamic Eigenvalue Problem of Concrete Slab Road Surface
Pawlak, Urszula; Szczecina, Michał
2017-10-01
The paper presents an analysis of the dynamic eigenvalue problem of concrete slab road surface. A sample concrete slab was modelled using Autodesk Robot Structural Analysis software and calculated with Finite Element Method. The slab was set on a one-parameter elastic subsoil, for which the modulus of elasticity was separately calculated. The eigen frequencies and eigenvectors (as maximal vertical nodal displacements) were presented. On the basis of the results of calculations, some basic recommendations for designers of concrete road surfaces were offered.
Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods.
Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti
2012-04-07
Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ₂ norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ₁/ℓ₂ mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ₁/ℓ₂ norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.
EFFECT OF INVERSION ON TREATMENT OF FENCE SUBJECTED TO SAP DISPLACEMENT METHOD
Directory of Open Access Journals (Sweden)
Juarez Benigno Paes
2014-03-01
Full Text Available http://dx.doi.org/10.5902/1980509813338This work aimed to evaluate the effect of inversion of Prosopis juliflora and Leucaena leucocephala fenceposts, in distribution, penetration and retention of copper chrome borate (CCB solution applied by sapdisplacement method. The Prosopis juliflora was collected in Brazilian Agricultural Research Company(EMBRAPA and the Leucaena leucocephala at the Federal University of Campina Grande in Patos,Paraíba state, Brazil. Trees with DAP from 5.0 to 10.0 cm were employed. Disks of 2.0 cm of thicknesswere retired on the top and on the base of pieces. The external disks were then discarded and the internones were employed to determine the wood characteristics, being the round pieces with 2.0 m. A solutionof 2% of active ingredients of CCB was used to treated woods. A total of 10 pieces of each species weretreated, and five of them remained in the solution for 8 days and the five ones had their tops inverted afterthe sixth day of treatment. The pieces were seasoned; disks of 2.0 cm of thickness were taken in 5 positions along of pieces and the analyses for determination of copper and boron penetration took place. The valuesof wood characteristics indicated that the pieces were homogeneous. The absorption of the solution was of19.9 liters (Prosopis juliflora and of 17.0 liters (Leucaena leucocephala. The nominal retentions of CCBwere 7.72 and 5.34 kg active ingredients (a.i./m3, respectively. In general, the inversion of the pieces inthe preservative solution is recommended, by providing a better distribution, penetration and retention ofCCB on treated pieces.
On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems
Directory of Open Access Journals (Sweden)
El-Sayed M. E. Mostafa
2017-01-01
Full Text Available The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples.
Identification of strain-rate and thermal sensitive material model with an inverse method
Directory of Open Access Journals (Sweden)
Peroni M.
2010-06-01
Full Text Available This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strainrates and temperatures. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena. Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work. The method presented requires strong effort both from experimental and numerical point of view, anyway it allows to precisely identify the parameters of different material models. This could provide great advantages when high reliability of the material behaviour is necessary. Applicability of this method is particularly indicated for special applications in the field of aerospace engineering, ballistic, crashworthiness studies or particle accelerator technologies, where materials could be submitted to strong plastic deformations at high-strain rate in a wide range of temperature. Thermal softening effect has been investigated in a temperature range between 20°C and 1000°C.
Directory of Open Access Journals (Sweden)
J. D. Hemingway
2017-11-01
Full Text Available Serial oxidation coupled with stable carbon and radiocarbon analysis of sequentially evolved CO2 is a promising method to characterize the relationship between organic carbon (OC chemical composition, source, and residence time in the environment. However, observed decay profiles depend on experimental conditions and oxidation pathway. It is therefore necessary to properly assess serial oxidation kinetics before utilizing decay profiles as a measure of OC reactivity. We present a regularized inverse method to estimate the distribution of OC activation energy (E, a proxy for bond strength, using serial oxidation. Here, we apply this method to ramped temperature pyrolysis or oxidation (RPO analysis but note that this approach is broadly applicable to any serial oxidation technique. RPO analysis directly compares thermal reactivity to isotope composition by determining the E range for OC decaying within each temperature interval over which CO2 is collected. By analyzing a decarbonated test sample at multiple masses and oven ramp rates, we show that OC decay during RPO analysis follows a superposition of parallel first-order kinetics and that resulting E distributions are independent of experimental conditions. We therefore propose the E distribution as a novel proxy to describe OC thermal reactivity and suggest that E vs. isotope relationships can provide new insight into the compositional controls on OC source and residence time.
Hemingway, Jordon D.; Rothman, Daniel H.; Rosengard, Sarah Z.; Galy, Valier V.
2017-11-01
Serial oxidation coupled with stable carbon and radiocarbon analysis of sequentially evolved CO2 is a promising method to characterize the relationship between organic carbon (OC) chemical composition, source, and residence time in the environment. However, observed decay profiles depend on experimental conditions and oxidation pathway. It is therefore necessary to properly assess serial oxidation kinetics before utilizing decay profiles as a measure of OC reactivity. We present a regularized inverse method to estimate the distribution of OC activation energy (E), a proxy for bond strength, using serial oxidation. Here, we apply this method to ramped temperature pyrolysis or oxidation (RPO) analysis but note that this approach is broadly applicable to any serial oxidation technique. RPO analysis directly compares thermal reactivity to isotope composition by determining the E range for OC decaying within each temperature interval over which CO2 is collected. By analyzing a decarbonated test sample at multiple masses and oven ramp rates, we show that OC decay during RPO analysis follows a superposition of parallel first-order kinetics and that resulting E distributions are independent of experimental conditions. We therefore propose the E distribution as a novel proxy to describe OC thermal reactivity and suggest that E vs. isotope relationships can provide new insight into the compositional controls on OC source and residence time.
Inverse PCR-based method for isolating novel SINEs from genome.
Han, Yawei; Chen, Liping; Guan, Lihong; He, Shunping
2014-04-01
Short interspersed elements (SINEs) are moderately repetitive DNA sequences in eukaryotic genomes. Although eukaryotic genomes contain numerous SINEs copy, it is very difficult and laborious to isolate and identify them by the reported methods. In this study, the inverse PCR was successfully applied to isolate SINEs from Opsariichthys bidens genome in Eastern Asian Cyprinid. A group of SINEs derived from tRNA(Ala) molecular had been identified, which were named Opsar according to Opsariichthys. SINEs characteristics were exhibited in Opsar, which contained a tRNA(Ala)-derived region at the 5' end, a tRNA-unrelated region, and AT-rich region at the 3' end. The tRNA-derived region of Opsar shared 76 % sequence similarity with tRNA(Ala) gene. This result indicated that Opsar could derive from the inactive or pseudogene of tRNA(Ala). The reliability of method was tested by obtaining C-SINE, Ct-SINE, and M-SINEs from Ctenopharyngodon idellus, Megalobrama amblycephala, and Cyprinus carpio genomes. This method is simpler than the previously reported, which successfully omitted many steps, such as preparation of probes, construction of genomic libraries, and hybridization.
The factorization method for inverse acoustic scattering in a layered medium
International Nuclear Information System (INIS)
Bondarenko, Oleksandr; Kirsch, Andreas; Liu, Xiaodong
2013-01-01
In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equation F-tilde g =φ z is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, F-tilde is a self-adjoint operator related to the far field operator and ϕ z is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and sound-hard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples. (paper)
Micro-seismic Imaging Using a Source Independent Waveform Inversion Method
Wang, Hanchen
2016-04-18
Micro-seismology is attracting more and more attention in the exploration seismology community. The main goal in micro-seismic imaging is to find the source location and the ignition time in order to track the fracture expansion, which will help engineers monitor the reservoirs. Conventional imaging methods work fine in this field but there are many limitations such as manual picking, incorrect migration velocity and low signal to noise ratio (S/N). In traditional surface survey imaging, full waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. Use the FWI technique, and overcomes the difficulties of manual pickings and incorrect velocity model for migration. However, the technique of waveform inversion of micro-seismic events faces its own problems. There is significant nonlinearity due to the unknown source location (space) and function (time). We have developed a source independent FWI of micro-seismic events to simultaneously invert for the source image, source function and velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. To examine the accuracy of the inverted source image and velocity model the extended image for source wavelet in z-axis is extracted. Also the angle gather is calculated to check the applicability of the migration velocity. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity in the synthetic experiments with both parts of the Marmousi and the SEG
Kong, Changduk; Lim, Semyeong
2011-12-01
Recently, the health monitoring system of major gas path components of gas turbine uses mostly the model based method like the Gas Path Analysis (GPA). This method is to find quantity changes of component performance characteristic parameters such as isentropic efficiency and mass flow parameter by comparing between measured engine performance parameters such as temperatures, pressures, rotational speeds, fuel consumption, etc. and clean engine performance parameters without any engine faults which are calculated by the base engine performance model. Currently, the expert engine diagnostic systems using the artificial intelligent methods such as Neural Networks (NNs), Fuzzy Logic and Genetic Algorithms (GAs) have been studied to improve the model based method. Among them the NNs are mostly used to the engine fault diagnostic system due to its good learning performance, but it has a drawback due to low accuracy and long learning time to build learning data base if there are large amount of learning data. In addition, it has a very complex structure for finding effectively single type faults or multiple type faults of gas path components. This work builds inversely a base performance model of a turboprop engine to be used for a high altitude operation UAV using measured performance data, and proposes a fault diagnostic system using the base engine performance model and the artificial intelligent methods such as Fuzzy logic and Neural Network. The proposed diagnostic system isolates firstly the faulted components using Fuzzy Logic, then quantifies faults of the identified components using the NN leaned by fault learning data base, which are obtained from the developed base performance model. In leaning the NN, the Feed Forward Back Propagation (FFBP) method is used. Finally, it is verified through several test examples that the component faults implanted arbitrarily in the engine are well isolated and quantified by the proposed diagnostic system.
International Nuclear Information System (INIS)
Gene Golub; Kwok Ko
2009-01-01
The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.
International Nuclear Information System (INIS)
Bahar, M.K.; Yasuk, F.
2013-01-01
Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)
Energy Technology Data Exchange (ETDEWEB)
Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica
1978-08-21
The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.
Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.
2014-12-01
Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.
Orlandi, A.; Ortolani, A.; Meneguzzo, F.; Levizzani, V.; Torricella, F.; Turk, F. J.
2004-03-01
In order to improve high-resolution forecasts, a specific method for assimilating rainfall rates into the Regional Atmospheric Modelling System model has been developed. It is based on the inversion of the Kuo convective parameterisation scheme. A nudging technique is applied to 'gently' increase with time the weight of the estimated precipitation in the assimilation process. A rough but manageable technique is explained to estimate the partition of convective precipitation from stratiform one, without requiring any ancillary measurement. The method is general purpose, but it is tuned for geostationary satellite rainfall estimation assimilation. Preliminary results are presented and discussed, both through totally simulated experiments and through experiments assimilating real satellite-based precipitation observations. For every case study, Rainfall data are computed with a rapid update satellite precipitation estimation algorithm based on IR and MW satellite observations. This research was carried out in the framework of the EURAINSAT project (an EC research project co-funded by the Energy, Environment and Sustainable Development Programme within the topic 'Development of generic Earth observation technologies', Contract number EVG1-2000-00030).
Application of random seismic inversion method based on tectonic model in thin sand body research
Dianju, W.; Jianghai, L.; Qingkai, F.
2017-12-01
The oil and gas exploitation at Songliao Basin, Northeast China have already progressed to the period with high water production. The previous detailed reservoir description that based on seismic image, sediment core, borehole logging has great limitations in small scale structural interpretation and thin sand body characterization. Thus, precise guidance for petroleum exploration is badly in need of a more advanced method. To do so, we derived the method of random seismic inversion constrained by tectonic model.It can effectively improve the depicting ability of thin sand bodies, combining numerical simulation techniques, which can credibly reducing the blindness of reservoir analysis from the whole to the local and from the macroscopic to the microscopic. At the same time, this can reduce the limitations of the study under the constraints of different geological conditions of the reservoir, accomplish probably the exact estimation for the effective reservoir. Based on the research, this paper has optimized the regional effective reservoir evaluation and the productive location adjustment of applicability, combined with the practical exploration and development in Aonan oil field.
Systematic hierarchical coarse-graining with the inverse Monte Carlo method
Energy Technology Data Exchange (ETDEWEB)
Lyubartsev, Alexander P., E-mail: alexander.lyubartsev@mmk.su.se [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); Naômé, Aymeric, E-mail: aymeric.naome@unamur.be [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); UCPTS Division, University of Namur, 61 Rue de Bruxelles, B 5000 Namur (Belgium); Vercauteren, Daniel P., E-mail: daniel.vercauteren@unamur.be [UCPTS Division, University of Namur, 61 Rue de Bruxelles, B 5000 Namur (Belgium); Laaksonen, Aatto, E-mail: aatto@mmk.su.se [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); Science for Life Laboratory, 17121 Solna (Sweden)
2015-12-28
We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730–3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.
Modified Inverse First Order Reliability Method (I-FORM) for Predicting Extreme Sea States.
Energy Technology Data Exchange (ETDEWEB)
Eckert-Gallup, Aubrey Celia; Sallaberry, Cedric Jean-Marie; Dallman, Ann Renee; Neary, Vincent Sinclair
2014-09-01
Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulation s as a part of the stand ard current practice for designing marine structure s to survive extreme sea states. Such environmental contours are characterized by combinations of significant wave height ( ) and energy period ( ) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first - order reliability method (IFORM) i s standard design practice for generating environmental contours. In this paper, the traditional appli cation of the IFORM to generating environmental contours representing extreme sea states is described in detail and its merits and drawbacks are assessed. The application of additional methods for analyzing sea state data including the use of principal component analysis (PCA) to create an uncorrelated representation of the data under consideration is proposed. A reexamination of the components of the IFORM application to the problem at hand including the use of new distribution fitting techniques are shown to contribute to the development of more accurate a nd reasonable representations of extreme sea states for use in survivability analysis for marine struc tures. Keywords: In verse FORM, Principal Component Analysis , Environmental Contours, Extreme Sea State Characteri zation, Wave Energy Converters
International Nuclear Information System (INIS)
Chang, Win-Jin; Fang, Te-Hua
2006-01-01
This study proposes a means for calculating the interaction force during the scanning process using a scanning near-field optical microscope (SNOM) probe. The determination of the interaction force in the scanning system is regarded as an inverse vibration problem. The conjugate gradient method is applied to treat the inverse problem using available displacement measurements. The results show that the conjugate gradient method is less sensitive to measurement errors and prior information on the functional form of quality was not required. Furthermore, the initial guesses for the interaction force can be arbitrarily chosen for the iteration process
A numerical study of the eigenvalues in the neutron diffusion theory
International Nuclear Information System (INIS)
Lima Bezerra, J. de.
1982-12-01
A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt
Numerical computations of interior transmission eigenvalues for scattering objects with cavities
International Nuclear Information System (INIS)
Peters, Stefan; Kleefeld, Andreas
2016-01-01
In this article we extend the inside-outside duality for acoustic transmission eigenvalue problems by allowing scattering objects that may contain cavities. In this context we provide the functional analytical framework necessary to transfer the techniques that have been used in Kirsch and Lechleiter (2013 Inverse Problems, 29 104011) to derive the inside-outside duality. Additionally, extensive numerical results are presented to show that we are able to successfully detect interior transmission eigenvalues with the inside-outside duality approach for a variety of obstacles with and without cavities in three dimensions. In this context, we also discuss the advantages and disadvantages of the inside-outside duality approach from a numerical point of view. Furthermore we derive the integral equations necessary to extend the algorithm in Kleefeld (2013 Inverse Problems, 29 104012) to compute highly accurate interior transmission eigenvalues for scattering objects with cavities, which we will then use as reference values to examine the accuracy of the inside-outside duality algorithm. (paper)
International Nuclear Information System (INIS)
Palmai, T.; Apagyi, B.; Horvath, M.
2008-01-01
Solution of the Cox-Thompson inverse scattering problem at fixed energy 1-3 is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered. (author)