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Sample records for equations domain decomposition

  1. Vector domain decomposition schemes for parabolic equations

    Science.gov (United States)

    Vabishchevich, P. N.

    2017-09-01

    A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.

  2. Domain decomposition method for solving the neutron diffusion equation

    International Nuclear Information System (INIS)

    Coulomb, F.

    1989-03-01

    The aim of this work is to study methods for solving the neutron diffusion equation; we are interested in methods based on a classical finite element discretization and well suited for use on parallel computers. Domain decomposition methods seem to answer this preoccupation. This study deals with a decomposition of the domain. A theoretical study is carried out for Lagrange finite elements and some examples are given; in the case of mixed dual finite elements, the study is based on examples [fr

  3. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich

    2010-01-01

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  4. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan

    2010-10-05

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  5. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.

    2010-01-01

    In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

  6. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.; Langer, U.

    2010-01-01

    of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series

  7. A mixed finite element domain decomposition method for nearly elastic wave equations in the frequency domain

    Energy Technology Data Exchange (ETDEWEB)

    Feng, Xiaobing [Univ. of Tennessee, Knoxville, TN (United States)

    1996-12-31

    A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.

  8. Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

    International Nuclear Information System (INIS)

    Berthe, P.M.

    2013-01-01

    In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

  9. Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

    2017-12-01

    We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.

  10. A non overlapping parallel domain decomposition method applied to the simplified transport equations

    International Nuclear Information System (INIS)

    Lathuiliere, B.; Barrault, M.; Ramet, P.; Roman, J.

    2009-01-01

    A reactivity computation requires to compute the highest eigenvalue of a generalized eigenvalue problem. An inverse power algorithm is used commonly. Very fine modelizations are difficult to tackle for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. So, we propose a non-overlapping domain decomposition method for the approximate resolution of the linear system to solve at each inverse power iteration. Our method brings to a low development effort as the inner multigroup solver can be re-use without modification, and allows us to adapt locally the numerical resolution (mesh, finite element order). Numerical results are obtained by a parallel implementation of the method on two different cases with a pin by pin discretization. This results are analyzed in terms of memory consumption and parallel efficiency. (authors)

  11. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains

    Energy Technology Data Exchange (ETDEWEB)

    El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com

    2006-11-20

    The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.

  12. A parallel algorithm for solving the multidimensional within-group discrete ordinates equations with spatial domain decomposition - 104

    International Nuclear Information System (INIS)

    Zerr, R.J.; Azmy, Y.Y.

    2010-01-01

    A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)

  13. Development of the hierarchical domain decomposition boundary element method for solving the three-dimensional multiregion neutron diffusion equations

    International Nuclear Information System (INIS)

    Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro

    2001-01-01

    A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the 'lower level' calculations. At the 'higher level' calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time. (author)

  14. A fast-multipole domain decomposition integral equation solver for characterizing electromagnetic wave propagation in mine environments

    KAUST Repository

    Yücel, Abdulkadir C.

    2013-07-01

    Reliable and effective wireless communication and tracking systems in mine environments are key to ensure miners\\' productivity and safety during routine operations and catastrophic events. The design of such systems greatly benefits from simulation tools capable of analyzing electromagnetic (EM) wave propagation in long mine tunnels and large mine galleries. Existing simulation tools for analyzing EM wave propagation in such environments employ modal decompositions (Emslie et. al., IEEE Trans. Antennas Propag., 23, 192-205, 1975), ray-tracing techniques (Zhang, IEEE Tran. Vehic. Tech., 5, 1308-1314, 2003), and full wave methods. Modal approaches and ray-tracing techniques cannot accurately account for the presence of miners and their equipments, as well as wall roughness (especially when the latter is comparable to the wavelength). Full-wave methods do not suffer from such restrictions but require prohibitively large computational resources. To partially alleviate this computational burden, a 2D integral equation-based domain decomposition technique has recently been proposed (Bakir et. al., in Proc. IEEE Int. Symp. APS, 1-2, 8-14 July 2012). © 2013 IEEE.

  15. Multi-domain/multi-method numerical approach for neutron transport equation; Couplage de methodes et decomposition de domaine pour la resolution de l'equation du transport des neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Girardi, E

    2004-12-15

    A new methodology for the solution of the neutron transport equation, based on domain decomposition has been developed. This approach allows us to employ different numerical methods together for a whole core calculation: a variational nodal method, a discrete ordinate nodal method and a method of characteristics. These new developments authorize the use of independent spatial and angular expansion, non-conformal Cartesian and unstructured meshes for each sub-domain, introducing a flexibility of modeling which is not allowed in today available codes. The effectiveness of our multi-domain/multi-method approach has been tested on several configurations. Among them, one particular application: the benchmark model of the Phebus experimental facility at Cea-Cadarache, shows why this new methodology is relevant to problems with strong local heterogeneities. This comparison has showed that the decomposition method brings more accuracy all along with an important reduction of the computer time.

  16. A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

    KAUST Repository

    Zheng, Xiang

    2015-03-01

    We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors. © 2015 Elsevier Inc.

  17. A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

    International Nuclear Information System (INIS)

    Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David

    2015-01-01

    We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors

  18. A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

    Science.gov (United States)

    Zheng, Xiang; Yang, Chao; Cai, Xiao-Chuan; Keyes, David

    2015-03-01

    We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton-Krylov-Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.

  19. A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D

    KAUST Repository

    Zheng, Xiang; Yang, Chao; Cai, Xiaochuan; Keyes, David E.

    2015-01-01

    We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn-Hilliard-Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation

  20. Domain decomposition method using a hybrid parallelism and a low-order acceleration for solving the Sn transport equation on unstructured geometry

    International Nuclear Information System (INIS)

    Odry, Nans

    2016-01-01

    Deterministic calculation schemes are devised to numerically solve the neutron transport equation in nuclear reactors. Dealing with core-sized problems is very challenging for computers, so much that the dedicated core calculations have no choice but to allow simplifying assumptions (assembly- then core scale steps..). The PhD work aims at overcoming some of these approximations: thanks to important changes in computer architecture and capacities (HPC), nowadays one can solve 3D core-sized problems, using both high mesh refinement and the transport operator. It is an essential step forward in order to perform, in the future, reference calculations using deterministic schemes. This work focuses on a spatial domain decomposition method (DDM). Using massive parallelism, DDM allows much more ambitious computations in terms of both memory requirements and calculation time. Developments were performed inside the Sn core solver Minaret, from the new CEA neutronics platform APOLLO3. Only fast reactors (hexagonal periodicity) are considered, even if all kinds of geometries can be dealt with, using Minaret. The work has been divided in four steps: 1) The spatial domain decomposition with no overlap is inserted into the standard algorithmic structure of Minaret. The fundamental idea involves splitting a core-sized problem into smaller, independent, spatial sub-problems. angular flux is exchanged between adjacent sub-domains. In doing so, all combined sub-problems converge to the global solution at the outcome of an iterative process. Various strategies were explored regarding both data management and algorithm design. Results (k eff and flux) are systematically compared to the reference in a numerical verification step. 2) Introducing more parallelism is an unprecedented opportunity to heighten performances of deterministic schemes. Domain decomposition is particularly suited to this. A two-layer hybrid parallelism strategy, suited to HPC, is chosen. It benefits from the

  1. Domain decomposition methods and deflated Krylov subspace iterations

    NARCIS (Netherlands)

    Nabben, R.; Vuik, C.

    2006-01-01

    The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which

  2. Multiple Shooting and Time Domain Decomposition Methods

    CERN Document Server

    Geiger, Michael; Körkel, Stefan; Rannacher, Rolf

    2015-01-01

    This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms.  The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics.  This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied...

  3. Domain decomposition and CMFD acceleration applied to discrete-ordinate methods for the solution of the neutron transport equation in XYZ geometries

    International Nuclear Information System (INIS)

    Masiello, Emiliano; Martin, Brunella; Do, Jean-Michel

    2011-01-01

    A new development for the IDT solver is presented for large reactor core applications in XYZ geometries. The multigroup discrete-ordinate neutron transport equation is solved using a Domain-Decomposition (DD) method coupled with the Coarse-Mesh Finite Differences (CMFD). The later is used for accelerating the DD convergence rate. In particular, the external power iterations are preconditioned for stabilizing the oscillatory behavior of the DD iterative process. A set of critical 2-D and 3-D numerical tests on a single processor will be presented for the analysis of the performances of the method. The results show that the application of the CMFD to the DD can be a good candidate for large 3D full-core parallel applications. (author)

  4. Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime

    Science.gov (United States)

    Lorin, E.; Yang, X.; Antoine, X.

    2016-06-01

    The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.

  5. A stable penalty method for the compressible Navier-Stokes equations: II: One-dimensional domain decomposition schemes

    DEFF Research Database (Denmark)

    Hesthaven, Jan

    1997-01-01

    This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res......This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions...... and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers's equation and developed for the compressible Navier-Stokes equations in general curvilinear coordinates. The versatility of the proposed scheme for the compressible Navier-Stokes equations is illustrated...

  6. High-speed parallel solution of the neutron diffusion equation with the hierarchical domain decomposition boundary element method incorporating parallel communications

    International Nuclear Information System (INIS)

    Tsuji, Masashi; Chiba, Gou

    2000-01-01

    A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers. (author)

  7. Domain decomposition methods and parallel computing

    International Nuclear Information System (INIS)

    Meurant, G.

    1991-01-01

    In this paper, we show how to efficiently solve large linear systems on parallel computers. These linear systems arise from discretization of scientific computing problems described by systems of partial differential equations. We show how to get a discrete finite dimensional system from the continuous problem and the chosen conjugate gradient iterative algorithm is briefly described. Then, the different kinds of parallel architectures are reviewed and their advantages and deficiencies are emphasized. We sketch the problems found in programming the conjugate gradient method on parallel computers. For this algorithm to be efficient on parallel machines, domain decomposition techniques are introduced. We give results of numerical experiments showing that these techniques allow a good rate of convergence for the conjugate gradient algorithm as well as computational speeds in excess of a billion of floating point operations per second. (author). 5 refs., 11 figs., 2 tabs., 1 inset

  8. Spatial domain decomposition for neutron transport problems

    International Nuclear Information System (INIS)

    Yavuz, M.; Larsen, E.W.

    1989-01-01

    A spatial Domain Decomposition method is proposed for modifying the Source Iteration (SI) and Diffusion Synthetic Acceleration (DSA) algorithms for solving discrete ordinates problems. The method, which consists of subdividing the spatial domain of the problem and performing the transport sweeps independently on each subdomain, has the advantage of being parallelizable because the calculations in each subdomain can be performed on separate processors. In this paper we describe the details of this spatial decomposition and study, by numerical experimentation, the effect of this decomposition on the SI and DSA algorithms. Our results show that the spatial decomposition has little effect on the convergence rates until the subdomains become optically thin (less than about a mean free path in thickness)

  9. Domain decomposition method for solving elliptic problems in unbounded domains

    International Nuclear Information System (INIS)

    Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1991-01-01

    Computational aspects of the box domain decomposition (DD) method for solving boundary value problems in an unbounded domain are discussed. A new variant of the DD-method for elliptic problems in unbounded domains is suggested. It is based on the partitioning of an unbounded domain adapted to the given asymptotic decay of an unknown function at infinity. The comparison of computational expenditures is given for boundary integral method and the suggested DD-algorithm. 29 refs.; 2 figs.; 2 tabs

  10. Multilevel domain decomposition for electronic structure calculations

    International Nuclear Information System (INIS)

    Barrault, M.; Cances, E.; Hager, W.W.; Le Bris, C.

    2007-01-01

    We introduce a new multilevel domain decomposition method (MDD) for electronic structure calculations within semi-empirical and density functional theory (DFT) frameworks. This method iterates between local fine solvers and global coarse solvers, in the spirit of domain decomposition methods. Using this approach, calculations have been successfully performed on several linear polymer chains containing up to 40,000 atoms and 200,000 atomic orbitals. Both the computational cost and the memory requirement scale linearly with the number of atoms. Additional speed-up can easily be obtained by parallelization. We show that this domain decomposition method outperforms the density matrix minimization (DMM) method for poor initial guesses. Our method provides an efficient preconditioner for DMM and other linear scaling methods, variational in nature, such as the orbital minimization (OM) procedure

  11. Domain decomposition methods for solving an image problem

    Energy Technology Data Exchange (ETDEWEB)

    Tsui, W.K.; Tong, C.S. [Hong Kong Baptist College (Hong Kong)

    1994-12-31

    The domain decomposition method is a technique to break up a problem so that ensuing sub-problems can be solved on a parallel computer. In order to improve the convergence rate of the capacitance systems, pre-conditioned conjugate gradient methods are commonly used. In the last decade, most of the efficient preconditioners are based on elliptic partial differential equations which are particularly useful for solving elliptic partial differential equations. In this paper, the authors apply the so called covering preconditioner, which is based on the information of the operator under investigation. Therefore, it is good for various kinds of applications, specifically, they shall apply the preconditioned domain decomposition method for solving an image restoration problem. The image restoration problem is to extract an original image which has been degraded by a known convolution process and additive Gaussian noise.

  12. Covariant Conformal Decomposition of Einstein Equations

    Science.gov (United States)

    Gourgoulhon, E.; Novak, J.

    It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

  13. Domain decomposition methods for fluid dynamics

    International Nuclear Information System (INIS)

    Clerc, S.

    1995-01-01

    A domain decomposition method for steady-state, subsonic fluid dynamics calculations, is proposed. The method is derived from the Schwarz alternating method used for elliptic problems, extended to non-linear hyperbolic problems. Particular emphasis is given on the treatment of boundary conditions. Numerical results are shown for a realistic three-dimensional two-phase flow problem with the FLICA-4 code for PWR cores. (from author). 4 figs., 8 refs

  14. Domain decomposition multigrid for unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Shapira, Yair

    1997-01-01

    A two-level preconditioning method for the solution of elliptic boundary value problems using finite element schemes on possibly unstructured meshes is introduced. It is based on a domain decomposition and a Galerkin scheme for the coarse level vertex unknowns. For both the implementation and the analysis, it is not required that the curves of discontinuity in the coefficients of the PDE match the interfaces between subdomains. Generalizations to nonmatching or overlapping grids are made.

  15. Domain decomposition methods for mortar finite elements

    Energy Technology Data Exchange (ETDEWEB)

    Widlund, O.

    1996-12-31

    In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.

  16. Bregmanized Domain Decomposition for Image Restoration

    KAUST Repository

    Langer, Andreas

    2012-05-22

    Computational problems of large-scale data are gaining attention recently due to better hardware and hence, higher dimensionality of images and data sets acquired in applications. In the last couple of years non-smooth minimization problems such as total variation minimization became increasingly important for the solution of these tasks. While being favorable due to the improved enhancement of images compared to smooth imaging approaches, non-smooth minimization problems typically scale badly with the dimension of the data. Hence, for large imaging problems solved by total variation minimization domain decomposition algorithms have been proposed, aiming to split one large problem into N > 1 smaller problems which can be solved on parallel CPUs. The N subproblems constitute constrained minimization problems, where the constraint enforces the support of the minimizer to be the respective subdomain. In this paper we discuss a fast computational algorithm to solve domain decomposition for total variation minimization. In particular, we accelerate the computation of the subproblems by nested Bregman iterations. We propose a Bregmanized Operator Splitting-Split Bregman (BOS-SB) algorithm, which enforces the restriction onto the respective subdomain by a Bregman iteration that is subsequently solved by a Split Bregman strategy. The computational performance of this new approach is discussed for its application to image inpainting and image deblurring. It turns out that the proposed new solution technique is up to three times faster than the iterative algorithm currently used in domain decomposition methods for total variation minimization. © Springer Science+Business Media, LLC 2012.

  17. Domain decomposition methods for the neutron diffusion problem

    International Nuclear Information System (INIS)

    Guerin, P.; Baudron, A. M.; Lautard, J. J.

    2010-01-01

    The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (SPN) or diffusion approximations are often used. The MINOS solver developed at CEA Saclay uses a mixed dual finite element method for the resolution of these problems. and has shown his efficiency. In order to take into account the heterogeneities of the geometry, a very fine mesh is generally required, and leads to expensive calculations for industrial applications. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose here two domain decomposition methods based on the MINOS solver. The first approach is a component mode synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is an iterative method based on a non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the adjacent sub-domains estimated at the previous iteration. Numerical results on parallel computers are presented for the diffusion model on realistic 2D and 3D cores. (authors)

  18. Scalable Domain Decomposition Preconditioners for Heterogeneous Elliptic Problems

    Directory of Open Access Journals (Sweden)

    Pierre Jolivet

    2014-01-01

    Full Text Available Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.

  19. Combinatorial geometry domain decomposition strategies for Monte Carlo simulations

    Energy Technology Data Exchange (ETDEWEB)

    Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z. [Institute of Applied Physics and Computational Mathematics, Beijing, 100094 (China)

    2013-07-01

    Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)

  20. Combinatorial geometry domain decomposition strategies for Monte Carlo simulations

    International Nuclear Information System (INIS)

    Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z.

    2013-01-01

    Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)

  1. Domain decomposition and multilevel integration for fermions

    International Nuclear Information System (INIS)

    Ce, Marco; Giusti, Leonardo; Schaefer, Stefan

    2016-01-01

    The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory. We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator. This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.

  2. Focal decompositions for linear differential equations of the second order

    Directory of Open Access Journals (Sweden)

    L. Birbrair

    2003-01-01

    two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.

  3. Neutron transport solver parallelization using a Domain Decomposition method

    International Nuclear Information System (INIS)

    Van Criekingen, S.; Nataf, F.; Have, P.

    2008-01-01

    A domain decomposition (DD) method is investigated for the parallel solution of the second-order even-parity form of the time-independent Boltzmann transport equation. The spatial discretization is performed using finite elements, and the angular discretization using spherical harmonic expansions (P N method). The main idea developed here is due to P.L. Lions. It consists in having sub-domains exchanging not only interface point flux values, but also interface flux 'derivative' values. (The word 'derivative' is here used with quotes, because in the case considered here, it in fact consists in the Ω.∇ operator, with Ω the angular variable vector and ∇ the spatial gradient operator.) A parameter α is introduced, as proportionality coefficient between point flux and 'derivative' values. This parameter can be tuned - so far heuristically - to optimize the method. (authors)

  4. Domain decomposition for the computation of radiosity in lighting simulation; Decomposition de domaines pour le calcul de la radiosite en simulation d'eclairage

    Energy Technology Data Exchange (ETDEWEB)

    Salque, B

    1998-07-01

    This work deals with the equation of radiosity, this equation describes the transport of light energy through a diffuse medium, its resolution enables us to simulate the presence of light sources. The equation of radiosity is an integral equation who admits a unique solution in realistic cases. The different methods of solving are reviewed. The equation of radiosity can not be formulated as the integral form of a classical partial differential equation, but this work shows that the technique of domain decomposition can be successfully applied to the equation of radiosity if this approach is framed by considerations of physics. This method provides a system of independent equations valid for each sub-domain and whose main parameter is luminance. Some numerical examples give an idea of the convergence of the algorithm. This method is applied to the optimization of the shape of a light reflector.

  5. Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Sheng-Ping Yan

    2014-01-01

    Full Text Available We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

  6. Solution of the porous media equation by Adomian's decomposition method

    International Nuclear Information System (INIS)

    Pamuk, Serdal

    2005-01-01

    The particular exact solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer, and in biological systems are obtained using Adomian's decomposition method. Also, numerical comparison of particular solutions in the decomposition method indicate that there is a very good agreement between the numerical solutions and particular exact solutions in terms of efficiency and accuracy

  7. Analysis of generalized Schwarz alternating procedure for domain decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Engquist, B.; Zhao, Hongkai [Univ. of California, Los Angeles, CA (United States)

    1996-12-31

    The Schwartz alternating method(SAM) is the theoretical basis for domain decomposition which itself is a powerful tool both for parallel computation and for computing in complicated domains. The convergence rate of the classical SAM is very sensitive to the overlapping size between each subdomain, which is not desirable for most applications. We propose a generalized SAM procedure which is an extension of the modified SAM proposed by P.-L. Lions. Instead of using only Dirichlet data at the artificial boundary between subdomains, we take a convex combination of u and {partial_derivative}u/{partial_derivative}n, i.e. {partial_derivative}u/{partial_derivative}n + {Lambda}u, where {Lambda} is some {open_quotes}positive{close_quotes} operator. Convergence of the modified SAM without overlapping in a quite general setting has been proven by P.-L.Lions using delicate energy estimates. The important questions remain for the generalized SAM. (1) What is the most essential mechanism for convergence without overlapping? (2) Given the partial differential equation, what is the best choice for the positive operator {Lambda}? (3) In the overlapping case, is the generalized SAM superior to the classical SAM? (4) What is the convergence rate and what does it depend on? (5) Numerically can we obtain an easy to implement operator {Lambda} such that the convergence is independent of the mesh size. To analyze the convergence of the generalized SAM we focus, for simplicity, on the Poisson equation for two typical geometry in two subdomain case.

  8. A convergent overlapping domain decomposition method for total variation minimization

    KAUST Repository

    Fornasier, Massimo; Langer, Andreas; Schö nlieb, Carola-Bibiane

    2010-01-01

    In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation

  9. Domain Decomposition: A Bridge between Nature and Parallel Computers

    Science.gov (United States)

    1992-09-01

    B., "Domain Decomposition Algorithms for Indefinite Elliptic Problems," S"IAM Journal of S; cientific and Statistical (’omputing, Vol. 13, 1992, pp...AD-A256 575 NASA Contractor Report 189709 ICASE Report No. 92-44 ICASE DOMAIN DECOMPOSITION: A BRIDGE BETWEEN NATURE AND PARALLEL COMPUTERS DTIC dE...effectively implemented on dis- tributed memory multiprocessors. In 1990 (as reported in Ref. 38 using the tile algo- rithm), a 103,201-unknown 2D elliptic

  10. Large Scale Simulation of Hydrogen Dispersion by a Stabilized Balancing Domain Decomposition Method

    Directory of Open Access Journals (Sweden)

    Qing-He Yao

    2014-01-01

    Full Text Available The dispersion behaviour of leaking hydrogen in a partially open space is simulated by a balancing domain decomposition method in this work. An analogy of the Boussinesq approximation is employed to describe the connection between the flow field and the concentration field. The linear systems of Navier-Stokes equations and the convection diffusion equation are symmetrized by a pressure stabilized Lagrange-Galerkin method, and thus a balancing domain decomposition method is enabled to solve the interface problem of the domain decomposition system. Numerical results are validated by comparing with the experimental data and available numerical results. The dilution effect of ventilation is investigated, especially at the doors, where flow pattern is complicated and oscillations appear in the past research reported by other researchers. The transient behaviour of hydrogen and the process of accumulation in the partially open space are discussed, and more details are revealed by large scale computation.

  11. Langevin equations with multiplicative noise: application to domain growth

    International Nuclear Information System (INIS)

    Sancho, J.M.; Hernandez-Machado, A.; Ramirez-Piscina, L.; Lacasta, A.M.

    1993-01-01

    Langevin equations of Ginzburg-Landau form with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hilliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical productions of the linear analysis. We also present simulation results for spinodal decomposition at large times. (author). 28 refs, 2 figs

  12. B-spline Collocation with Domain Decomposition Method

    International Nuclear Information System (INIS)

    Hidayat, M I P; Parman, S; Ariwahjoedi, B

    2013-01-01

    A global B-spline collocation method has been previously developed and successfully implemented by the present authors for solving elliptic partial differential equations in arbitrary complex domains. However, the global B-spline approximation, which is simply reduced to Bezier approximation of any degree p with C 0 continuity, has led to the use of B-spline basis of high order in order to achieve high accuracy. The need for B-spline bases of high order in the global method would be more prominent in domains of large dimension. For the increased collocation points, it may also lead to the ill-conditioning problem. In this study, overlapping domain decomposition of multiplicative Schwarz algorithm is combined with the global method. Our objective is two-fold that improving the accuracy with the combination technique, and also investigating influence of the combination technique to the employed B-spline basis orders with respect to the obtained accuracy. It was shown that the combination method produced higher accuracy with the B-spline basis of much lower order than that needed in implementation of the initial method. Hence, the approximation stability of the B-spline collocation method was also increased.

  13. Mixed first- and second-order transport method using domain decomposition techniques for reactor core calculations

    International Nuclear Information System (INIS)

    Girardi, E.; Ruggieri, J.M.

    2003-01-01

    The aim of this paper is to present the last developments made on a domain decomposition method applied to reactor core calculations. In this method, two kind of balance equation with two different numerical methods dealing with two different unknowns are coupled. In the first part the two balance transport equations (first order and second order one) are presented with the corresponding following numerical methods: Variational Nodal Method and Discrete Ordinate Nodal Method. In the second part, the Multi-Method/Multi-Domain algorithm is introduced by applying the Schwarz domain decomposition to the multigroup eigenvalue problem of the transport equation. The resulting algorithm is then provided. The projection operators used to coupled the two methods are detailed in the last part of the paper. Finally some preliminary numerical applications on benchmarks are given showing encouraging results. (authors)

  14. A PARALLEL NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR STOKES PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Mei-qun Jiang; Pei-liang Dai

    2006-01-01

    A nonoverlapping domain decomposition iterative procedure is developed and analyzed for generalized Stokes problems and their finite element approximate problems in RN(N=2,3). The method is based on a mixed-type consistency condition with two parameters as a transmission condition together with a derivative-free transmission data updating technique on the artificial interfaces. The method can be applied to a general multi-subdomain decomposition and implemented on parallel machines with local simple communications naturally.

  15. Implementation of domain decomposition and data decomposition algorithms in RMC code

    International Nuclear Information System (INIS)

    Liang, J.G.; Cai, Y.; Wang, K.; She, D.

    2013-01-01

    The applications of Monte Carlo method in reactor physics analysis is somewhat restricted due to the excessive memory demand in solving large-scale problems. Memory demand in MC simulation is analyzed firstly, it concerns geometry data, data of nuclear cross-sections, data of particles, and data of tallies. It appears that tally data is dominant in memory cost and should be focused on in solving the memory problem. Domain decomposition and tally data decomposition algorithms are separately designed and implemented in the reactor Monte Carlo code RMC. Basically, the domain decomposition algorithm is a strategy of 'divide and rule', which means problems are divided into different sub-domains to be dealt with separately and some rules are established to make sure the whole results are correct. Tally data decomposition consists in 2 parts: data partition and data communication. Two algorithms with differential communication synchronization mechanisms are proposed. Numerical tests have been executed to evaluate performance of the new algorithms. Domain decomposition algorithm shows potentials to speed up MC simulation as a space parallel method. As for tally data decomposition algorithms, memory size is greatly reduced

  16. 22nd International Conference on Domain Decomposition Methods

    CERN Document Server

    Gander, Martin; Halpern, Laurence; Krause, Rolf; Pavarino, Luca

    2016-01-01

    These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures, and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.

  17. Load Estimation by Frequency Domain Decomposition

    DEFF Research Database (Denmark)

    Pedersen, Ivar Chr. Bjerg; Hansen, Søren Mosegaard; Brincker, Rune

    2007-01-01

    When performing operational modal analysis the dynamic loading is unknown, however, once the modal properties of the structure have been estimated, the transfer matrix can be obtained, and the loading can be estimated by inverse filtering. In this paper loads in frequency domain are estimated by ...

  18. Unstructured characteristic method embedded with variational nodal method using domain decomposition techniques

    Energy Technology Data Exchange (ETDEWEB)

    Girardi, E.; Ruggieri, J.M. [CEA Cadarache (DER/SPRC/LEPH), 13 - Saint-Paul-lez-Durance (France). Dept. d' Etudes des Reacteurs; Santandrea, S. [CEA Saclay, Dept. Modelisation de Systemes et Structures DM2S/SERMA/LENR, 91 - Gif sur Yvette (France)

    2005-07-01

    This paper describes a recently-developed extension of our 'Multi-methods,multi-domains' (MM-MD) method for the solution of the multigroup transport equation. Based on a domain decomposition technique, our approach allows us to treat the one-group equation by cooperatively employing several numerical methods together. In this work, we describe the coupling between the Method of Characteristics (integro-differential equation, unstructured meshes) with the Variational Nodal Method (even parity equation, cartesian meshes). Then, the coupling method is applied to the benchmark model of the Phebus experimental facility (Cea Cadarache). Our domain decomposition method give us the capability to employ a very fine mesh in describing a particular fuel bundle with an appropriate numerical method (MOC), while using a much large mesh size in the rest of the core, in conjunction with a coarse-mesh method (VNM). This application shows the benefits of our MM-MD approach, in terms of accuracy and computing time: the domain decomposition method allows us to reduce the Cpu time, while preserving a good accuracy of the neutronic indicators: reactivity, core-to-bundle power coupling coefficient and flux error. (authors)

  19. Unstructured characteristic method embedded with variational nodal method using domain decomposition techniques

    International Nuclear Information System (INIS)

    Girardi, E.; Ruggieri, J.M.

    2005-01-01

    This paper describes a recently-developed extension of our 'Multi-methods,multi-domains' (MM-MD) method for the solution of the multigroup transport equation. Based on a domain decomposition technique, our approach allows us to treat the one-group equation by cooperatively employing several numerical methods together. In this work, we describe the coupling between the Method of Characteristics (integro-differential equation, unstructured meshes) with the Variational Nodal Method (even parity equation, cartesian meshes). Then, the coupling method is applied to the benchmark model of the Phebus experimental facility (Cea Cadarache). Our domain decomposition method give us the capability to employ a very fine mesh in describing a particular fuel bundle with an appropriate numerical method (MOC), while using a much large mesh size in the rest of the core, in conjunction with a coarse-mesh method (VNM). This application shows the benefits of our MM-MD approach, in terms of accuracy and computing time: the domain decomposition method allows us to reduce the Cpu time, while preserving a good accuracy of the neutronic indicators: reactivity, core-to-bundle power coupling coefficient and flux error. (authors)

  20. A physics-motivated Centroidal Voronoi Particle domain decomposition method

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Lin, E-mail: lin.fu@tum.de; Hu, Xiangyu Y., E-mail: xiangyu.hu@tum.de; Adams, Nikolaus A., E-mail: nikolaus.adams@tum.de

    2017-04-15

    In this paper, we propose a novel domain decomposition method for large-scale simulations in continuum mechanics by merging the concepts of Centroidal Voronoi Tessellation (CVT) and Voronoi Particle dynamics (VP). The CVT is introduced to achieve a high-level compactness of the partitioning subdomains by the Lloyd algorithm which monotonically decreases the CVT energy. The number of computational elements between neighboring partitioning subdomains, which scales the communication effort for parallel simulations, is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect-ratios. Moreover, Voronoi Particle dynamics employing physical analogy with a tailored equation of state is developed, which relaxes the particle system towards the target partition with good load balance. Since the equilibrium is computed by an iterative approach, the partitioning subdomains exhibit locality and the incremental property. Numerical experiments reveal that the proposed Centroidal Voronoi Particle (CVP) based algorithm produces high-quality partitioning with high efficiency, independently of computational-element types. Thus it can be used for a wide range of applications in computational science and engineering.

  1. Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem

    International Nuclear Information System (INIS)

    Guerin, P.

    2007-12-01

    The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

  2. Domain decomposition methods for core calculations using the MINOS solver

    International Nuclear Information System (INIS)

    Guerin, P.; Baudron, A. M.; Lautard, J. J.

    2007-01-01

    Cell by cell homogenized transport calculations of an entire nuclear reactor core are currently too expensive for industrial applications, even if a simplified transport (SPn) approximation is used. In order to take advantage of parallel computers, we propose here two domain decomposition methods using the mixed dual finite element solver MINOS. The first one is a modal synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second one is an iterative method based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the close sub-domains estimated at the previous iteration. For these two methods, we give numerical results which demonstrate their accuracy and their efficiency for the diffusion model on realistic 2D and 3D cores. (authors)

  3. Statistical CT noise reduction with multiscale decomposition and penalized weighted least squares in the projection domain

    International Nuclear Information System (INIS)

    Tang Shaojie; Tang Xiangyang

    2012-01-01

    Purposes: The suppression of noise in x-ray computed tomography (CT) imaging is of clinical relevance for diagnostic image quality and the potential for radiation dose saving. Toward this purpose, statistical noise reduction methods in either the image or projection domain have been proposed, which employ a multiscale decomposition to enhance the performance of noise suppression while maintaining image sharpness. Recognizing the advantages of noise suppression in the projection domain, the authors propose a projection domain multiscale penalized weighted least squares (PWLS) method, in which the angular sampling rate is explicitly taken into consideration to account for the possible variation of interview sampling rate in advanced clinical or preclinical applications. Methods: The projection domain multiscale PWLS method is derived by converting an isotropic diffusion partial differential equation in the image domain into the projection domain, wherein a multiscale decomposition is carried out. With adoption of the Markov random field or soft thresholding objective function, the projection domain multiscale PWLS method deals with noise at each scale. To compensate for the degradation in image sharpness caused by the projection domain multiscale PWLS method, an edge enhancement is carried out following the noise reduction. The performance of the proposed method is experimentally evaluated and verified using the projection data simulated by computer and acquired by a CT scanner. Results: The preliminary results show that the proposed projection domain multiscale PWLS method outperforms the projection domain single-scale PWLS method and the image domain multiscale anisotropic diffusion method in noise reduction. In addition, the proposed method can preserve image sharpness very well while the occurrence of “salt-and-pepper” noise and mosaic artifacts can be avoided. Conclusions: Since the interview sampling rate is taken into account in the projection domain

  4. Representation of discrete Steklov-Poincare operator arising in domain decomposition methods in wavelet basis

    Energy Technology Data Exchange (ETDEWEB)

    Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)

    1996-12-31

    This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.

  5. On fictitious domain formulations for Maxwell's equations

    DEFF Research Database (Denmark)

    Dahmen, W.; Jensen, Torben Klint; Urban, K.

    2003-01-01

    We consider fictitious domain-Lagrange multiplier formulations for variational problems in the space H(curl: Omega) derived from Maxwell's equations. Boundary conditions and the divergence constraint are imposed weakly by using Lagrange multipliers. Both the time dependent and time harmonic formu...

  6. A 3D domain decomposition approach for the identification of spatially varying elastic material parameters

    KAUST Repository

    Moussawi, Ali

    2015-02-24

    Summary: The post-treatment of (3D) displacement fields for the identification of spatially varying elastic material parameters is a large inverse problem that remains out of reach for massive 3D structures. We explore here the potential of the constitutive compatibility method for tackling such an inverse problem, provided an appropriate domain decomposition technique is introduced. In the method described here, the statically admissible stress field that can be related through the known constitutive symmetry to the kinematic observations is sought through minimization of an objective function, which measures the violation of constitutive compatibility. After this stress reconstruction, the local material parameters are identified with the given kinematic observations using the constitutive equation. Here, we first adapt this method to solve 3D identification problems and then implement it within a domain decomposition framework which allows for reduced computational load when handling larger problems.

  7. Europlexus: a domain decomposition method in explicit dynamics

    International Nuclear Information System (INIS)

    Faucher, V.; Hariddh, Bung; Combescure, A.

    2003-01-01

    Explicit time integration methods are used in structural dynamics to simulate fast transient phenomena, such as impacts or explosions. A very fine analysis is required in the vicinity of the loading areas but extending the same method, and especially the same small time-step, to the whole structure frequently yields excessive calculation times. We thus perform a dual Schur domain decomposition, to divide the global problem into several independent ones, to which is added a reduced size interface problem, to ensure connections between sub-domains. Each sub-domain is given its own time-step and its own mesh fineness. Non-matching meshes at the interfaces are handled. An industrial example demonstrates the interest of our approach. (authors)

  8. A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Fluid Flow Problems on Triangulated Domains

    Science.gov (United States)

    Barth, Timothy J.; Chan, Tony F.; Tang, Wei-Pai

    1998-01-01

    This paper considers an algebraic preconditioning algorithm for hyperbolic-elliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of triangulation vertices which separates subdomain and interface solution unknowns. The reordering induces a natural 2 x 2 block partitioning of the discretization matrix. Exact LU factorization of this block system yields a Schur complement matrix which couples subdomains and the interface together. The remaining sections of this paper present a family of approximate techniques for both constructing and applying the Schur complement as a domain-decomposition preconditioner. The approximate Schur complement serves as an algebraic coarse space operator, thus avoiding the known difficulties associated with the direct formation of a coarse space discretization. In developing Schur complement approximations, particular attention has been given to improving sequential and parallel efficiency of implementations without significantly degrading the quality of the preconditioner. A computer code based on these developments has been tested on the IBM SP2 using MPI message passing protocol. A number of 2-D calculations are presented for both scalar advection-diffusion equations as well as the Euler equations governing compressible fluid flow to demonstrate performance of the preconditioning algorithm.

  9. Hybrid meshes and domain decomposition for the modeling of oil reservoirs; Maillages hybrides et decomposition de domaine pour la modelisation des reservoirs petroliers

    Energy Technology Data Exchange (ETDEWEB)

    Gaiffe, St

    2000-03-23

    In this thesis, we are interested in the modeling of fluid flow through porous media with 2-D and 3-D unstructured meshes, and in the use of domain decomposition methods. The behavior of flow through porous media is strongly influenced by heterogeneities: either large-scale lithological discontinuities or quite localized phenomena such as fluid flow in the neighbourhood of wells. In these two typical cases, an accurate consideration of the singularities requires the use of adapted meshes. After having shown the limits of classic meshes we present the future prospects offered by hybrid and flexible meshes. Next, we consider the generalization possibilities of the numerical schemes traditionally used in reservoir simulation and we draw two available approaches: mixed finite elements and U-finite volumes. The investigated phenomena being also characterized by different time-scales, special treatments in terms of time discretization on various parts of the domain are required. We think that the combination of domain decomposition methods with operator splitting techniques may provide a promising approach to obtain high flexibility for a local tune-steps management. Consequently, we develop a new numerical scheme for linear parabolic equations which allows to get a higher flexibility in the local space and time steps management. To conclude, a priori estimates and error estimates on the two variables of interest, namely the pressure and the velocity are proposed. (author)

  10. A TFETI domain decomposition solver for elastoplastic problems

    Czech Academy of Sciences Publication Activity Database

    Čermák, M.; Kozubek, T.; Sysala, Stanislav; Valdman, J.

    2014-01-01

    Roč. 231, č. 1 (2014), s. 634-653 ISSN 0096-3003 Institutional support: RVO:68145535 Keywords : elastoplasticity * Total FETI domain decomposition method * Finite element method * Semismooth Newton method Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014 http://ac.els-cdn.com/S0096300314000253/1-s2.0-S0096300314000253-main.pdf?_tid=33a29cf4-996a-11e3-8c5a-00000aacb360&acdnat=1392816896_4584697dc26cf934dcf590c63f0dbab7

  11. Non-linear scalable TFETI domain decomposition based contact algorithm

    Czech Academy of Sciences Publication Activity Database

    Dobiáš, Jiří; Pták, Svatopluk; Dostál, Z.; Vondrák, V.; Kozubek, T.

    2010-01-01

    Roč. 10, č. 1 (2010), s. 1-10 ISSN 1757-8981. [World Congress on Computational Mechanics/9./. Sydney, 19.07.2010 - 23.07.2010] R&D Projects: GA ČR GA101/08/0574 Institutional research plan: CEZ:AV0Z20760514 Keywords : finite element method * domain decomposition method * contact Subject RIV: BA - General Mathematics http://iopscience.iop.org/1757-899X/10/1/012161/pdf/1757-899X_10_1_012161.pdf

  12. Simplified approaches to some nonoverlapping domain decomposition methods

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Jinchao

    1996-12-31

    An attempt will be made in this talk to present various domain decomposition methods in a way that is intuitively clear and technically coherent and concise. The basic framework used for analysis is the {open_quotes}parallel subspace correction{close_quotes} or {open_quotes}additive Schwarz{close_quotes} method, and other simple technical tools include {open_quotes}local-global{close_quotes} and {open_quotes}global-local{close_quotes} techniques, the formal one is for constructing subspace preconditioner based on a preconditioner on the whole space whereas the later one for constructing preconditioner on the whole space based on a subspace preconditioner. The domain decomposition methods discussed in this talk fall into two major categories: one, based on local Dirichlet problems, is related to the {open_quotes}substructuring method{close_quotes} and the other, based on local Neumann problems, is related to the {open_quotes}Neumann-Neumann method{close_quotes} and {open_quotes}balancing method{close_quotes}. All these methods will be presented in a systematic and coherent manner and the analysis for both two and three dimensional cases are carried out simultaneously. In particular, some intimate relationship between these algorithms are observed and some new variants of the algorithms are obtained.

  13. Construct solitary solutions of discrete hybrid equation by Adomian Decomposition Method

    International Nuclear Information System (INIS)

    Wang Zhen; Zhang Hongqing

    2009-01-01

    In this paper, we apply the Adomian Decomposition Method to solving the differential-difference equations. A typical example is applied to illustrate the validity and the great potential of the Adomian Decomposition Method in solving differential-difference equation. Kink shaped solitary solution and Bell shaped solitary solution are presented. Comparisons are made between the results of the proposed method and exact solutions. The results show that the Adomian Decomposition Method is an attractive method in solving the differential-difference equations.

  14. Koopman decomposition of Burgers' equation: What can we learn?

    Science.gov (United States)

    Page, Jacob; Kerswell, Rich

    2017-11-01

    Burgers' equation is a well known 1D model of the Navier-Stokes equations and admits a selection of equilibria and travelling wave solutions. A series of Burgers' trajectories are examined with Dynamic Mode Decomposition (DMD) to probe the capability of the method to extract coherent structures from ``run-down'' simulations. The performance of the method depends critically on the choice of observable. We use the Cole-Hopf transformation to derive an observable which has linear, autonomous dynamics and for which the DMD modes overlap exactly with Koopman modes. This observable can accurately predict the flow evolution beyond the time window of the data used in the DMD, and in that sense outperforms other observables motivated by the nonlinearity in the governing equation. The linearizing observable also allows us to make informed decisions about often ambiguous choices in nonlinear problems, such as rank truncation and snapshot spacing. A number of rules of thumb for connecting DMD with the Koopman operator for nonlinear PDEs are distilled from the results. Related problems in low Reynolds number fluid turbulence are also discussed.

  15. Domain decomposition methods for flows in faulted porous media; Methodes de decomposition de domaine pour les ecoulements en milieux poreux failles

    Energy Technology Data Exchange (ETDEWEB)

    Flauraud, E.

    2004-05-01

    In this thesis, we are interested in using domain decomposition methods for solving fluid flows in faulted porous media. This study comes within the framework of sedimentary basin modeling which its aim is to predict the presence of possible oil fields in the subsoil. A sedimentary basin is regarded as a heterogeneous porous medium in which fluid flows (water, oil, gas) occur. It is often subdivided into several blocks separated by faults. These faults create discontinuities that have a tremendous effect on the fluid flow in the basin. In this work, we present two approaches to model faults from the mathematical point of view. The first approach consists in considering faults as sub-domains, in the same way as blocks but with their own geological properties. However, because of the very small width of the faults in comparison with the size of the basin, the second and new approach consists in considering faults no longer as sub-domains, but as interfaces between the blocks. A mathematical study of the two models is carried out in order to investigate the existence and the uniqueness of solutions. Then; we are interested in using domain decomposition methods for solving the previous models. The main part of this study is devoted to the design of Robin interface conditions and to the formulation of the interface problem. The Schwarz algorithm can be seen as a Jacobi method for solving the interface problem. In order to speed up the convergence, this problem can be solved by a Krylov type algorithm (BICGSTAB). We discretize the equations with a finite volume scheme, and perform extensive numerical tests to compare the different methods. (author)

  16. Parallel algorithms for nuclear reactor analysis via domain decomposition method

    International Nuclear Information System (INIS)

    Kim, Yong Hee

    1995-02-01

    In this thesis, the neutron diffusion equation in reactor physics is discretized by the finite difference method and is solved on a parallel computer network which is composed of T-800 transputers. T-800 transputer is a message-passing type MIMD (multiple instruction streams and multiple data streams) architecture. A parallel variant of Schwarz alternating procedure for overlapping subdomains is developed with domain decomposition. The thesis provides convergence analysis and improvement of the convergence of the algorithm. The convergence of the parallel Schwarz algorithms with DN(or ND), DD, NN, and mixed pseudo-boundary conditions(a weighted combination of Dirichlet and Neumann conditions) is analyzed for both continuous and discrete models in two-subdomain case and various underlying features are explored. The analysis shows that the convergence rate of the algorithm highly depends on the pseudo-boundary conditions and the theoretically best one is the mixed boundary conditions(MM conditions). Also it is shown that there may exist a significant discrepancy between continuous model analysis and discrete model analysis. In order to accelerate the convergence of the parallel Schwarz algorithm, relaxation in pseudo-boundary conditions is introduced and the convergence analysis of the algorithm for two-subdomain case is carried out. The analysis shows that under-relaxation of the pseudo-boundary conditions accelerates the convergence of the parallel Schwarz algorithm if the convergence rate without relaxation is negative, and any relaxation(under or over) decelerates convergence if the convergence rate without relaxation is positive. Numerical implementation of the parallel Schwarz algorithm on an MIMD system requires multi-level iterations: two levels for fixed source problems, three levels for eigenvalue problems. Performance of the algorithm turns out to be very sensitive to the iteration strategy. In general, multi-level iterations provide good performance when

  17. A convergent overlapping domain decomposition method for total variation minimization

    KAUST Repository

    Fornasier, Massimo

    2010-06-22

    In this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint. To our knowledge, this is the first successful attempt of addressing such a strategy for the nonlinear, nonadditive, and nonsmooth problem of total variation minimization. We provide several numerical experiments, showing the successful application of the algorithm for the restoration of 1D signals and 2D images in interpolation/inpainting problems, respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles. © 2010 Springer-Verlag.

  18. Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem; Methodes de decomposition de domaine pour la formulation mixte duale du probleme critique de la diffusion des neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Guerin, P

    2007-12-15

    The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

  19. Domain Decomposition Preconditioners for Multiscale Flows in High-Contrast Media

    KAUST Repository

    Galvis, Juan; Efendiev, Yalchin

    2010-01-01

    In this paper, we study domain decomposition preconditioners for multiscale flows in high-contrast media. We consider flow equations governed by elliptic equations in heterogeneous media with a large contrast in the coefficients. Our main goal is to develop domain decomposition preconditioners with the condition number that is independent of the contrast when there are variations within coarse regions. This is accomplished by designing coarse-scale spaces and interpolators that represent important features of the solution within each coarse region. The important features are characterized by the connectivities of high-conductivity regions. To detect these connectivities, we introduce an eigenvalue problem that automatically detects high-conductivity regions via a large gap in the spectrum. A main observation is that this eigenvalue problem has a few small, asymptotically vanishing eigenvalues. The number of these small eigenvalues is the same as the number of connected high-conductivity regions. The coarse spaces are constructed such that they span eigenfunctions corresponding to these small eigenvalues. These spaces are used within two-level additive Schwarz preconditioners as well as overlapping methods for the Schur complement to design preconditioners. We show that the condition number of the preconditioned systems is independent of the contrast. More detailed studies are performed for the case when the high-conductivity region is connected within coarse block neighborhoods. Our numerical experiments confirm the theoretical results presented in this paper. © 2010 Society for Industrial and Applied Mathematics.

  20. Simulation of two-phase flows by domain decomposition

    International Nuclear Information System (INIS)

    Dao, T.H.

    2013-01-01

    This thesis deals with numerical simulations of compressible fluid flows by implicit finite volume methods. Firstly, we studied and implemented an implicit version of the Roe scheme for compressible single-phase and two-phase flows. Thanks to Newton method for solving nonlinear systems, our schemes are conservative. Unfortunately, the resolution of nonlinear systems is very expensive. It is therefore essential to use an efficient algorithm to solve these systems. For large size matrices, we often use iterative methods whose convergence depends on the spectrum. We have studied the spectrum of the linear system and proposed a strategy, called Scaling, to improve the condition number of the matrix. Combined with the classical ILU pre-conditioner, our strategy has reduced significantly the GMRES iterations for local systems and the computation time. We also show some satisfactory results for low Mach-number flows using the implicit centered scheme. We then studied and implemented a domain decomposition method for compressible fluid flows. We have proposed a new interface variable which makes the Schur complement method easy to build and allows us to treat diffusion terms. Using GMRES iterative solver rather than Richardson for the interface system also provides a better performance compared to other methods. We can also decompose the computational domain into any number of sub-domains. Moreover, the Scaling strategy for the interface system has improved the condition number of the matrix and reduced the number of GMRES iterations. In comparison with the classical distributed computing, we have shown that our method is more robust and efficient. (author) [fr

  1. A balancing domain decomposition method by constraints for advection-diffusion problems

    Energy Technology Data Exchange (ETDEWEB)

    Tu, Xuemin; Li, Jing

    2008-12-10

    The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.

  2. Scalable domain decomposition solvers for stochastic PDEs in high performance computing

    International Nuclear Information System (INIS)

    Desai, Ajit; Pettit, Chris; Poirel, Dominique; Sarkar, Abhijit

    2017-01-01

    Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

  3. An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods

    International Nuclear Information System (INIS)

    Zhang Hongbo; Wu Hongchun; Cao Liangzhi

    2011-01-01

    Highlights: → We convert MOC into linear system solved by GMRES as an acceleration method. → We use domain decomposition method to overcome the inefficiency on large matrices. → Parallel technology is applied and a matched ray tracing system is developed. → Results show good efficiency even in large-scale and strong scattering problems. → The emphasis is that the technique is geometry-flexible. - Abstract: The method of characteristics (MOC) has great geometrical flexibility but poor computational efficiency in neutron transport calculations. The generalized minimal residual (GMRES) method, a type of Krylov subspace method, is utilized to accelerate a 2D generalized geometry characteristics solver AutoMOC. In this technique, a form of linear algebraic equation system for angular flux moments and boundary fluxes is derived to replace the conventional characteristics sweep (i.e. inner iteration) scheme, and then the GMRES method is implemented as an efficient linear system solver. This acceleration method is proved to be reliable in theory and simple for implementation. Furthermore, as introducing no restriction in geometry treatment, it is suitable for acceleration of an arbitrary geometry MOC solver. However, it is observed that the speedup decreases when the matrix becomes larger. The spatial domain decomposition method and multiprocessing parallel technology are then employed to overcome the problem. The calculation domain is partitioned into several sub-domains. For each of them, a smaller matrix is established and solved by GMRES; and the adjacent sub-domains are coupled by 'inner-edges', where the trajectory mismatches are considered adequately. Moreover, a matched ray tracing system is developed on the basis of AutoCAD, which allows a user to define the sub-domains on demand conveniently. Numerical results demonstrate that the acceleration techniques are efficient without loss of accuracy, even in the case of large-scale and strong scattering

  4. On solution of Maxwell's equations in axisymmetric domains with edges. Part I: Theoretical aspects

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    In this paper we present the basic mathematical tools for treating boundary value problems for the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges by means of partial Fourier analysis. We consider the decomposition of the classical and regularized time-harmonic three-dimensional Maxwell's equations into variational equations in the plane meridian domain of the axisymmetric domain and define suitable weighted Sobolev spaces for their treatment. The trace properties of these spaces on the rotational axis and some properties of the solutions are proved, which are important for further numerical treatment, e.g. by the finite-element method. Particularly, a priori estimates of the solutions of the reduced system are given and the asymptotic behavior of these solutions near reentrant corners of the meridian domain is explicitly described by suitable singular functions. (author)

  5. Adomian decomposition method for solving the telegraph equation in charged particle transport

    International Nuclear Information System (INIS)

    Abdou, M.A.

    2005-01-01

    In this paper, the analysis for the telegraph equation in case of isotropic small angle scattering from the Boltzmann transport equation for charged particle is presented. The Adomian decomposition is used to solve the telegraph equation. By means of MAPLE the Adomian polynomials of obtained series (ADM) solution have been calculated. The behaviour of the distribution function are shown graphically. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solution of linear and nonlinear problems

  6. Domain decomposition method of stochastic PDEs: a two-level scalable preconditioner

    International Nuclear Information System (INIS)

    Subber, Waad; Sarkar, Abhijit

    2012-01-01

    For uncertainty quantification in many practical engineering problems, the stochastic finite element method (SFEM) may be computationally challenging. In SFEM, the size of the algebraic linear system grows rapidly with the spatial mesh resolution and the order of the stochastic dimension. In this paper, we describe a non-overlapping domain decomposition method, namely the iterative substructuring method to tackle the large-scale linear system arising in the SFEM. The SFEM is based on domain decomposition in the geometric space and a polynomial chaos expansion in the probabilistic space. In particular, a two-level scalable preconditioner is proposed for the iterative solver of the interface problem for the stochastic systems. The preconditioner is equipped with a coarse problem which globally connects the subdomains both in the geometric and probabilistic spaces via their corner nodes. This coarse problem propagates the information quickly across the subdomains leading to a scalable preconditioner. For numerical illustrations, a two-dimensional stochastic elliptic partial differential equation (SPDE) with spatially varying non-Gaussian random coefficients is considered. The numerical scalability of the the preconditioner is investigated with respect to the mesh size, subdomain size, fixed problem size per subdomain and order of polynomial chaos expansion. The numerical experiments are performed on a Linux cluster using MPI and PETSc parallel libraries.

  7. Resolution of unsteady Maxwell equations with charges in non convex domains

    International Nuclear Information System (INIS)

    Garcia, Emmanuelle

    2002-01-01

    This research thesis deals with the modelling and numerical resolution of problems related to plasma physics. The interaction of charged particles (electrons and ions) with electromagnetic fields is modelled with the system of unsteady Vlasov-Maxwell coupled equations (the Vlasov system describes the transport of charged particles and the Maxwell equations describe the wave propagation). The author presents definitions related to singular domains, establishes a Helmholtz decomposition in a space of electro-magnetostatic solutions. He reports a mathematical analysis of decompositions into a regular and a singular part of general functional spaces intervening in the investigation of the Maxwell system in complex geometries. The method is then implemented for bi-dimensional domains. A last part addressed the study and the numerical resolution of three-dimensional problems

  8. Two-phase flow steam generator simulations on parallel computers using domain decomposition method

    International Nuclear Information System (INIS)

    Belliard, M.

    2003-01-01

    Within the framework of the Domain Decomposition Method (DDM), we present industrial steady state two-phase flow simulations of PWR Steam Generators (SG) using iteration-by-sub-domain methods: standard and Adaptive Dirichlet/Neumann methods (ADN). The averaged mixture balance equations are solved by a Fractional-Step algorithm, jointly with the Crank-Nicholson scheme and the Finite Element Method. The algorithm works with overlapping or non-overlapping sub-domains and with conforming or nonconforming meshing. Computations are run on PC networks or on massively parallel mainframe computers. A CEA code-linker and the PVM package are used (master-slave context). SG mock-up simulations, involving up to 32 sub-domains, highlight the efficiency (speed-up, scalability) and the robustness of the chosen approach. With the DDM, the computational problem size is easily increased to about 1,000,000 cells and the CPU time is significantly reduced. The difficulties related to industrial use are also discussed. (author)

  9. A multi-domain spectral method for time-fractional differential equations

    Science.gov (United States)

    Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

    2015-07-01

    This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

  10. Domain of composition and finite volume schemes on non-matching grids; Decomposition de domaine et schemas volumes finis sur maillages non-conformes

    Energy Technology Data Exchange (ETDEWEB)

    Saas, L.

    2004-05-01

    This Thesis deals with sedimentary basin modeling whose goal is the prediction through geological times of the localizations and appraisal of hydrocarbons quantities present in the ground. Due to the natural and evolutionary decomposition of the sedimentary basin in blocks and stratigraphic layers, domain decomposition methods are requested to simulate flows of waters and of hydrocarbons in the ground. Conservations laws are used to model the flows in the ground and form coupled partial differential equations which must be discretized by finite volume method. In this report we carry out a study on finite volume methods on non-matching grids solved by domain decomposition methods. We describe a family of finite volume schemes on non-matching grids and we prove that the associated global discretized problem is well posed. Then we give an error estimate. We give two examples of finite volume schemes on non matching grids and the corresponding theoretical results (Constant scheme and Linear scheme). Then we present the resolution of the global discretized problem by a domain decomposition method using arbitrary interface conditions (for example Robin conditions). Finally we give numerical results which validate the theoretical results and study the use of finite volume methods on non-matching grids for basin modeling. (author)

  11. Domain decomposition method for nonconforming finite element approximations of anisotropic elliptic problems on nonmatching grids

    Energy Technology Data Exchange (ETDEWEB)

    Maliassov, S.Y. [Texas A& M Univ., College Station, TX (United States)

    1996-12-31

    An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.

  12. Decomposition of a hierarchy of nonlinear evolution equations

    International Nuclear Information System (INIS)

    Geng Xianguo

    2003-01-01

    The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

  13. Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method

    Directory of Open Access Journals (Sweden)

    Shao-Hong Yan

    2014-01-01

    Full Text Available The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set.

  14. Domain decomposition techniques for boundary elements application to fluid flow

    CERN Document Server

    Brebbia, C A; Skerget, L

    2007-01-01

    The sub-domain techniques in the BEM are nowadays finding its place in the toolbox of numerical modellers, especially when dealing with complex 3D problems. We see their main application in conjunction with the classical BEM approach, which is based on a single domain, when part of the domain needs to be solved using a single domain approach, the classical BEM, and part needs to be solved using a domain approach, BEM subdomain technique. This has usually been done in the past by coupling the BEM with the FEM, however, it is much more efficient to use a combination of the BEM and a BEM sub-domain technique. The advantage arises from the simplicity of coupling the single domain and multi-domain solutions, and from the fact that only one formulation needs to be developed, rather than two separate formulations based on different techniques. There are still possibilities for improving the BEM sub-domain techniques. However, considering the increased interest and research in this approach we believe that BEM sub-do...

  15. Multiscale analysis of damage using dual and primal domain decomposition techniques

    NARCIS (Netherlands)

    Lloberas-Valls, O.; Everdij, F.P.X.; Rixen, D.J.; Simone, A.; Sluys, L.J.

    2014-01-01

    In this contribution, dual and primal domain decomposition techniques are studied for the multiscale analysis of failure in quasi-brittle materials. The multiscale strategy essentially consists in decomposing the structure into a number of nonoverlapping domains and considering a refined spatial

  16. Implicit upwind schemes for computational fluid dynamics. Solution by domain decomposition

    International Nuclear Information System (INIS)

    Clerc, S.

    1998-01-01

    In this work, the numerical simulation of fluid dynamics equations is addressed. Implicit upwind schemes of finite volume type are used for this purpose. The first part of the dissertation deals with the improvement of the computational precision in unfavourable situations. A non-conservative treatment of some source terms is studied in order to correct some shortcomings of the usual operator-splitting method. Besides, finite volume schemes based on Godunov's approach are unsuited to compute low Mach number flows. A modification of the up-winding by preconditioning is introduced to correct this defect. The second part deals with the solution of steady-state problems arising from an implicit discretization of the equations. A well-posed linearized boundary value problem is formulated. We prove the convergence of a domain decomposition algorithm of Schwartz type for this problem. This algorithm is implemented either directly, or in a Schur complement framework. Finally, another approach is proposed, which consists in decomposing the non-linear steady state problem. (author)

  17. Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

    Science.gov (United States)

    Ford, Neville J.; Connolly, Joseph A.

    2009-07-01

    We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

  18. Solution of the Burgers Equation in the Time Domain

    Directory of Open Access Journals (Sweden)

    M. Bednařík

    2002-01-01

    Full Text Available This paper deals with a theoretical description of the propagation of a finite amplitude acoustic waves. The theory based on the homogeneous Burgers equation of the second order of accuracy is presented here. This equation takes into account both nonlinear effects and dissipation. The method for solving this equation, using the well-known Cole-Hopf transformation, is presented. Two methods for numerical solution of these equations in the time domain are presented. The first is based on the simple Simpson method, which is suitable for smaller Goldberg numbers. The second uses the more advanced saddle point method, and is appropriate for large Goldberg numbers.

  19. Lattice QCD with Domain Decomposition on Intel Xeon Phi Co-Processors

    Energy Technology Data Exchange (ETDEWEB)

    Heybrock, Simon; Joo, Balint; Kalamkar, Dhiraj D; Smelyanskiy, Mikhail; Vaidyanathan, Karthikeyan; Wettig, Tilo; Dubey, Pradeep

    2014-12-01

    The gap between the cost of moving data and the cost of computing continues to grow, making it ever harder to design iterative solvers on extreme-scale architectures. This problem can be alleviated by alternative algorithms that reduce the amount of data movement. We investigate this in the context of Lattice Quantum Chromodynamics and implement such an alternative solver algorithm, based on domain decomposition, on Intel Xeon Phi co-processor (KNC) clusters. We demonstrate close-to-linear on-chip scaling to all 60 cores of the KNC. With a mix of single- and half-precision the domain-decomposition method sustains 400-500 Gflop/s per chip. Compared to an optimized KNC implementation of a standard solver [1], our full multi-node domain-decomposition solver strong-scales to more nodes and reduces the time-to-solution by a factor of 5.

  20. Modal Identification from Ambient Responses using Frequency Domain Decomposition

    DEFF Research Database (Denmark)

    Brincker, Rune; Zhang, L.; Andersen, P.

    2000-01-01

    In this paper a new frequency domain technique is introduced for the modal identification from ambient responses, ie. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical ...

  1. Modal Identification from Ambient Responses Using Frequency Domain Decomposition

    DEFF Research Database (Denmark)

    Brincker, Rune; Zhang, Lingmi; Andersen, Palle

    2000-01-01

    In this paper a new frequency domain technique is introduced for the modal identification from ambient responses, i.e. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical...

  2. Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

    International Nuclear Information System (INIS)

    Kaya, Dogan; El-Sayed, Salah M.

    2003-01-01

    In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

  3. Appling Laplace Adomian decomposition method for delay differential equations with boundary value problems

    Science.gov (United States)

    Yousef, Hamood Mohammed; Ismail, Ahmad Izani

    2017-11-01

    In this paper, Laplace Adomian decomposition method (LADM) was applied to solve Delay differential equations with Boundary Value Problems. The solution is in the form of a convergent series which is easy to compute. This approach is tested on two test problem. The findings obtained exhibit the reliability and efficiency of the proposed method.

  4. Dynamic load balancing algorithm for molecular dynamics based on Voronoi cells domain decompositions

    Energy Technology Data Exchange (ETDEWEB)

    Fattebert, J.-L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Richards, D.F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Glosli, J.N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2012-12-01

    We present a new algorithm for automatic parallel load balancing in classical molecular dynamics. It assumes a spatial domain decomposition of particles into Voronoi cells. It is a gradient method which attempts to minimize a cost function by displacing Voronoi sites associated with each processor/sub-domain along steepest descent directions. Excellent load balance has been obtained for quasi-2D and 3D practical applications, with up to 440·106 particles on 65,536 MPI tasks.

  5. On a Paneitz type equation in six dimensional domains

    International Nuclear Information System (INIS)

    Chtioui, Hichem; El Mehdi, Khalil

    2003-09-01

    In this paper, we consider the equation Δ 2 u = Ku 5 , u > 0 in Ω, u = Δu = 0 on ∂Ω, where K is a positive function and Ω is a bounded and smooth domain in R 6 . Using the theory of critical points at infinity, we give some topological conditions on K to ensure some existence results. (author)

  6. Rothe's method for parabolic equations on non-cylindrical domains

    Czech Academy of Sciences Publication Activity Database

    Dasht, J.; Engström, J.; Kufner, Alois; Persson, L.E.

    2006-01-01

    Roč. 1, č. 1 (2006), s. 59-80 ISSN 0973-2306 Institutional research plan: CEZ:AV0Z10190503 Keywords : parabolic equations * non-cylindrical domains * Rothe's method * time-discretization Subject RIV: BA - General Mathematics

  7. Time space domain decomposition methods for reactive transport - Application to CO2 geological storage

    International Nuclear Information System (INIS)

    Haeberlein, F.

    2011-01-01

    Reactive transport modelling is a basic tool to model chemical reactions and flow processes in porous media. A totally reduced multi-species reactive transport model including kinetic and equilibrium reactions is presented. A structured numerical formulation is developed and different numerical approaches are proposed. Domain decomposition methods offer the possibility to split large problems into smaller subproblems that can be treated in parallel. The class of Schwarz-type domain decomposition methods that have proved to be high-performing algorithms in many fields of applications is presented with a special emphasis on the geometrical viewpoint. Numerical issues for the realisation of geometrical domain decomposition methods and transmission conditions in the context of finite volumes are discussed. We propose and validate numerically a hybrid finite volume scheme for advection-diffusion processes that is particularly well-suited for the use in a domain decomposition context. Optimised Schwarz waveform relaxation methods are studied in detail on a theoretical and numerical level for a two species coupled reactive transport system with linear and nonlinear coupling terms. Well-posedness and convergence results are developed and the influence of the coupling term on the convergence behaviour of the Schwarz algorithm is studied. Finally, we apply a Schwarz waveform relaxation method on the presented multi-species reactive transport system. (author)

  8. Multigrid and multilevel domain decomposition for unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.; Smith, B.

    1994-12-31

    Multigrid has proven itself to be a very versatile method for the iterative solution of linear and nonlinear systems of equations arising from the discretization of PDES. In some applications, however, no natural multilevel structure of grids is available, and these must be generated as part of the solution procedure. In this presentation the authors will consider the problem of generating a multigrid algorithm when only a fine, unstructured grid is given. Their techniques generate a sequence of coarser grids by first forming an approximate maximal independent set of the vertices and then applying a Cavendish type algorithm to form the coarser triangulation. Numerical tests indicate that convergence using this approach can be as fast as standard multigrid on a structured mesh, at least in two dimensions.

  9. Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

    Science.gov (United States)

    Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu

    2018-04-01

    A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

  10. Parallel finite elements with domain decomposition and its pre-processing

    International Nuclear Information System (INIS)

    Yoshida, A.; Yagawa, G.; Hamada, S.

    1993-01-01

    This paper describes a parallel finite element analysis using a domain decomposition method, and the pre-processing for the parallel calculation. Computer simulations are about to replace experiments in various fields, and the scale of model to be simulated tends to be extremely large. On the other hand, computational environment has drastically changed in these years. Especially, parallel processing on massively parallel computers or computer networks is considered to be promising techniques. In order to achieve high efficiency on such parallel computation environment, large granularity of tasks, a well-balanced workload distribution are key issues. It is also important to reduce the cost of pre-processing in such parallel FEM. From the point of view, the authors developed the domain decomposition FEM with the automatic and dynamic task-allocation mechanism and the automatic mesh generation/domain subdivision system for it. (author)

  11. Newton-Raphson based modified Laplace Adomian decomposition method for solving quadratic Riccati differential equations

    Directory of Open Access Journals (Sweden)

    Mishra Vinod

    2016-01-01

    Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.

  12. Exterior domain problems and decomposition of tensor fields in weighted Sobolev spaces

    OpenAIRE

    Schwarz, Günter

    1996-01-01

    The Hodge decompOsition is a useful tool for tensor analysis on compact manifolds with boundary. This paper aims at generalising the decomposition to exterior domains G ⊂ IR n. Let L 2a Ω k(G) be the space weighted square integrable differential forms with weight function (1 + |χ|²)a, let d a be the weighted perturbation of the exterior derivative and δ a its adjoint. Then L 2a Ω k(G) splits into the orthogonal sum of the subspaces of the d a-exact forms with vanishi...

  13. On a Paneitz type equation in six dimensional domains

    Energy Technology Data Exchange (ETDEWEB)

    Chtioui, Hichem [Departement de Mathematiques, Faculte des Sciences de Sfax, Route Soukra, Sfax (Tunisia); El Mehdi, Khalil [Faculte des Sciences et Techniques, Universite de Nouakchott, Nouakchott (Morocco); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: khalil@univ-nkc.mr; it, elmehdik@ictp trieste

    2003-09-01

    In this paper, we consider the equation {delta}{sup 2}u = Ku{sup 5}, u > 0 in {omega}, u = {delta}u = 0 on {partial_derivative}{omega}, where K is a positive function and {omega} is a bounded and smooth domain in R{sup 6}. Using the theory of critical points at infinity, we give some topological conditions on K to ensure some existence results. (author)

  14. From aerodynamics towards aeroacoustics: a novel natural velocity decomposition for the Navier-Stokes equations

    CERN Document Server

    Morino, Luigi

    2015-01-01

    A novel formulation for the analysis of viscous incompressible and compressible aerodynamics/aeroacoustics fields is presented. The paper is primarily of a theoretical nature, and presents the transition path from aerodynamics towards aeroacoustics. The basis of the paper is a variant of the so-called natural velocity decomposition, as v = ▿φ + w, where w is obtained from its own governing equation and not from the vorticity. With the novel decomposition, the governing equation for w and the generalized Bernoulli theorem for viscous fields assume a very elegant form. Another improvement pertains to the so-called material covariant components of w: For inviscid incompressible flows, they remain constant in time; minor modifications occur when we deal with viscous flows. In addition, interesting simplifications of the formulation are presented for almost-potential flows, namely for flows that are irrotational everywhere except for thin vortex layers, such as boundary layers and wakes. It is shown that, if th...

  15. Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation

    Science.gov (United States)

    Abuasad, Salah; Hashim, Ishak

    2018-04-01

    In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.

  16. Multitasking domain decomposition fast Poisson solvers on the Cray Y-MP

    Science.gov (United States)

    Chan, Tony F.; Fatoohi, Rod A.

    1990-01-01

    The results of multitasking implementation of a domain decomposition fast Poisson solver on eight processors of the Cray Y-MP are presented. The object of this research is to study the performance of domain decomposition methods on a Cray supercomputer and to analyze the performance of different multitasking techniques using highly parallel algorithms. Two implementations of multitasking are considered: macrotasking (parallelism at the subroutine level) and microtasking (parallelism at the do-loop level). A conventional FFT-based fast Poisson solver is also multitasked. The results of different implementations are compared and analyzed. A speedup of over 7.4 on the Cray Y-MP running in a dedicated environment is achieved for all cases.

  17. Solving radiative transfer problems in highly heterogeneous media via domain decomposition and convergence acceleration techniques

    International Nuclear Information System (INIS)

    Previti, Alberto; Furfaro, Roberto; Picca, Paolo; Ganapol, Barry D.; Mostacci, Domiziano

    2011-01-01

    This paper deals with finding accurate solutions for photon transport problems in highly heterogeneous media fastly, efficiently and with modest memory resources. We propose an extended version of the analytical discrete ordinates method, coupled with domain decomposition-derived algorithms and non-linear convergence acceleration techniques. Numerical performances are evaluated using a challenging case study available in the literature. A study of accuracy versus computational time and memory requirements is reported for transport calculations that are relevant for remote sensing applications.

  18. Coupling parallel adaptive mesh refinement with a nonoverlapping domain decomposition solver

    Czech Academy of Sciences Publication Activity Database

    Kůs, Pavel; Šístek, Jakub

    2017-01-01

    Roč. 110, August (2017), s. 34-54 ISSN 0965-9978 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : adaptive mesh refinement * parallel algorithms * domain decomposition Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.000, year: 2016 http://www.sciencedirect.com/science/article/pii/S0965997816305737

  19. An additive matrix preconditioning method with application for domain decomposition and two-level matrix partitionings

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe

    2010-01-01

    Roč. 5910, - (2010), s. 76-83 ISSN 0302-9743. [International Conference on Large-Scale Scientific Computations, LSSC 2009 /7./. Sozopol, 04.06.2009-08.06.2009] R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z30860518 Keywords : additive matrix * condition number * domain decomposition Subject RIV: BA - General Mathematics www.springerlink.com

  20. Coupling parallel adaptive mesh refinement with a nonoverlapping domain decomposition solver

    Czech Academy of Sciences Publication Activity Database

    Kůs, Pavel; Šístek, Jakub

    2017-01-01

    Roč. 110, August (2017), s. 34-54 ISSN 0965-9978 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : adaptive mesh refinement * parallel algorithms * domain decomposition Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.000, year: 2016 http://www.sciencedirect.com/science/ article /pii/S0965997816305737

  1. Java-Based Coupling for Parallel Predictive-Adaptive Domain Decomposition

    Directory of Open Access Journals (Sweden)

    Cécile Germain‐Renaud

    1999-01-01

    Full Text Available Adaptive domain decomposition exemplifies the problem of integrating heterogeneous software components with intermediate coupling granularity. This paper describes an experiment where a data‐parallel (HPF client interfaces with a sequential computation server through Java. We show that seamless integration of data‐parallelism is possible, but requires most of the tools from the Java palette: Java Native Interface (JNI, Remote Method Invocation (RMI, callbacks and threads.

  2. Decomposition and Cross-Product-Based Method for Computing the Dynamic Equation of Robots

    Directory of Open Access Journals (Sweden)

    Ching-Long Shih

    2012-08-01

    Full Text Available This paper aims to demonstrate a clear relationship between Lagrange equations and Newton-Euler equations regarding computational methods for robot dynamics, from which we derive a systematic method for using either symbolic or on-line numerical computations. Based on the decomposition approach and cross-product operation, a computing method for robot dynamics can be easily developed. The advantages of this computing framework are that: it can be used for both symbolic and on-line numeric computation purposes, and it can also be applied to biped systems, as well as some simple closed-chain robot systems.

  3. Communication strategies for angular domain decomposition of transport calculations on message passing multiprocessors

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    1997-01-01

    The effect of three communication schemes for solving Arbitrarily High Order Transport (AHOT) methods of the Nodal type on parallel performance is examined via direct measurements and performance models. The target architecture in this study is Oak Ridge National Laboratory's 128 node Paragon XP/S 5 computer and the parallelization is based on the Parallel Virtual Machine (PVM) library. However, the conclusions reached can be easily generalized to a large class of message passing platforms and communication software. The three schemes considered here are: (1) PVM's global operations (broadcast and reduce) which utilizes the Paragon's native corresponding operations based on a spanning tree routing; (2) the Bucket algorithm wherein the angular domain decomposition of the mesh sweep is complemented with a spatial domain decomposition of the accumulation process of the scalar flux from the angular flux and the convergence test; (3) a distributed memory version of the Bucket algorithm that pushes the spatial domain decomposition one step farther by actually distributing the fixed source and flux iterates over the memories of the participating processes. Their conclusion is that the Bucket algorithm is the most efficient of the three if all participating processes have sufficient memories to hold the entire problem arrays. Otherwise, the third scheme becomes necessary at an additional cost to speedup and parallel efficiency that is quantifiable via the parallel performance model

  4. A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

    Science.gov (United States)

    Jokhio, G. A.; Izzuddin, B. A.

    2015-05-01

    This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

  5. Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms

    KAUST Repository

    Efendiev, Yalchin

    2012-02-22

    An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into "local" subspaces and a global "coarse" space is developed. Particular applications of this abstract framework include practically important problems in porous media applications such as: the scalar elliptic (pressure) equation and the stream function formulation of its mixed form, Stokes\\' and Brinkman\\'s equations. The constant in the corresponding abstract energy estimate is shown to be robust with respect to mesh parameters as well as the contrast, which is defined as the ratio of high and low values of the conductivity (or permeability). The derived stable decomposition allows to construct additive overlapping Schwarz iterative methods with condition numbers uniformly bounded with respect to the contrast and mesh parameters. The coarse spaces are obtained by patching together the eigenfunctions corresponding to the smallest eigenvalues of certain local problems. A detailed analysis of the abstract setting is provided. The proposed decomposition builds on a method of Galvis and Efendiev [Multiscale Model. Simul. 8 (2010) 1461-1483] developed for second order scalar elliptic problems with high contrast. Applications to the finite element discretizations of the second order elliptic problem in Galerkin and mixed formulation, the Stokes equations, and Brinkman\\'s problem are presented. A number of numerical experiments for these problems in two spatial dimensions are provided. © EDP Sciences, SMAI, 2012.

  6. Numerical integration of the Teukolsky equation in the time domain

    International Nuclear Information System (INIS)

    Pazos-Avalos, Enrique; Lousto, Carlos O.

    2005-01-01

    We present a fourth-order convergent (2+1)-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in r* and θ directions. The correct power-law tail, ∼1/t 2l+3 , for general initial data, and ∼1/t 2l+4 , for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code

  7. Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition.

    Directory of Open Access Journals (Sweden)

    Guido Polles

    Full Text Available Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available.

  8. Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method

    International Nuclear Information System (INIS)

    Song Lina; Wang Weiguo

    2010-01-01

    In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.

  9. Partial differential equation-based approach for empirical mode decomposition: application on image analysis.

    Science.gov (United States)

    Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques

    2012-09-01

    The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.

  10. Constraint propagation equations of the 3+1 decomposition of f(R) gravity

    International Nuclear Information System (INIS)

    Paschalidis, Vasileios; Shapiro, Stuart L; Halataei, Seyyed M H; Sawicki, Ignacy

    2011-01-01

    Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term (ω = 0). Using this equivalence and a 3+1 decomposition of the theory, it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (Hamiltonian and momentum) constraints. In this paper, we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.

  11. Explicit solution of Calderon preconditioned time domain integral equations

    KAUST Repository

    Ulku, Huseyin Arda

    2013-07-01

    An explicit marching on-in-time (MOT) scheme for solving Calderon-preconditioned time domain integral equations is proposed. The scheme uses Rao-Wilton-Glisson and Buffa-Christiansen functions to discretize the domain and range of the integral operators and a PE(CE)m type linear multistep to march on in time. Unlike its implicit counterpart, the proposed explicit solver requires the solution of an MOT system with a Gram matrix that is sparse and well-conditioned independent of the time step size. Numerical results demonstrate that the explicit solver maintains its accuracy and stability even when the time step size is chosen as large as that typically used by an implicit solver. © 2013 IEEE.

  12. Optimal Control Problems for Partial Differential Equations on Reticulated Domains

    CERN Document Server

    Kogut, Peter I

    2011-01-01

    In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu

  13. Solution of the isotopic depletion equation using decomposition method and analytical solution

    Energy Technology Data Exchange (ETDEWEB)

    Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear

    2011-07-01

    In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

  14. Solution of the isotopic depletion equation using decomposition method and analytical solution

    International Nuclear Information System (INIS)

    Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.

    2011-01-01

    In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

  15. Solving Hammerstein Type Integral Equation by New Discrete Adomian Decomposition Methods

    Directory of Open Access Journals (Sweden)

    Huda O. Bakodah

    2013-01-01

    Full Text Available New discrete Adomian decomposition methods are presented by using some identified Clenshaw-Curtis quadrature rules. We investigate two mixed quadrature rules one of precision five and the other of precision seven. The first rule is formed by using the Fejér second rule of precision three and Simpson rule of precision three, while the second rule is formed by using the Fejér second rule of precision five and the Boole rule of precision five. Our methods were applied to a nonlinear integral equation of the Hammerstein type and some examples are given to illustrate the validity of our methods.

  16. Using Enhanced Frequency Domain Decomposition as a Robust Technique to Harmonic Excitation in Operational Modal Analysis

    DEFF Research Database (Denmark)

    Jacobsen, Niels-Jørgen; Andersen, Palle; Brincker, Rune

    2006-01-01

    The presence of harmonic components in the measured responses is unavoidable in many applications of Operational Modal Analysis. This is especially true when measuring on mechanical structures containing rotating or reciprocating parts. This paper describes a new method based on the popular...... agreement is found and the method is proven to be an easy-to-use and robust tool for handling responses with deterministic and stochastic content....... Enhanced Frequency Domain Decomposition technique for eliminating the influence of these harmonic components in the modal parameter extraction process. For various experiments, the quality of the method is assessed and compared to the results obtained using broadband stochastic excitation forces. Good...

  17. Parallel computing of a climate model on the dawn 1000 by domain decomposition method

    Science.gov (United States)

    Bi, Xunqiang

    1997-12-01

    In this paper the parallel computing of a grid-point nine-level atmospheric general circulation model on the Dawn 1000 is introduced. The model was developed by the Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS). The Dawn 1000 is a MIMD massive parallel computer made by National Research Center for Intelligent Computer (NCIC), CAS. A two-dimensional domain decomposition method is adopted to perform the parallel computing. The potential ways to increase the speed-up ratio and exploit more resources of future massively parallel supercomputation are also discussed.

  18. Parallel performance of the angular versus spatial domain decomposition for discrete ordinates transport methods

    International Nuclear Information System (INIS)

    Fischer, J.W.; Azmy, Y.Y.

    2003-01-01

    A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of

  19. A domain decomposition method for analyzing a coupling between multiple acoustical spaces (L).

    Science.gov (United States)

    Chen, Yuehua; Jin, Guoyong; Liu, Zhigang

    2017-05-01

    This letter presents a domain decomposition method to predict the acoustic characteristics of an arbitrary enclosure made up of any number of sub-spaces. While the Lagrange multiplier technique usually has good performance for conditional extremum problems, the present method avoids involving extra coupling parameters and theoretically ensures the continuity conditions of both sound pressure and particle velocity at the coupling interface. Comparisons with the finite element results illustrate the accuracy and efficiency of the present predictions and the effect of coupling parameters between sub-spaces on the natural frequencies and mode shapes of the overall enclosure is revealed.

  20. Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2014-01-01

    Full Text Available We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

  1. Combined spatial/angular domain decomposition SN algorithms for shared memory parallel machines

    International Nuclear Information System (INIS)

    Hunter, M.A.; Haghighat, A.

    1993-01-01

    Several parallel processing algorithms on the basis of spatial and angular domain decomposition methods are developed and incorporated into a two-dimensional discrete ordinates transport theory code. These algorithms divide the spatial and angular domains into independent subdomains so that the flux calculations within each subdomain can be processed simultaneously. Two spatial parallel algorithms (Block-Jacobi, red-black), one angular parallel algorithm (η-level), and their combinations are implemented on an eight processor CRAY Y-MP. Parallel performances of the algorithms are measured using a series of fixed source RZ geometry problems. Some of the results are also compared with those executed on an IBM 3090/600J machine. (orig.)

  2. On the wave equations with memory in noncylindrical domains

    Directory of Open Access Journals (Sweden)

    Mauro de Lima Santos

    2007-10-01

    Full Text Available In this paper we prove the exponential and polynomial decays rates in the case $n > 2$, as time approaches infinity of regular solutions of the wave equations with memory $$ u_{tt}-Delta u+int^{t}_{0}g(t-sDelta u(sds=0 quad mbox{in } widehat{Q} $$ where $widehat{Q}$ is a non cylindrical domains of $mathbb{R}^{n+1}$, $(nge1$. We show that the dissipation produced by memory effect is strong enough to produce exponential decay of solution provided the relaxation function $g$ also decays exponentially. When the relaxation function decay polynomially, we show that the solution decays polynomially with the same rate. For this we introduced a new multiplier that makes an important role in the obtaining of the exponential and polynomial decays of the energy of the system. Existence, uniqueness and regularity of solutions for any $n ge 1$ are investigated. The obtained result extends known results from cylindrical to non-cylindrical domains.

  3. Domain decomposition based iterative methods for nonlinear elliptic finite element problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

    1994-12-31

    The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

  4. Singular solution of the Feller diffusion equation via a spectral decomposition

    Science.gov (United States)

    Gan, Xinjun; Waxman, David

    2015-01-01

    Feller studied a branching process and found that the distribution for this process approximately obeys a diffusion equation [W. Feller, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley and Los Angeles, 1951), pp. 227-246]. This diffusion equation and its generalizations play an important role in many scientific problems, including, physics, biology, finance, and probability theory. We work under the assumption that the fundamental solution represents a probability density and should account for all of the probability in the problem. Thus, under the circumstances where the random process can be irreversibly absorbed at the boundary, this should lead to the presence of a Dirac delta function in the fundamental solution at the boundary. However, such a feature is not present in the standard approach (Laplace transformation). Here we require that the total integrated probability is conserved. This yields a fundamental solution which, when appropriate, contains a term proportional to a Dirac delta function at the boundary. We determine the fundamental solution directly from the diffusion equation via spectral decomposition. We obtain exact expressions for the eigenfunctions, and when the fundamental solution contains a Dirac delta function at the boundary, every eigenfunction of the forward diffusion operator contains a delta function. We show how these combine to produce a weight of the delta function at the boundary which ensures the total integrated probability is conserved. The solution we present covers cases where parameters are time dependent, thereby greatly extending its applicability.

  5. Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

    KAUST Repository

    Tamellini, L.; Le Maî tre, O.; Nouy, A.

    2014-01-01

    In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.

  6. Domain decomposition method for dynamic faulting under slip-dependent friction

    International Nuclear Information System (INIS)

    Badea, Lori; Ionescu, Ioan R.; Wolf, Sylvie

    2004-01-01

    The anti-plane shearing problem on a system of finite faults under a slip-dependent friction in a linear elastic domain is considered. Using a Newmark method for the time discretization of the problem, we have obtained an elliptic variational inequality at each time step. An upper bound for the time step size, which is not a CFL condition, is deduced from the solution uniqueness criterion using the first eigenvalue of the tangent problem. Finite element form of the variational inequality is solved by a Schwarz method assuming that the inner nodes of the domain lie in one subdomain and the nodes on the fault lie in other subdomains. Two decompositions of the domain are analyzed, one made up of two subdomains and another one with three subdomains. Numerical experiments are performed to illustrate convergence for a single time step (convergence of the Schwarz algorithm, influence of the mesh size, influence of the time step), convergence in time (instability capturing, energy dissipation, optimal time step) and an application to a relevant physical problem (interacting parallel fault segments)

  7. The Poisson equation in axisymmetric domains with conical points

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2003-01-01

    This paper analyzes the application of the Fourier-finite-element method (FFEM) for the resolution of the Derichlet problem for the Poisson equation -Δu-circumflex = f-circumflex in axisymmetric domains Ω-circumflex subset of R 3 with conical points on the rotation axis. The FFEM combines the approximate Fourier method with respect to one space direction with the finite element method for the approximate calculation of the Fourier coefficients of the solution. Here, the influence of the conical points on the regularity of the Fourier coefficients of the solution is analyzed and the asymptotic behaviour of the coefficients near the conical points is described by some singularity functions and treated numerically by mesh grading in the two-dimensional meridian of Ω-circumflex. It is proved that for f-circumflex in L 2 (Ω-circumflex), the rate of convergence of the combined approximations in the Sobolev space W 2 1 (Ω-circumflex) is of the order O(h + N -1 ), where h and N represent, respectively, the parameters of the finite-element- and the Fourier-approximation, with h → 0 and n → ∞. (author)

  8. Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

    Energy Technology Data Exchange (ETDEWEB)

    Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

    2017-07-01

    In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)

  9. Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

    DEFF Research Database (Denmark)

    Ganji, D.D; Miansari, Mo; B, Ganjavi

    2008-01-01

    In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

  10. DOMAIN DECOMPOSITION FOR POROELASTICITY AND ELASTICITY WITH DG JUMPS AND MORTARS

    KAUST Repository

    GIRAULT, V.

    2011-01-01

    We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme. © 2011 World Scientific Publishing Company.

  11. A domain decomposition approach for full-field measurements based identification of local elastic parameters

    KAUST Repository

    Lubineau, Gilles

    2015-03-01

    We propose a domain decomposition formalism specifically designed for the identification of local elastic parameters based on full-field measurements. This technique is made possible by a multi-scale implementation of the constitutive compatibility method. Contrary to classical approaches, the constitutive compatibility method resolves first some eigenmodes of the stress field over the structure rather than directly trying to recover the material properties. A two steps micro/macro reconstruction of the stress field is performed: a Dirichlet identification problem is solved first over every subdomain, the macroscopic equilibrium is then ensured between the subdomains in a second step. We apply the method to large linear elastic 2D identification problems to efficiently produce estimates of the material properties at a much lower computational cost than classical approaches.

  12. Domain decomposition parallel computing for transient two-phase flow of nuclear reactors

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jae Ryong; Yoon, Han Young [KAERI, Daejeon (Korea, Republic of); Choi, Hyoung Gwon [Seoul National University, Seoul (Korea, Republic of)

    2016-05-15

    KAERI (Korea Atomic Energy Research Institute) has been developing a multi-dimensional two-phase flow code named CUPID for multi-physics and multi-scale thermal hydraulics analysis of Light water reactors (LWRs). The CUPID code has been validated against a set of conceptual problems and experimental data. In this work, the CUPID code has been parallelized based on the domain decomposition method with Message passing interface (MPI) library. For domain decomposition, the CUPID code provides both manual and automatic methods with METIS library. For the effective memory management, the Compressed sparse row (CSR) format is adopted, which is one of the methods to represent the sparse asymmetric matrix. CSR format saves only non-zero value and its position (row and column). By performing the verification for the fundamental problem set, the parallelization of the CUPID has been successfully confirmed. Since the scalability of a parallel simulation is generally known to be better for fine mesh system, three different scales of mesh system are considered: 40000 meshes for coarse mesh system, 320000 meshes for mid-size mesh system, and 2560000 meshes for fine mesh system. In the given geometry, both single- and two-phase calculations were conducted. In addition, two types of preconditioners for a matrix solver were compared: Diagonal and incomplete LU preconditioner. In terms of enhancement of the parallel performance, the OpenMP and MPI hybrid parallel computing for a pressure solver was examined. It is revealed that the scalability of hybrid calculation was enhanced for the multi-core parallel computation.

  13. Finite element analysis of multi-material models using a balancing domain decomposition method combined with the diagonal scaling preconditioner

    International Nuclear Information System (INIS)

    Ogino, Masao

    2016-01-01

    Actual problems in science and industrial applications are modeled by multi-materials and large-scale unstructured mesh, and the finite element analysis has been widely used to solve such problems on the parallel computer. However, for large-scale problems, the iterative methods for linear finite element equations suffer from slow or no convergence. Therefore, numerical methods having both robust convergence and scalable parallel efficiency are in great demand. The domain decomposition method is well known as an iterative substructuring method, and is an efficient approach for parallel finite element methods. Moreover, the balancing preconditioner achieves robust convergence. However, in case of problems consisting of very different materials, the convergence becomes bad. There are some research to solve this issue, however not suitable for cases of complex shape and composite materials. In this study, to improve convergence of the balancing preconditioner for multi-materials, a balancing preconditioner combined with the diagonal scaling preconditioner, called Scaled-BDD method, is proposed. Some numerical results are included which indicate that the proposed method has robust convergence for the number of subdomains and shows high performances compared with the original balancing preconditioner. (author)

  14. A New Efficient Algorithm for the 2D WLP-FDTD Method Based on Domain Decomposition Technique

    Directory of Open Access Journals (Sweden)

    Bo-Ao Xu

    2016-01-01

    Full Text Available This letter introduces a new efficient algorithm for the two-dimensional weighted Laguerre polynomials finite difference time-domain (WLP-FDTD method based on domain decomposition scheme. By using the domain decomposition finite difference technique, the whole computational domain is decomposed into several subdomains. The conventional WLP-FDTD and the efficient WLP-FDTD methods are, respectively, used to eliminate the splitting error and speed up the calculation in different subdomains. A joint calculation scheme is presented to reduce the amount of calculation. Through our work, the iteration is not essential to obtain the accurate results. Numerical example indicates that the efficiency and accuracy are improved compared with the efficient WLP-FDTD method.

  15. A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

    Energy Technology Data Exchange (ETDEWEB)

    Taverniers, Søren; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

    2017-02-01

    Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement of path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.

  16. Domain Decomposition strategy for pin-wise full-core Monte Carlo depletion calculation with the reactor Monte Carlo Code

    Energy Technology Data Exchange (ETDEWEB)

    Liang, Jingang; Wang, Kan; Qiu, Yishu [Dept. of Engineering Physics, LiuQing Building, Tsinghua University, Beijing (China); Chai, Xiao Ming; Qiang, Sheng Long [Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu (China)

    2016-06-15

    Because of prohibitive data storage requirements in large-scale simulations, the memory problem is an obstacle for Monte Carlo (MC) codes in accomplishing pin-wise three-dimensional (3D) full-core calculations, particularly for whole-core depletion analyses. Various kinds of data are evaluated and quantificational total memory requirements are analyzed based on the Reactor Monte Carlo (RMC) code, showing that tally data, material data, and isotope densities in depletion are three major parts of memory storage. The domain decomposition method is investigated as a means of saving memory, by dividing spatial geometry into domains that are simulated separately by parallel processors. For the validity of particle tracking during transport simulations, particles need to be communicated between domains. In consideration of efficiency, an asynchronous particle communication algorithm is designed and implemented. Furthermore, we couple the domain decomposition method with MC burnup process, under a strategy of utilizing consistent domain partition in both transport and depletion modules. A numerical test of 3D full-core burnup calculations is carried out, indicating that the RMC code, with the domain decomposition method, is capable of pin-wise full-core burnup calculations with millions of depletion regions.

  17. A difference-equation formalism for the nodal domains of separable billiards

    Energy Technology Data Exchange (ETDEWEB)

    Manjunath, Naren; Samajdar, Rhine [Indian Institute of Science, Bangalore 560012 (India); Jain, Sudhir R., E-mail: srjain@barc.gov.in [Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)

    2016-09-15

    Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

  18. A numerical method for the solution of three-dimensional incompressible viscous flow using the boundary-fitted curvilinear coordinate transformation and domain decomposition technique

    International Nuclear Information System (INIS)

    Umegaki, Kikuo; Miki, Kazuyoshi

    1990-01-01

    A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdomains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90deg elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor. (author)

  19. Hybrid and Parallel Domain-Decomposition Methods Development to Enable Monte Carlo for Reactor Analyses

    International Nuclear Information System (INIS)

    Wagner, John C.; Mosher, Scott W.; Evans, Thomas M.; Peplow, Douglas E.; Turner, John A.

    2010-01-01

    This paper describes code and methods development at the Oak Ridge National Laboratory focused on enabling high-fidelity, large-scale reactor analyses with Monte Carlo (MC). Current state-of-the-art tools and methods used to perform real commercial reactor analyses have several undesirable features, the most significant of which is the non-rigorous spatial decomposition scheme. Monte Carlo methods, which allow detailed and accurate modeling of the full geometry and are considered the gold standard for radiation transport solutions, are playing an ever-increasing role in correcting and/or verifying the deterministic, multi-level spatial decomposition methodology in current practice. However, the prohibitive computational requirements associated with obtaining fully converged, system-wide solutions restrict the role of MC to benchmarking deterministic results at a limited number of state-points for a limited number of relevant quantities. The goal of this research is to change this paradigm by enabling direct use of MC for full-core reactor analyses. The most significant of the many technical challenges that must be overcome are the slow, non-uniform convergence of system-wide MC estimates and the memory requirements associated with detailed solutions throughout a reactor (problems involving hundreds of millions of different material and tally regions due to fuel irradiation, temperature distributions, and the needs associated with multi-physics code coupling). To address these challenges, our research has focused on the development and implementation of (1) a novel hybrid deterministic/MC method for determining high-precision fluxes throughout the problem space in k-eigenvalue problems and (2) an efficient MC domain-decomposition (DD) algorithm that partitions the problem phase space onto multiple processors for massively parallel systems, with statistical uncertainty estimation. The hybrid method development is based on an extension of the FW-CADIS method, which

  20. Hybrid and parallel domain-decomposition methods development to enable Monte Carlo for reactor analyses

    International Nuclear Information System (INIS)

    Wagner, J.C.; Mosher, S.W.; Evans, T.M.; Peplow, D.E.; Turner, J.A.

    2010-01-01

    This paper describes code and methods development at the Oak Ridge National Laboratory focused on enabling high-fidelity, large-scale reactor analyses with Monte Carlo (MC). Current state-of-the-art tools and methods used to perform 'real' commercial reactor analyses have several undesirable features, the most significant of which is the non-rigorous spatial decomposition scheme. Monte Carlo methods, which allow detailed and accurate modeling of the full geometry and are considered the 'gold standard' for radiation transport solutions, are playing an ever-increasing role in correcting and/or verifying the deterministic, multi-level spatial decomposition methodology in current practice. However, the prohibitive computational requirements associated with obtaining fully converged, system-wide solutions restrict the role of MC to benchmarking deterministic results at a limited number of state-points for a limited number of relevant quantities. The goal of this research is to change this paradigm by enabling direct use of MC for full-core reactor analyses. The most significant of the many technical challenges that must be overcome are the slow, non-uniform convergence of system-wide MC estimates and the memory requirements associated with detailed solutions throughout a reactor (problems involving hundreds of millions of different material and tally regions due to fuel irradiation, temperature distributions, and the needs associated with multi-physics code coupling). To address these challenges, our research has focused on the development and implementation of (1) a novel hybrid deterministic/MC method for determining high-precision fluxes throughout the problem space in k-eigenvalue problems and (2) an efficient MC domain-decomposition (DD) algorithm that partitions the problem phase space onto multiple processors for massively parallel systems, with statistical uncertainty estimation. The hybrid method development is based on an extension of the FW-CADIS method

  1. A solution of nonlinear equation for the gravity wave spectra from Adomian decomposition method: a first approach

    Directory of Open Access Journals (Sweden)

    Antonio Gledson Goulart

    2013-12-01

    Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.

  2. Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

    KAUST Repository

    Wang, T.

    2017-05-26

    Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.

  3. Low-order modelling of shallow water equations for sensitivity analysis using proper orthogonal decomposition

    Science.gov (United States)

    Zokagoa, Jean-Marie; Soulaïmani, Azzeddine

    2012-06-01

    This article presents a reduced-order model (ROM) of the shallow water equations (SWEs) for use in sensitivity analyses and Monte-Carlo type applications. Since, in the real world, some of the physical parameters and initial conditions embedded in free-surface flow problems are difficult to calibrate accurately in practice, the results from numerical hydraulic models are almost always corrupted with uncertainties. The main objective of this work is to derive a ROM that ensures appreciable accuracy and a considerable acceleration in the calculations so that it can be used as a surrogate model for stochastic and sensitivity analyses in real free-surface flow problems. The ROM is derived using the proper orthogonal decomposition (POD) method coupled with Galerkin projections of the SWEs, which are discretised through a finite-volume method. The main difficulty of deriving an efficient ROM is the treatment of the nonlinearities involved in SWEs. Suitable approximations that provide rapid online computations of the nonlinear terms are proposed. The proposed ROM is applied to the simulation of hypothetical flood flows in the Bordeaux breakwater, a portion of the 'Rivière des Prairies' located near Laval (a suburb of Montreal, Quebec). A series of sensitivity analyses are performed by varying the Manning roughness coefficient and the inflow discharge. The results are satisfactorily compared to those obtained by the full-order finite volume model.

  4. A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

    Science.gov (United States)

    Pioldi, Fabio; Rizzi, Egidio

    2017-07-01

    Output-only structural identification is developed by a refined Frequency Domain Decomposition ( rFDD) approach, towards assessing current modal properties of heavy-damped buildings (in terms of identification challenge), under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type II bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames (with variable structural features) are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 "Far-Field" (22 NS, 22 WE) earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.

  5. Analysis of spinodal decomposition in Fe-32 and 40 at.% Cr alloys using phase field method based on linear and nonlinear Cahn-Hilliard equations

    Directory of Open Access Journals (Sweden)

    Orlando Soriano-Vargas

    2016-12-01

    Full Text Available Spinodal decomposition was studied during aging of Fe-Cr alloys by means of the numerical solution of the linear and nonlinear Cahn-Hilliard differential partial equations using the explicit finite difference method. Results of the numerical simulation permitted to describe appropriately the mechanism, morphology and kinetics of phase decomposition during the isothermal aging of these alloys. The growth kinetics of phase decomposition was observed to occur very slowly during the early stages of aging and it increased considerably as the aging progressed. The nonlinear equation was observed to be more suitable for describing the early stages of spinodal decomposition than the linear one.

  6. Solving the Schroedinger equation using the finite difference time domain method

    International Nuclear Information System (INIS)

    Sudiarta, I Wayan; Geldart, D J Wallace

    2007-01-01

    In this paper, we solve the Schroedinger equation using the finite difference time domain (FDTD) method to determine energies and eigenfunctions. In order to apply the FDTD method, the Schroedinger equation is first transformed into a diffusion equation by the imaginary time transformation. The resulting time-domain diffusion equation is then solved numerically by the FDTD method. The theory and an algorithm are provided for the procedure. Numerical results are given for illustrative examples in one, two and three dimensions. It is shown that the FDTD method accurately determines eigenfunctions and energies of these systems

  7. Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

    Science.gov (United States)

    Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

    2018-04-01

    The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional

  8. A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas

    International Nuclear Information System (INIS)

    Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.

    2013-01-01

    Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of the wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods

  9. On the mixed discretization of the time domain magnetic field integral equation

    KAUST Repository

    Ulku, Huseyin Arda; Bogaert, Ignace; Cools, Kristof; Andriulli, Francesco P.; Bagci, Hakan

    2012-01-01

    Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed

  10. Time-domain single-source integral equations for analyzing scattering from homogeneous penetrable objects

    KAUST Repository

    Valdé s, Felipe; Andriulli, Francesco P.; Bagci, Hakan; Michielssen, Eric

    2013-01-01

    Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis

  11. Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain.

    Science.gov (United States)

    Liu, Jinghuai; Zhang, Litao

    2016-01-01

    In this paper, we investigate the existence of anti-periodic (or anti-periodic differentiable) mild solutions to the semilinear differential equation [Formula: see text] with nondense domain. Furthermore, an example is given to illustrate our results.

  12. Almost Automorphic and Pseudo-Almost Automorphic Solutions to Semilinear Evolution Equations with Nondense Domain

    Directory of Open Access Journals (Sweden)

    Bruno de Andrade

    2009-01-01

    Full Text Available We study the existence and uniqueness of almost automorphic (resp., pseudo-almost automorphic solutions to a first-order differential equation with linear part dominated by a Hille-Yosida type operator with nondense domain.

  13. Deformation from symmetry for Schrodinger equations of higher order on unbounded domains

    Directory of Open Access Journals (Sweden)

    Addolorata Salvatore

    2003-06-01

    Full Text Available By means of a perturbation method recently introduced by Bolle, we discuss the existence of infinitely many solutions for a class of perturbed symmetric higher order Schrodinger equations with non-homogeneous boundary data on unbounded domains.

  14. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong; Schuster, Gerard T.; Luo, Yi

    2012-01-01

    way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity

  15. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

    KAUST Repository

    Bessaih, Hakima; Efendiev, Yalchin; Maris, Florin

    2015-01-01

    The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior

  16. On the initial condition problem of the time domain PMCHWT surface integral equation

    KAUST Repository

    Uysal, Ismail Enes; Bagci, Hakan; Ergin, A. Arif; Ulku, H. Arda

    2017-01-01

    Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced

  17. The Navier-Stokes equations on a bounded domain

    International Nuclear Information System (INIS)

    Scheffer, V.

    1980-01-01

    Suppose U is an open bounded subset of 3-space such that the boundary of U has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solution u to the time dependent Navier-Stokes equations of incompressible fluid flow in U such that the curl of u is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite. (orig.)

  18. Numerical solutions of ordinary and partial differential equations in the frequency domain

    International Nuclear Information System (INIS)

    Hazi, G.; Por, G.

    1997-01-01

    Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

  19. BOUNDARY VALUE PROBLEM FOR A LOADED EQUATION ELLIPTIC-HYPERBOLIC TYPE IN A DOUBLY CONNECTED DOMAIN

    Directory of Open Access Journals (Sweden)

    O.Kh. Abdullaev

    2014-06-01

    Full Text Available We study the existence and uniqueness of the solution of one boundary value problem for the loaded elliptic-hyperbolic equation of the second order with two lines of change of type in double-connected domain. Similar results have been received by D.M.Kuryhazov, when investigated domain is one-connected.

  20. Diffusion phenomenon for linear dissipative wave equations in an exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  1. The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains

    Czech Academy of Sciences Publication Activity Database

    Medková, Dagmar

    2009-01-01

    Roč. 63, č. 21 (2009), s. 227-247 ISSN 0378-620X Institutional research plan: CEZ:AV0Z10190503 Keywords : Poisson equation * Neumann problem * integral equation method Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2009

  2. Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms

    KAUST Repository

    Efendiev, Yalchin; Galvis, Juan; Lazarov, Raytcho; Willems, Joerg

    2012-01-01

    An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into "local" subspaces and a global "coarse" space is developed. Particular applications of this abstract

  3. Homogenization of the evolution Stokes equation in a perforated domain with a stochastic Fourier boundary condition

    KAUST Repository

    Bessaih, Hakima

    2015-04-01

    The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.

  4. Partial Fourier analysis of time-harmonic Maxwell's equations in axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-01-01

    We analyze the Fourier method for treating time-harmonic Maxwell's equations in three-dimensional axisymmetric domains with non-axisymmetric data. The Fourier method reduces the three-dimensional boundary value problem to a system of decoupled two-dimensional boundary value problems on the plane meridian domain of the axisymmetric domain. The reduction process is fully described and suitable weighted spaces are introduced on the meridian domain to characterize the two-dimensional solutions. In particular, existence and uniqueness of solutions of the two-dimensional problems is proved and a priori estimates for the solutions are given. (author)

  5. Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media

    DEFF Research Database (Denmark)

    Guo, Hairun; Zeng, Xianglong; Zhou, Binbin

    2013-01-01

    We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...

  6. Ordinary differential equations introduction to the theory of ordinary differential equations in the real domain

    CERN Document Server

    Kurzweil, J

    1986-01-01

    The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Car

  7. Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

    Science.gov (United States)

    Eu, Byung Chan

    2008-09-07

    In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

  8. Stable multi-domain spectral penalty methods for fractional partial differential equations

    Science.gov (United States)

    Xu, Qinwu; Hesthaven, Jan S.

    2014-01-01

    We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

  9. On solution of Maxwell's equations in axisymmetric domains with edges. Part II: Numerical aspects

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    In this paper we consider the Fourier-finite-element method for treating the Maxwell's equations in three-dimensional axisymmetric domains with reentrant edges. By means of partial Fourier analysis, the 3D BVP is decomposed into an infinite sequence of 2D variational equations in the plane meridian domain of the axisymmetric domain, a finite number of which is considered and treated using nodal H 1 -conforming finite elements. For domains with reentrant edges, the singular field method is employed to compensate the singular behavior of the solutions. Emphases are given to estimates of the Fourier-finite-element approximation error and convergence analysis in the H 1 -norm under different regularity assumptions. (author)

  10. High-Order Calderón Preconditioned Time Domain Integral Equation Solvers

    KAUST Repository

    Valdes, Felipe

    2013-05-01

    Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.

  11. High-Order Calderón Preconditioned Time Domain Integral Equation Solvers

    KAUST Repository

    Valdes, Felipe; Ghaffari-Miab, Mohsen; Andriulli, Francesco P.; Cools, Kristof; Michielssen,

    2013-01-01

    Two high-order accurate Calderón preconditioned time domain electric field integral equation (TDEFIE) solvers are presented. In contrast to existing Calderón preconditioned time domain solvers, the proposed preconditioner allows for high-order surface representations and current expansions by using a novel set of fully-localized high-order div-and quasi curl-conforming (DQCC) basis functions. Numerical results demonstrate that the linear systems of equations obtained using the proposed basis functions converge rapidly, regardless of the mesh density and of the order of the current expansion. © 1963-2012 IEEE.

  12. Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries

    International Nuclear Information System (INIS)

    Karimov, Ruslan Kh; Kozhevnikova, Larisa M

    2010-01-01

    The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain D=(0,∞)xΩ. Upper bounds are obtained, which give the rate of decay of the solutions as t→∞ as a function of the geometry of the unbounded domain Ω subset of R n , n≥2. Bibliography: 18 titles.

  13. A Generalized FDM for solving the Poisson's Equation on 3D Irregular Domains

    Directory of Open Access Journals (Sweden)

    J. Izadian

    2014-01-01

    Full Text Available In this paper a new method for solving the Poisson's equation with Dirichlet conditions on irregular domains is presented. For this purpose a generalized finite differences method is applied for numerical differentiation on irregular meshes. Three examples on cylindrical and spherical domains are considered. The numerical results are compared with analytical solution. These results show the performance and efficiency of the proposed method.

  14. Finite difference method and algebraic polynomial interpolation for numerically solving Poisson's equation over arbitrary domains

    Directory of Open Access Journals (Sweden)

    Tsugio Fukuchi

    2014-06-01

    Full Text Available The finite difference method (FDM based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.

  15. Image Watermarking Algorithm Based on Multiobjective Ant Colony Optimization and Singular Value Decomposition in Wavelet Domain

    Directory of Open Access Journals (Sweden)

    Khaled Loukhaoukha

    2013-01-01

    Full Text Available We present a new optimal watermarking scheme based on discrete wavelet transform (DWT and singular value decomposition (SVD using multiobjective ant colony optimization (MOACO. A binary watermark is decomposed using a singular value decomposition. Then, the singular values are embedded in a detailed subband of host image. The trade-off between watermark transparency and robustness is controlled by multiple scaling factors (MSFs instead of a single scaling factor (SSF. Determining the optimal values of the multiple scaling factors (MSFs is a difficult problem. However, a multiobjective ant colony optimization is used to determine these values. Experimental results show much improved performances of the proposed scheme in terms of transparency and robustness compared to other watermarking schemes. Furthermore, it does not suffer from the problem of high probability of false positive detection of the watermarks.

  16. Some nonlinear space decomposition algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)

    1996-12-31

    Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

  17. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  18. Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

    KAUST Repository

    Bonito, Andrea

    2013-12-01

    This note establishes regularity estimates for the solution of the Maxwell equations in Lipschitz domains with non-smooth coefficients and minimal regularity assumptions. The argumentation relies on elliptic regularity estimates for the Poisson problem with non-smooth coefficients. © 2013 Elsevier Ltd.

  19. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  20. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2Japon. 55 (2002) 33) plays an effective role.

  1. Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

    Science.gov (United States)

    Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

    2011-10-01

    This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

  2. Continuous and Lp estimates for the complex Monge-Ampère equation on bounded domains in ℂn

    Directory of Open Access Journals (Sweden)

    Patrick W. Darko

    2002-01-01

    Full Text Available Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.

  3. A Fourth Order Accurate Discretization for the Laplace and Heat Equations on Arbitrary Domains, with Applications to the Stefan Problem

    National Research Council Canada - National Science Library

    Gibou, Frederic; Fedkiw, Ronald

    2004-01-01

    In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains...

  4. Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

    Directory of Open Access Journals (Sweden)

    Weam Alharbi

    2018-04-01

    Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.

  5. An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders

    DEFF Research Database (Denmark)

    Paulsen, Bo Terp; Bredmose, Henrik; Bingham, Harry B.

    2014-01-01

    A fully nonlinear domain decomposed solver is proposed for efficient computations of wave loads on surface piercing structures in the time domain. A fully nonlinear potential flow solver was combined with a fully nonlinear Navier–Stokes/VOF solver via generalized coupling zones of arbitrary shape....... Sensitivity tests of the extent of the inner Navier–Stokes/VOF domain were carried out. Numerical computations of wave loads on surface piercing circular cylinders at intermediate water depths are presented. Four different test cases of increasing complexity were considered; 1) weakly nonlinear regular waves...

  6. A Temporal Domain Decomposition Algorithmic Scheme for Large-Scale Dynamic Traffic Assignment

    Directory of Open Access Journals (Sweden)

    Eric J. Nava

    2012-03-01

    This paper presents a temporal decomposition scheme for large spatial- and temporal-scale dynamic traffic assignment, in which the entire analysis period is divided into Epochs. Vehicle assignment is performed sequentially in each Epoch, thus improving the model scalability and confining the peak run-time memory requirement regardless of the total analysis period. A proposed self-turning scheme adaptively searches for the run-time-optimal Epoch setting during iterations regardless of the characteristics of the modeled network. Extensive numerical experiments confirm the promising performance of the proposed algorithmic schemes.

  7. Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

    Science.gov (United States)

    Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemí

    2012-08-01

    The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J* u- u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on {R^NsetminusΩ} . When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.

  8. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

    Science.gov (United States)

    Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

  9. A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

    Science.gov (United States)

    Benhammouda, Brahim

    2016-01-01

    Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

  10. Symbolic computation on integrable decompositions for the cylindrical Kadomtsev-Petviashvili equation from dusty plasmas and Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Li Juan; Xu Tao; Zhang Haiqiang; Gao Yitian; Tian Bo

    2008-01-01

    In this paper, the cylindrical Kadomtsev-Petviashvili (KP) equation arising from dusty plasmas and Bose-Einstein condensates is investigated by the decomposition method. Through the nonlinearization of a single Lax pair, this equation is decomposed into a generalized variable-coefficient Burgers equation and its third-order extension, and then a series of analytic soliton-like solutions are obtained. Furthermore, with the aid of symbolic computation, a symmetry potential constraint in terms of the squared eigenfunctions is proposed to nonlinearize two symmetry Lax pairs into the first two variable-coefficient 2N-coupled soliton systems in the same hierarchy. Based on the Lax representation for these two decomposed soliton systems, a Darboux transformation is constructed to iteratively generate the multi-soliton-like solutions. Via the obtained analytic soliton-like solutions, the graphical analysis is devoted to the one-parabola soliton structure, compressive and rarefactive soliton resonance phenomena occurring in dusty plasmas and Bose-Einstein condensates

  11. Retarded potentials and time domain boundary integral equations a road map

    CERN Document Server

    Sayas, Francisco-Javier

    2016-01-01

    This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...

  12. Planar ESPAR Array Design with Nonsymmetrical Pattern by Means of Finite-Element Method, Domain Decomposition, and Spherical Wave Expansion

    Directory of Open Access Journals (Sweden)

    Jesús García

    2012-01-01

    Full Text Available The application of a 3D domain decomposition finite-element and spherical mode expansion for the design of planar ESPAR (electronically steerable passive array radiator made with probe-fed circular microstrip patches is presented in this work. A global generalized scattering matrix (GSM in terms of spherical modes is obtained analytically from the GSM of the isolated patches by using rotation and translation properties of spherical waves. The whole behaviour of the array is characterized including all the mutual coupling effects between its elements. This procedure has been firstly validated by analyzing an array of monopoles on a ground plane, and then it has been applied to synthesize a prescribed radiation pattern optimizing the reactive loads connected to the feeding ports of the array of circular patches by means of a genetic algorithm.

  13. Enhancements to the Combinatorial Geometry Particle Tracker in the Mercury Monte Carlo Transport Code: Embedded Meshes and Domain Decomposition

    International Nuclear Information System (INIS)

    Greenman, G.M.; O'Brien, M.J.; Procassini, R.J.; Joy, K.I.

    2009-01-01

    Two enhancements to the combinatorial geometry (CG) particle tracker in the Mercury Monte Carlo transport code are presented. The first enhancement is a hybrid particle tracker wherein a mesh region is embedded within a CG region. This method permits efficient calculations of problems with contain both large-scale heterogeneous and homogeneous regions. The second enhancement relates to the addition of parallelism within the CG tracker via spatial domain decomposition. This permits calculations of problems with a large degree of geometric complexity, which are not possible through particle parallelism alone. In this method, the cells are decomposed across processors and a particles is communicated to an adjacent processor when it tracks to an interprocessor boundary. Applications that demonstrate the efficacy of these new methods are presented

  14. Modal Identification of Output-Only Systems using Frequency Domain Decomposition

    DEFF Research Database (Denmark)

    Brincker, Rune; Zhang, L.; Andersen, P.

    2000-01-01

    In this paper a new frequency domain technique is introduced for the modal identification from ambient responses, ie. in the case where the modal parameters must be estimated without knowing the input exciting the system. By its user friendliness the technique is closely related to the classical ...

  15. Application of multi-thread computing and domain decomposition to the 3-D neutronics Fem code Cronos

    International Nuclear Information System (INIS)

    Ragusa, J.C.

    2003-01-01

    The purpose of this paper is to present the parallelization of the flux solver and the isotopic depletion module of the code, either using Message Passing Interface (MPI) or OpenMP. Thread parallelism using OpenMP was used to parallelize the mixed dual FEM (finite element method) flux solver MINOS. Investigations regarding the opportunity of mixing parallelism paradigms will be discussed. The isotopic depletion module was parallelized using domain decomposition and MPI. An attempt at using OpenMP was unsuccessful and will be explained. This paper is organized as follows: the first section recalls the different types of parallelism. The mixed dual flux solver and its parallelization are then presented. In the third section, we describe the isotopic depletion solver and its parallelization; and finally conclude with some future perspectives. Parallel applications are mandatory for fine mesh 3-dimensional transport and simplified transport multigroup calculations. The MINOS solver of the FEM neutronics code CRONOS2 was parallelized using the directive based standard OpenMP. An efficiency of 80% (resp. 60%) was achieved with 2 (resp. 4) threads. Parallelization of the isotopic depletion solver was obtained using domain decomposition principles and MPI. Efficiencies greater than 90% were reached. These parallel implementations were tested on a shared memory symmetric multiprocessor (SMP) cluster machine. The OpenMP implementation in the solver MINOS is only the first step towards fully using the SMPs cluster potential with a mixed mode parallelism. Mixed mode parallelism can be achieved by combining message passing interface between clusters with OpenMP implicit parallelism within a cluster

  16. Application of multi-thread computing and domain decomposition to the 3-D neutronics Fem code Cronos

    Energy Technology Data Exchange (ETDEWEB)

    Ragusa, J.C. [CEA Saclay, Direction de l' Energie Nucleaire, Service d' Etudes des Reacteurs et de Modelisations Avancees (DEN/SERMA), 91 - Gif sur Yvette (France)

    2003-07-01

    The purpose of this paper is to present the parallelization of the flux solver and the isotopic depletion module of the code, either using Message Passing Interface (MPI) or OpenMP. Thread parallelism using OpenMP was used to parallelize the mixed dual FEM (finite element method) flux solver MINOS. Investigations regarding the opportunity of mixing parallelism paradigms will be discussed. The isotopic depletion module was parallelized using domain decomposition and MPI. An attempt at using OpenMP was unsuccessful and will be explained. This paper is organized as follows: the first section recalls the different types of parallelism. The mixed dual flux solver and its parallelization are then presented. In the third section, we describe the isotopic depletion solver and its parallelization; and finally conclude with some future perspectives. Parallel applications are mandatory for fine mesh 3-dimensional transport and simplified transport multigroup calculations. The MINOS solver of the FEM neutronics code CRONOS2 was parallelized using the directive based standard OpenMP. An efficiency of 80% (resp. 60%) was achieved with 2 (resp. 4) threads. Parallelization of the isotopic depletion solver was obtained using domain decomposition principles and MPI. Efficiencies greater than 90% were reached. These parallel implementations were tested on a shared memory symmetric multiprocessor (SMP) cluster machine. The OpenMP implementation in the solver MINOS is only the first step towards fully using the SMPs cluster potential with a mixed mode parallelism. Mixed mode parallelism can be achieved by combining message passing interface between clusters with OpenMP implicit parallelism within a cluster.

  17. Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

    OpenAIRE

    Cortazar, C.; Elgueta, M.; Quiros, F.; Wolanski, N.

    2011-01-01

    The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\\mathbb{R}^N\\setminus\\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves...

  18. Perfectly Matched Layer for the Wave Equation Finite Difference Time Domain Method

    Science.gov (United States)

    Miyazaki, Yutaka; Tsuchiya, Takao

    2012-07-01

    The perfectly matched layer (PML) is introduced into the wave equation finite difference time domain (WE-FDTD) method. The WE-FDTD method is a finite difference method in which the wave equation is directly discretized on the basis of the central differences. The required memory of the WE-FDTD method is less than that of the standard FDTD method because no particle velocity is stored in the memory. In this study, the WE-FDTD method is first combined with the standard FDTD method. Then, Berenger's PML is combined with the WE-FDTD method. Some numerical demonstrations are given for the two- and three-dimensional sound fields.

  19. Matrix equation decomposition and parallel solution of systems resulting from unstructured finite element problems in electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)

    1996-12-31

    Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.

  20. A boundary value problem for a third order hyperbolic equation with degeneration of order inside the domain

    Directory of Open Access Journals (Sweden)

    Ruzanna Kh. Makaova

    2017-12-01

    Full Text Available In this paper we study the boundary value problem for a degenerating third order equation of hyperbolic type in a mixed domain. The equation under consideration in the positive part of the domain coincides with the Hallaire equation, which is a pseudoparabolic type equation. Moreover, in the negative part of the domain it coincides with a degenerating hyperbolic equation of the first kind, the particular case of the Bitsadze–Lykov equation. The existence and uniqueness theorem for the solution is proved. The uniqueness of the solution to the problem is proved with the Tricomi method. Using the functional relationships of the positive and negative parts of the domain on the degeneration line, we arrive at the convolution type Volterra integral equation of the 2nd kind with respect to the desired solution by a derivative trace. With the Laplace transform method, we obtain the solution of the integral equation in its explicit form. At last, the solution to the problem under study is written out explicitly as the solution of the second boundary-value problem in the positive part of the domain for the Hallaire equation and as the solution to the Cauchy problem in the negative part of the domain for a degenerate hyperbolic equation of the first kind.

  1. Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

    Energy Technology Data Exchange (ETDEWEB)

    Petersson, N. Anders; Sjögreen, Björn

    2014-10-01

    Abstract

    We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more

  2. Integral equation approach to time-dependent kinematic dynamos in finite domains

    International Nuclear Information System (INIS)

    Xu Mingtian; Stefani, Frank; Gerbeth, Gunter

    2004-01-01

    The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α 2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples - the α 2 dynamo model with radially varying α and the Bullard-Gellman model - illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α 2 dynamo in rectangular domains

  3. On the initial condition problem of the time domain PMCHWT surface integral equation

    KAUST Repository

    Uysal, Ismail Enes

    2017-05-13

    Non-physical, linearly increasing and constant current components are induced in marching on-in-time solution of time domain surface integral equations when initial conditions on time derivatives of (unknown) equivalent currents are not enforced properly. This problem can be remedied by solving the time integral of the surface integral for auxiliary currents that are defined to be the time derivatives of the equivalent currents. Then the equivalent currents are obtained by numerically differentiating the auxiliary ones. In this work, this approach is applied to the marching on-in-time solution of the time domain Poggio-Miller-Chan-Harrington-Wu-Tsai surface integral equation enforced on dispersive/plasmonic scatterers. Accuracy of the proposed method is demonstrated by a numerical example.

  4. A higher order space-time Galerkin scheme for time domain integral equations

    KAUST Repository

    Pray, Andrew J.; Beghein, Yves; Nair, Naveen V.; Cools, Kristof; Bagci, Hakan; Shanker, Balasubramaniam

    2014-01-01

    Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

  5. Stability equation and two-component Eigenmode for domain walls in scalar potential model

    International Nuclear Information System (INIS)

    Dias, G.S.; Graca, E.L.; Rodrigues, R. de Lima

    2002-08-01

    Supersymmetric quantum mechanics involving a two-component representation and two-component eigenfunctions is applied to obtain the stability equation associated to a potential model formulated in terms of two coupled real scalar fields. We investigate the question of stability by introducing an operator technique for the Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS states on two domain walls in a scalar potential model with minimal N 1-supersymmetry. (author)

  6. Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

    KAUST Repository

    Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric

    2012-01-01

    An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

  7. Explicit solution of the time domain magnetic field integral equation using a predictor-corrector scheme

    KAUST Repository

    Ulku, Huseyin Arda

    2012-09-01

    An explicit yet stable marching-on-in-time (MOT) scheme for solving the time domain magnetic field integral equation (TD-MFIE) is presented. The stability of the explicit scheme is achieved via (i) accurate evaluation of the MOT matrix elements using closed form expressions and (ii) a PE(CE) m type linear multistep method for time marching. Numerical results demonstrate the accuracy and stability of the proposed explicit MOT-TD-MFIE solver. © 2012 IEEE.

  8. Time-domain single-source integral equations for analyzing scattering from homogeneous penetrable objects

    KAUST Repository

    Valdés, Felipe

    2013-03-01

    Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.

  9. On solution of Lame equations in axisymmetric domains with conical points

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    Partial Fourier series expansion is applied to the Dirichlet problem for the Lame equations in axisymmetric domains Ω-circumflex is a subset of R 3 with conical points on the rotation axis. This leads to dimension reduction of the three-dimensional boundary value problem resulting to an infinite sequence of two-dimensional boundary value problems on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with solutions u n (n = 0,1,2, ...) being the Fourier coefficients of the solution u-circumflex of the 3D BVP. The asymptotic behavior of the Fourier coefficients u n (n = 0,1,2, ...) near the angular points of the meridian domain Ω a is fully described by singular vector-functions which are related to the zeros α n of some transcendental equations involving Legendre functions of the first kind. Equations which determine the values of α n are given and a numerical algorithm for the computation of α n is proposed with some plots of values obtained presented. The singular vector functions for the solution of the 3D BVP is obtained by Fourier synthesis. (author)

  10. Quantum-corrected plasmonic field analysis using a time domain PMCHWT integral equation

    KAUST Repository

    Uysal, Ismail E.

    2016-03-13

    When two structures are within sub-nanometer distance of each other, quantum tunneling, i.e., electrons "jumping" from one structure to another, becomes relevant. Classical electromagnetic solvers do not directly account for this additional path of current. In this work, an auxiliary tunnel made of Drude material is used to "connect" the structures as a support for this current path (R. Esteban et al., Nat. Commun., 2012). The plasmonic fields on the resulting connected structure are analyzed using a time domain surface integral equation solver. Time domain samples of the dispersive medium Green function and the dielectric permittivities are computed from the analytical inverse Fourier transform applied to the rational function representation of their frequency domain samples.

  11. A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

    Science.gov (United States)

    Johansen, Hans; Colella, Phillip

    1998-11-01

    We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.

  12. Knowledge, Skills and Competence Modelling in Nuclear Engineering Domain using Singular Value Decomposition (SVD) and Latent Semantic Analysis (LSA)

    International Nuclear Information System (INIS)

    Kuo, V.

    2016-01-01

    Full text: The European Qualifications Framework categorizes learning objectives into three qualifiers “knowledge”, “skills”, and “competences” (KSCs) to help improve the comparability between different fields and disciplines. However, the management of KSCs remains a great challenge given their semantic fuzziness. Similar texts may describe different concepts and different texts may describe similar concepts among different domains. This is difficult for the indexing, searching and matching of semantically similar KSCs within an information system, to facilitate transfer and mobility of KSCs. We present a working example using a semantic inference method known as Latent Semantic Analysis, employing a matrix operation called Singular Value Decomposition, which have been shown to infer semantic associations within unstructured textual data comparable to that of human interpretations. In our example, a few natural language text passages representing KSCs in the nuclear sector are used to demonstrate the capabilities of the system. It can be shown that LSA is able to infer latent semantic associations between texts, and cluster and match separate text passages semantically based on these associations. We propose this methodology for modelling existing natural language KSCs in the nuclear domain so they can be semantically queried, retrieved and filtered upon request. (author

  13. Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations

    KAUST Repository

    Ulku, Huseyin Arda

    2014-07-06

    Effects of material nonlinearities on electromagnetic field interactions become dominant as field amplitudes increase. A typical example is observed in plasmonics, where highly localized fields “activate” Kerr nonlinearities. Naturally, time domain solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation easier and the material nonlinearity can be easily accounted for using an auxiliary differential equation (J.H. Green and A. Taflove, Opt. Express, 14(18), 8305-8310, 2006). On the other hand, explicit marching on-in-time (MOT)-based time domain integral equation (TDIE) solvers have never been used for the same purpose even though they offer several advantages over FDTD (E. Michielssen, et al., ECCOMAS CFD, The Netherlands, Sep. 5-8, 2006). This is because explicit MOT solvers have never been stabilized until not so long ago. Recently an explicit but stable MOT scheme has been proposed for solving the time domain surface magnetic field integral equation (H.A. Ulku, et al., IEEE Trans. Antennas Propag., 61(8), 4120-4131, 2013) and later it has been extended for the time domain volume electric field integral equation (TDVEFIE) (S. B. Sayed, et al., Pr. Electromagn. Res. S., 378, Stockholm, 2013). This explicit MOT scheme uses predictor-corrector updates together with successive over relaxation during time marching to stabilize the solution even when time step is as large as in the implicit counterpart. In this work, an explicit MOT-TDVEFIE solver is proposed for analyzing electromagnetic wave interactions on scatterers exhibiting Kerr nonlinearity. Nonlinearity is accounted for using the constitutive relation between the electric field intensity and flux density. Then, this relation and the TDVEFIE are discretized together by expanding the intensity and flux - sing half

  14. Domain decomposition with local refinement for flow simulation around a nuclear waste disposal site: direct computation versus simulation using code coupling with OCamlP3L

    Energy Technology Data Exchange (ETDEWEB)

    Clement, F.; Vodicka, A.; Weis, P. [Institut National de Recherches Agronomiques (INRA), 78 - Le Chesnay (France); Martin, V. [Institut National de Recherches Agronomiques (INRA), 92 - Chetenay Malabry (France); Di Cosmo, R. [Institut National de Recherches Agronomiques (INRA), 78 - Le Chesnay (France); Paris-7 Univ., 75 (France)

    2003-07-01

    We consider the application of a non-overlapping domain decomposition method with non-matching grids based on Robin interface conditions to the problem of flow surrounding an underground nuclear waste disposal. We show with a simple example how one can refine the mesh locally around the storage with this technique. A second aspect is studied in this paper. The coupling between the sub-domains can be achieved by computing in two ways: either directly (i.e. the domain decomposition algorithm is included in the code that solves the problems on the sub-domains) or using code coupling. In the latter case, each sub-domain problem is solved separately and the coupling is performed by another program. We wrote a coupling program in the functional language Ocaml, using the OcamIP31 environment devoted to ease the parallelism. This at the same time we test the code coupling and we use the natural parallel property of domain decomposition methods. Some simple 2D numerical tests show promising results, and further studies are under way. (authors)

  15. Domain decomposition with local refinement for flow simulation around a nuclear waste disposal site: direct computation versus simulation using code coupling with OCamlP3L

    International Nuclear Information System (INIS)

    Clement, F.; Vodicka, A.; Weis, P.; Martin, V.; Di Cosmo, R.

    2003-01-01

    We consider the application of a non-overlapping domain decomposition method with non-matching grids based on Robin interface conditions to the problem of flow surrounding an underground nuclear waste disposal. We show with a simple example how one can refine the mesh locally around the storage with this technique. A second aspect is studied in this paper. The coupling between the sub-domains can be achieved by computing in two ways: either directly (i.e. the domain decomposition algorithm is included in the code that solves the problems on the sub-domains) or using code coupling. In the latter case, each sub-domain problem is solved separately and the coupling is performed by another program. We wrote a coupling program in the functional language Ocaml, using the OcamIP31 environment devoted to ease the parallelism. This at the same time we test the code coupling and we use the natural parallel property of domain decomposition methods. Some simple 2D numerical tests show promising results, and further studies are under way. (authors)

  16. A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

    Science.gov (United States)

    Malagón-Romero, A.; Luque, A.

    2018-04-01

    At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions in the radial direction for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation. Finally, we apply the method to solve Poisson's equation in cylindrical coordinates with free boundary conditions in both radial and longitudinal directions. This case is of particular interest for the initial stages of discharges in long gaps or natural discharges in the atmosphere, where it is not practical to extend the simulation volume to be bounded by two electrodes.

  17. A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver

    KAUST Repository

    Liu, Yang

    2015-10-26

    © 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT)-based surface integral equation (SIE) solvers, it reduces the computational and memory costs of transient analysis from equation and equation to equation and equation, respectively, where Nt and Ns denote the number of temporal and spatial unknowns (Ergin et al., IEEE Trans. Antennas Mag., 41, 39-52, 1999). In the past, PWTD-accelerated MOT-SIE solvers have been applied to transient problems involving half million spatial unknowns (Shanker et al., IEEE Trans. Antennas Propag., 51, 628-641, 2003). Recently, a scalable parallel PWTD-accelerated MOT-SIE solver that leverages a hiearchical parallelization strategy has been developed and successfully applied to the transient problems involving ten million spatial unknowns (Liu et. al., in URSI Digest, 2013). We further enhanced the capabilities of this solver by implementing a compression scheme based on local cosine wavelet bases (LCBs) that exploits the sparsity in the temporal dimension (Liu et. al., in URSI Digest, 2014). Specifically, the LCB compression scheme was used to reduce the memory requirement of the PWTD ray data and computational cost of operations in the PWTD translation stage.

  18. Time Domain Surface Integral Equation Solvers for Quantum Corrected Electromagnetic Analysis of Plasmonic Nanostructures

    KAUST Repository

    Uysal, Ismail Enes

    2016-10-01

    Plasmonic structures are utilized in many applications ranging from bio-medicine to solar energy generation and transfer. Numerical schemes capable of solving equations of classical electrodynamics have been the method of choice for characterizing scattering properties of such structures. However, as dimensions of these plasmonic structures reduce to nanometer scale, quantum mechanical effects start to appear. These effects cannot be accurately modeled by available classical numerical methods. One of these quantum effects is the tunneling, which is observed when two structures are located within a sub-nanometer distance of each other. At these small distances electrons “jump" from one structure to another and introduce a path for electric current to flow. Classical equations of electrodynamics and the schemes used for solving them do not account for this additional current path. This limitation can be lifted by introducing an auxiliary tunnel with material properties obtained using quantum models and applying a classical solver to the structures connected by this auxiliary tunnel. Early work on this topic focused on quantum models that are generated using a simple one-dimensional wave function to find the tunneling probability and assume a simple Drude model for the permittivity of the tunnel. These tunnel models are then used together with a classical frequency domain solver. In this thesis, a time domain surface integral equation solver for quantum corrected analysis of transient plasmonic interactions is proposed. This solver has several advantages: (i) As opposed to frequency domain solvers, it provides results at a broad band of frequencies with a single simulation. (ii) As opposed to differential equation solvers, it only discretizes surfaces (reducing number of unknowns), enforces the radiation condition implicitly (increasing the accuracy), and allows for time step selection independent of spatial discretization (increasing efficiency). The quantum model

  19. On Stability of Exact Transparent Boundary Condition for the Parabolic Equation in Rectangular Computational Domain

    Science.gov (United States)

    Feshchenko, R. M.

    Recently a new exact transparent boundary condition (TBC) for the 3D parabolic wave equation (PWE) in rectangular computational domain was derived. However in the obtained form it does not appear to be unconditionally stable when used with, for instance, the Crank-Nicolson finite-difference scheme. In this paper two new formulations of the TBC for the 3D PWE in rectangular computational domain are reported, which are likely to be unconditionally stable. They are based on an unconditionally stable fully discrete TBC for the Crank-Nicolson scheme for the 2D PWE. These new forms of the TBC can be used for numerical solution of the 3D PWE when a higher precision is required.

  20. analysis of large electromagnetic pulse simulators using the electric field integral equation method in time domain

    International Nuclear Information System (INIS)

    Jamali, J.; Aghajafari, R.; Moini, R.; Sadeghi, H.

    2002-01-01

    A time-domain approach is presented to calculate electromagnetic fields inside a large Electromagnetic Pulse (EMP) simulator. This type of EMP simulator is used for studying the effect of electromagnetic pulses on electrical apparatus in various structures such as vehicles, a reoplanes, etc. The simulator consists of three planar transmission lines. To solve the problem, we first model the metallic structure of the simulator as a grid of conducting wires. The numerical solution of the governing electric field integral equation is then obtained using the method of moments in time domain. To demonstrate the accuracy of the model, we consider a typical EMP simulator. The comparison of our results with those obtained experimentally in the literature validates the model introduced in this paper

  1. Existence of solutions to Burgers equations in domains that can be transformed into rectangles

    Directory of Open Access Journals (Sweden)

    Yassine Benia

    2016-06-01

    Full Text Available This work is concerned with Burgers equation $\\partial _{t}u+u\\partial_x u-\\partial _x^2u=f$ (with Dirichlet boundary conditions in the non rectangular domain $\\Omega =\\{(t,x\\in R^2;\\ 0domain will be transformed into a rectangle by a regular change of variables. The right-hand side lies in the Lebesgue space $L^2(\\Omega $, and the initial condition is in the usual Sobolev space $H_0^{1}$. Our goal is to establish the existence, uniqueness and the optimal regularity of the solution in the anisotropic Sobolev space.

  2. Parallel, explicit, and PWTD-enhanced time domain volume integral equation solver

    KAUST Repository

    Liu, Yang

    2013-07-01

    Time domain volume integral equations (TDVIEs) are useful for analyzing transient scattering from inhomogeneous dielectric objects in applications as varied as photonics, optoelectronics, and bioelectromagnetics. TDVIEs typically are solved by implicit marching-on-in-time (MOT) schemes [N. T. Gres et al., Radio Sci., 36, 379-386, 2001], requiring the solution of a system of equations at each and every time step. To reduce the computational cost associated with such schemes, [A. Al-Jarro et al., IEEE Trans. Antennas Propagat., 60, 5203-5215, 2012] introduced an explicit MOT-TDVIE method that uses a predictor-corrector technique to stably update field values throughout the scatterer. By leveraging memory-efficient nodal spatial discretization and scalable parallelization schemes [A. Al-Jarro et al., in 28th Int. Rev. Progress Appl. Computat. Electromagn., 2012], this solver has been successfully applied to the analysis of scattering phenomena involving 0.5 million spatial unknowns. © 2013 IEEE.

  3. The Laplace equation boundary value problems on bounded and unbounded Lipschitz domains

    CERN Document Server

    Medková, Dagmar

    2018-01-01

    This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.

  4. Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

    KAUST Repository

    Al Jarro, Ahmed; Salem, Mohamed; Bagci, Hakan; Benson, Trevor; Sewell, Phillip D.; Vuković, Ana

    2012-01-01

    An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

  5. On the mixed discretization of the time domain magnetic field integral equation

    KAUST Repository

    Ulku, Huseyin Arda

    2012-09-01

    Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

  6. Recovery of inclusions in 2D and 3D domains for Poisson’s equation

    International Nuclear Information System (INIS)

    Ito, Kazufumi; Liu, Ji-Chuan

    2013-01-01

    In this paper, we consider the recovery problem of inclusions in three-dimensional and three-dimensional domains for Poisson’s equation from noisy observation data. We propose effective reconstruction algorithms to recover hidden inclusions within a body when one can only make measurements of voltage and current on the external boundary. Our motivation is to detect the number, the location, the size and the shape of inclusions. This problem is nonlinear and severely ill posed, thus we should apply regularization techniques in our approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods. (paper)

  7. Explicit solution of the time domain volume integral equation using a stable predictor-corrector scheme

    KAUST Repository

    Al Jarro, Ahmed

    2012-11-01

    An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements.

  8. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

    2015-01-01

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  9. Recent advances in marching-on-in-time schemes for solving time domain volume integral equations

    KAUST Repository

    Sayed, Sadeed Bin

    2015-05-16

    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are constructed by setting the summation of the incident and scattered field intensities to the total field intensity on the volumetric support of the scatterer. The unknown can be the field intensity or flux/current density. Representing the total field intensity in terms of the unknown using the relevant constitutive relation and the scattered field intensity in terms of the spatiotemporal convolution of the unknown with the Green function yield the final form of the TDVIE. The unknown is expanded in terms of local spatial and temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation at discrete times yield a system of equations that is solved by the marching on-in-time (MOT) scheme. At each time step, a smaller system of equations, termed MOT system is solved for the coefficients of the expansion. The right-hand side of this system consists of the tested incident field and discretized spatio-temporal convolution of the unknown samples computed at the previous time steps with the Green function.

  10. Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media

    KAUST Repository

    Zampini, Stefano; Tu, Xuemin

    2017-01-01

    Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications.

  11. A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

    Science.gov (United States)

    Heinkenschloss, Matthias

    2005-01-01

    We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

  12. Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media

    KAUST Repository

    Zampini, Stefano

    2017-08-03

    Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications.

  13. Fast resolution of the neutron diffusion equation through public domain Ode codes

    Energy Technology Data Exchange (ETDEWEB)

    Garcia, V.M.; Vidal, V.; Garayoa, J. [Universidad Politecnica de Valencia, Departamento de Sistemas Informaticos, Valencia (Spain); Verdu, G. [Universidad Politecnica de Valencia, Departamento de Ingenieria Quimica y Nuclear, Valencia (Spain); Gomez, R. [I.E.S. de Tavernes Blanques, Valencia (Spain)

    2003-07-01

    The time-dependent neutron diffusion equation is a partial differential equation with source terms. The resolution method usually includes discretizing the spatial domain, obtaining a large system of linear, stiff ordinary differential equations (ODEs), whose resolution is computationally very expensive. Some standard techniques use a fixed time step to solve the ODE system. This can result in errors (if the time step is too large) or in long computing times (if the time step is too little). To speed up the resolution method, two well-known public domain codes have been selected: DASPK and FCVODE that are powerful codes for the resolution of large systems of stiff ODEs. These codes can estimate the error after each time step, and, depending on this estimation can decide which is the new time step and, possibly, which is the integration method to be used in the next step. With these mechanisms, it is possible to keep the overall error below the chosen tolerances, and, when the system behaves smoothly, to take large time steps increasing the execution speed. In this paper we address the use of the public domain codes DASPK and FCVODE for the resolution of the time-dependent neutron diffusion equation. The efficiency of these codes depends largely on the preconditioning of the big systems of linear equations that must be solved. Several pre-conditioners have been programmed and tested; it was found that the multigrid method is the best of the pre-conditioners tested. Also, it has been found that DASPK has performed better than FCVODE, being more robust for our problem.We can conclude that the use of specialized codes for solving large systems of ODEs can reduce drastically the computational work needed for the solution; and combining them with appropriate pre-conditioners, the reduction can be still more important. It has other crucial advantages, since it allows the user to specify the allowed error, which cannot be done in fixed step implementations; this, of course

  14. A higher order space-time Galerkin scheme for time domain integral equations

    KAUST Repository

    Pray, Andrew J.

    2014-12-01

    Stability of time domain integral equation (TDIE) solvers has remained an elusive goal formany years. Advancement of this research has largely progressed on four fronts: 1) Exact integration, 2) Lubich quadrature, 3) smooth temporal basis functions, and 4) space-time separation of convolutions with the retarded potential. The latter method\\'s efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was previously reported for first-order surface descriptions (flat elements) and zeroth-order functions as the temporal basis. In this work, we develop the methodology necessary to extend the scheme to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. These basis functions are then used in a space-time Galerkin framework. A number of results are presented that demonstrate convergence in time. The viability of the space-time separation method in producing stable results is demonstrated experimentally for these examples.

  15. From analytical solutions of solute transport equations to multidimensional time-domain random walk (TDRW) algorithms

    Science.gov (United States)

    Bodin, Jacques

    2015-03-01

    In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

  16. Massive parallelization of a 3D finite difference electromagnetic forward solution using domain decomposition methods on multiple CUDA enabled GPUs

    Science.gov (United States)

    Schultz, A.

    2010-12-01

    describe our ongoing efforts to achieve massive parallelization on a novel hybrid GPU testbed machine currently configured with 12 Intel Westmere Xeon CPU cores (or 24 parallel computational threads) with 96 GB DDR3 system memory, 4 GPU subsystems which in aggregate contain 960 NVidia Tesla GPU cores with 16 GB dedicated DDR3 GPU memory, and a second interleved bank of 4 GPU subsystems containing in aggregate 1792 NVidia Fermi GPU cores with 12 GB dedicated DDR5 GPU memory. We are applying domain decomposition methods to a modified version of Weiss' (2001) 3D frequency domain full physics EM finite difference code, an open source GPL licensed f90 code available for download from www.OpenEM.org. This will be the core of a new hybrid 3D inversion that parallelizes frequencies across CPUs and individual forward solutions across GPUs. We describe progress made in modifying the code to use direct solvers in GPU cores dedicated to each small subdomain, iteratively improving the solution by matching adjacent subdomain boundary solutions, rather than iterative Krylov space sparse solvers as currently applied to the whole domain.

  17. Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations

    Science.gov (United States)

    Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane

    2018-04-01

    Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.

  18. Terahertz time domain spectroscopy of amorphous and crystalline aluminum oxide nanostructures synthesized by thermal decomposition of AACH

    Energy Technology Data Exchange (ETDEWEB)

    Mehboob, Shoaib, E-mail: smehboob@pieas.edu.pk [National Center for Nanotechnology, Department of Metallurgy and Materials Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore 45650, Islamabad (Pakistan); Mehmood, Mazhar [National Center for Nanotechnology, Department of Metallurgy and Materials Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore 45650, Islamabad (Pakistan); Ahmed, Mushtaq [National Institute of Lasers and Optronics (NILOP), Nilore 45650, Islamabad (Pakistan); Ahmad, Jamil; Tanvir, Muhammad Tauseef [National Center for Nanotechnology, Department of Metallurgy and Materials Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore 45650, Islamabad (Pakistan); Ahmad, Izhar [National Institute of Lasers and Optronics (NILOP), Nilore 45650, Islamabad (Pakistan); Hassan, Syed Mujtaba ul [National Center for Nanotechnology, Department of Metallurgy and Materials Engineering, Pakistan Institute of Engineering and Applied Sciences (PIEAS), Nilore 45650, Islamabad (Pakistan)

    2017-04-15

    The objective of this work is to study the changes in optical and dielectric properties with the transformation of aluminum ammonium carbonate hydroxide (AACH) to α-alumina, using terahertz time domain spectroscopy (THz-TDS). The nanostructured AACH was synthesized by hydrothermal treatment of the raw chemicals at 140 °C for 12 h. This AACH was then calcined at different temperatures. The AACH was decomposed to amorphous phase at 400 °C and transformed to δ* + α-alumina at 1000 °C. Finally, the crystalline α-alumina was achieved at 1200 °C. X-ray diffraction (XRD) and Fourier transform infrared (FTIR) spectroscopy were employed to identify the phases formed after calcination. The morphology of samples was studied using scanning electron microscopy (SEM), which revealed that the AACH sample had rod-like morphology which was retained in the calcined samples. THz-TDS measurements showed that AACH had lowest refractive index in the frequency range of measurements. The refractive index at 0.1 THZ increased from 2.41 for AACH to 2.58 for the amorphous phase and to 2.87 for the crystalline α-alumina. The real part of complex permittivity increased with the calcination temperature. Further, the absorption coefficient was highest for AACH, which reduced with calcination temperature. The amorphous phase had higher absorption coefficient than the crystalline alumina. - Highlights: • Aluminum oxide nanostructures were obtained by thermal decomposition of AACH. • Crystalline phases of aluminum oxide have higher refractive index than that of amorphous phase. • The removal of heavier ionic species led to the lower absorption of THz radiations.

  19. Analytical approximate solutions of the time-domain diffusion equation in layered slabs.

    Science.gov (United States)

    Martelli, Fabrizio; Sassaroli, Angelo; Yamada, Yukio; Zaccanti, Giovanni

    2002-01-01

    Time-domain analytical solutions of the diffusion equation for photon migration through highly scattering two- and three-layered slabs have been obtained. The effect of the refractive-index mismatch with the external medium is taken into account, and approximate boundary conditions at the interface between the diffusive layers have been considered. A Monte Carlo code for photon migration through a layered slab has also been developed. Comparisons with the results of Monte Carlo simulations showed that the analytical solutions correctly describe the mean path length followed by photons inside each diffusive layer and the shape of the temporal profile of received photons, while discrepancies are observed for the continuous-wave reflectance or transmittance.

  20. Lagrangian fractional step method for the incompressible Navier--Stokes equations on a periodic domain

    International Nuclear Information System (INIS)

    Boergers, C.; Peskin, C.S.

    1987-01-01

    In the Lagrangian fractional step method introduced in this paper, the fluid velocity and pressure are defined on a collection of N fluid markers. At each time step, these markers are used to generate a Voronoi diagram, and this diagram is used to construct finite-difference operators corresponding to the divergence, gradient, and Laplacian. The splitting of the Navier--Stokes equations leads to discrete Helmholtz and Poisson problems, which we solve using a two-grid method. The nonlinear convection terms are modeled simply by the displacement of the fluid markers. We have implemented this method on a periodic domain in the plane. We describe an efficient algorithm for the numerical construction of periodic Voronoi diagrams, and we report on numerical results which indicate the the fractional step method is convergent of first order. The overall work per time step is proportional to N log N. copyright 1987 Academic Press, Inc

  1. Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains

    Directory of Open Access Journals (Sweden)

    Arnaldo Simal do Nascimento

    1997-12-01

    Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.

  2. Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

    KAUST Repository

    Liu, Yang

    2016-03-25

    A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

  3. The Fourier-finite-element approximation of the lame equations in axisymmetric domains with edges

    International Nuclear Information System (INIS)

    Nkemzil, Boniface

    2003-10-01

    This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lame equations in axisymmetric domains Ω-circumflex is contained in R 3 with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree N (N →∞), with the finite-element method on the plane meridian domain of Ω-circumflex with mesh size h (h → 0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singular functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For the right-hand side f-circumflex is an element of (L 2 (Ω-circumflex)) 3 , it is proved that the rate of convergence of the combined approximations in the norms of (W 2 1 (Ω-circumflex)) 3 is of the order O(h 2-l +N -(2-l) ) (l=0,1). (author)

  4. Parallel PWTD-Accelerated Explicit Solution of the Time Domain Electric Field Volume Integral Equation

    KAUST Repository

    Liu, Yang; Al-Jarro, Ahmed; Bagci, Hakan; Michielssen, Eric

    2016-01-01

    A parallel plane-wave time-domain (PWTD)-accelerated explicit marching-on-in-time (MOT) scheme for solving the time domain electric field volume integral equation (TD-EFVIE) is presented. The proposed scheme leverages pulse functions and Lagrange polynomials to spatially and temporally discretize the electric flux density induced throughout the scatterers, and a finite difference scheme to compute the electric fields from the Hertz electric vector potentials radiated by the flux density. The flux density is explicitly updated during time marching by a predictor-corrector (PC) scheme and the vector potentials are efficiently computed by a scalar PWTD scheme. The memory requirement and computational complexity of the resulting explicit PWTD-PC-EFVIE solver scale as ( log ) s s O N N and ( ) s t O N N , respectively. Here, s N is the number of spatial basis functions and t N is the number of time steps. A scalable parallelization of the proposed MOT scheme on distributed- memory CPU clusters is described. The efficiency, accuracy, and applicability of the resulting (parallelized) PWTD-PC-EFVIE solver are demonstrated via its application to the analysis of transient electromagnetic wave interactions on canonical and real-life scatterers represented with up to 25 million spatial discretization elements.

  5. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong

    2015-05-26

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  6. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    CERN Document Server

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  7. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    KAUST Repository

    Zhang, Sanzong; Luo, Yi; Schuster, Gerard T.

    2015-01-01

    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  8. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong

    2012-11-04

    The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

  9. Stabilization of a semilinear parabolic equation in the exterior of a bounded domain by means of boundary controls

    International Nuclear Information System (INIS)

    Gorshkov, A V

    2003-01-01

    The problem of the stabilization of a semilinear equation in the exterior of a bounded domain is considered. In view of the impossibility of an exponential stabilization of the form e -σt of the solution of a parabolic equation in an unbounded domain no matter what the boundary control is, one poses the problem of power-like stabilization by means of a boundary control. For a fixed initial condition and parameter k>0 of the rate of stabilization the existence of a boundary control such that the solution approaches zero at the rate 1/t k is demonstrated

  10. Analytical solutions of linear diffusion and wave equations in semi-infinite domains by using a new integral transform

    Directory of Open Access Journals (Sweden)

    Gao Lin

    2017-01-01

    Full Text Available Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics.

  11. A Laplace transform certified reduced basis method; application to the heat equation and wave equation

    OpenAIRE

    Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

    2010-01-01

    We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

  12. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    International Nuclear Information System (INIS)

    Dufresne, L.; Dumas, G.

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r→∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions

  13. The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain

    Directory of Open Access Journals (Sweden)

    Natalya V. Zaitseva

    2016-12-01

    Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.

  14. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    CERN Document Server

    Dufresne, L

    2003-01-01

    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the theta and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r-> infinity. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the lo...

  15. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN

    OpenAIRE

    Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development.

  16. Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

    Science.gov (United States)

    Adem, Abdullahi Rashid; Moawad, Salah M.

    2018-05-01

    In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

  17. Primal Domain Decomposition Method with Direct and Iterative Solver for Circuit-Field-Torque Coupled Parallel Finite Element Method to Electric Machine Modelling

    Directory of Open Access Journals (Sweden)

    Daniel Marcsa

    2015-01-01

    Full Text Available The analysis and design of electromechanical devices involve the solution of large sparse linear systems, and require therefore high performance algorithms. In this paper, the primal Domain Decomposition Method (DDM with parallel forward-backward and with parallel Preconditioned Conjugate Gradient (PCG solvers are introduced in two-dimensional parallel time-stepping finite element formulation to analyze rotating machine considering the electromagnetic field, external circuit and rotor movement. The proposed parallel direct and the iterative solver with two preconditioners are analyzed concerning its computational efficiency and number of iterations of the solver with different preconditioners. Simulation results of a rotating machine is also presented.

  18. On parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations

    International Nuclear Information System (INIS)

    Phan Thanh An; Phan Le Na; Ngo Quoc Chung

    2004-05-01

    We describe a practical implementation for finding parametric domain for asymptotic stability with probability one of zero solution of linear Ito stochastic differential equations based on Korenevskij and Mitropolskij's sufficient condition and our sufficient conditions. Numerical results show that all of these sufficient conditions are crucial in the implementation. (author)

  19. A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

    Science.gov (United States)

    Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

    2010-02-01

    Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

  20. Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

    Science.gov (United States)

    Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

    2018-01-01

    The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

  1. MO-FG-204-03: Using Edge-Preserving Algorithm for Significantly Improved Image-Domain Material Decomposition in Dual Energy CT

    International Nuclear Information System (INIS)

    Zhao, W; Niu, T; Xing, L; Xiong, G; Elmore, K; Min, J; Zhu, J; Wang, L

    2015-01-01

    Purpose: To significantly improve dual energy CT (DECT) imaging by establishing a new theoretical framework of image-domain material decomposition with incorporation of edge-preserving techniques. Methods: The proposed algorithm, HYPR-NLM, combines the edge-preserving non-local mean filter (NLM) with the HYPR-LR (Local HighlY constrained backPRojection Reconstruction) framework. Image denoising using HYPR-LR framework depends on the noise level of the composite image which is the average of the different energy images. For DECT, the composite image is the average of high- and low-energy images. To further reduce noise, one may want to increase the window size of the filter of the HYPR-LR, leading resolution degradation. By incorporating the NLM filtering and the HYPR-LR framework, HYPR-NLM reduces the boost material decomposition noise using energy information redundancies as well as the non-local mean. We demonstrate the noise reduction and resolution preservation of the algorithm with both iodine concentration numerical phantom and clinical patient data by comparing the HYPR-NLM algorithm to the direct matrix inversion, HYPR-LR and iterative image-domain material decomposition (Iter-DECT). Results: The results show iterative material decomposition method reduces noise to the lowest level and provides improved DECT images. HYPR-NLM significantly reduces noise while preserving the accuracy of quantitative measurement and resolution. For the iodine concentration numerical phantom, the averaged noise levels are about 2.0, 0.7, 0.2 and 0.4 for direct inversion, HYPR-LR, Iter- DECT and HYPR-NLM, respectively. For the patient data, the noise levels of the water images are about 0.36, 0.16, 0.12 and 0.13 for direct inversion, HYPR-LR, Iter-DECT and HYPR-NLM, respectively. Difference images of both HYPR-LR and Iter-DECT show edge effect, while no significant edge effect is shown for HYPR-NLM, suggesting spatial resolution is well preserved for HYPR-NLM. Conclusion: HYPR

  2. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    EL Safadi, M

    2007-03-15

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  3. Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain

    International Nuclear Information System (INIS)

    Elmhirst, Toby; Stewart, Ian; Doebeli, Michael

    2008-01-01

    We present a class of systems of ordinary differential equations (ODEs), which we call 'pod systems', that offers a new perspective on dynamical systems defined on a spatial domain. Such systems are typically studied as partial differential equations, but pod systems bring the analytic techniques of ODE theory to bear on the problems, and are thus able to study behaviours and bifurcations that are not easily accessible to the standard methods. In particular, pod systems are specifically designed to study spatial dynamical systems that exhibit multi-modal solutions. A pod system is essentially a linear combination of parametrized functions in which the coefficients and parameters are variables whose dynamics are specified by a system of ODEs. That is, pod systems are concerned with the dynamics of functions of the form Ψ(s, t) = y 1 (t) φ(s; x 1 (t)) + ··· + y N (t) φ(s; x N (t)), where s in R n is the spatial variable and φ: R n × R d → R. The parameters x i in R d and coefficients y i in R are dynamic variables which evolve according to some system of ODEs, x-dot i = G i (x, y) and y-dot i = H i (x, y), for i = 1, ..., N. The dynamics of Ψ in function space can then be studied through the dynamics of the x and y in finite dimensions. A vital feature of pod systems is that the ODEs that specify the dynamics of the x and y variables are not arbitrary; restrictions on G i and H i are required to guarantee that the dynamics of Ψ in function space are well defined (that is, that trajectories are unique). One important restriction is symmetry in the ODEs which arises because Ψ is invariant under permutations of the indices of the (x i , y i ) pairs. However, this is not the whole story, and the primary goal of this paper is to determine the necessary structure of the ODEs explicitly to guarantee that the dynamics of Ψ are well defined

  4. Implicit Boundary Integral Methods for the Helmholtz Equation in Exterior Domains

    Science.gov (United States)

    2016-06-01

    solve the Helmholtz equation as ∂Ω goes through significant change in its shape and topology — applications for which implicit representation of the...boundary-value problems for the wave equation and maxwell’s equations. Russian Math . Surv., 1965. [16] S. Reutskiy. The method of fundamental

  5. Fast analysis of wide-band scattering from electrically large targets with time-domain parabolic equation method

    Science.gov (United States)

    He, Zi; Chen, Ru-Shan

    2016-03-01

    An efficient three-dimensional time domain parabolic equation (TDPE) method is proposed to fast analyze the narrow-angle wideband EM scattering properties of electrically large targets. The finite difference (FD) of Crank-Nicolson (CN) scheme is used as the traditional tool to solve the time-domain parabolic equation. However, a huge computational resource is required when the meshes become dense. Therefore, the alternating direction implicit (ADI) scheme is introduced to discretize the time-domain parabolic equation. In this way, the reduced transient scattered fields can be calculated line by line in each transverse plane for any time step with unconditional stability. As a result, less computational resources are required for the proposed ADI-based TDPE method when compared with both the traditional CN-based TDPE method and the finite-different time-domain (FDTD) method. By employing the rotating TDPE method, the complete bistatic RCS can be obtained with encouraging accuracy for any observed angle. Numerical examples are given to demonstrate the accuracy and efficiency of the proposed method.

  6. Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

    Science.gov (United States)

    Jun, Li; Huicheng, Yin

    2018-05-01

    The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

  7. State equation approximation of transfer matrices and its application to the phase domain calculation of electromagnetic transients

    International Nuclear Information System (INIS)

    Soysal, A.O.; Semlyen, A.

    1994-01-01

    A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time

  8. Spinodal decomposition in fluid mixtures

    International Nuclear Information System (INIS)

    Kawasaki, Kyozi; Koga, Tsuyoshi

    1993-01-01

    We study the late stage dynamics of spinodal decomposition in binary fluids by the computer simulation of the time-dependent Ginzburg-Landau equation. We obtain a temporary linear growth law of the characteristic length of domains in the late stage. This growth law has been observed in many real experiments of binary fluids and indicates that the domain growth proceeds by the flow caused by the surface tension of interfaces. We also find that the dynamical scaling law is satisfied in this hydrodynamic domain growth region. By comparing the scaling functions for fluids with that for the case without hydrodynamic effects, we find that the scaling functions for the two systems are different. (author)

  9. On the energy inequality for weak solutions to the Navier-Stokes equations of compressible fluids on unbounded domains

    Czech Academy of Sciences Publication Activity Database

    Dell'Oro, Filippo; Feireisl, Eduard

    2015-01-01

    Roč. 128, November (2015), s. 136-148 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes equations * unbounded domain * weak solutions * energy inequality Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X15002692

  10. Endothermic decompositions of inorganic monocrystalline thin plates. I. Shape of polycrystalline product domains versus constraints and time

    Science.gov (United States)

    Bertrand, G.; Comperat, M.; Lallemant, M.; Watelle, G.

    1980-03-01

    Copper sulfate pentahydrate dehydration into trihydrate was investigated using monocrystalline platelets with varying crystallographic orientations. The morphological and kinetic features of the trihydrate domains were examined. Different shapes were observed: polygons (parallelograms, hexagons) and ellipses; their conditions of occurrence are reported in the (P, T) diagram. At first (for about 2 min), the ratio of the long to the short axes of elliptical domains changes with time; these subsequently develop homothetically and the rate ratio is then only pressure dependent. Temperature influence is inferred from that of pressure. Polygonal shapes are time dependent and result in ellipses. So far, no model can be put forward. Yet, qualitatively, the polygonal shape of a domain may be explained by the prevalence of the crystal arrangement and the elliptical shape by that of the solid tensorial properties. The influence of those factors might be modulated versus pressure, temperature, interface extent, and, thus, time.

  11. A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Sidler, Rolf, E-mail: rsidler@gmail.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, José M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)

    2013-02-15

    We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

  12. Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

    Science.gov (United States)

    Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

    2018-01-01

    An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

  13. Dynamic Programming Algorithms for Planning and Robotics in Continuous Domains and the Hamilton-Jacobi Equation

    Science.gov (United States)

    2008-09-22

    function essentially binary • Value function measures cost to go – Solution of Eikonal equation – Gradient determines optimal control typical laser...of nodes – Dijkstra’s algorithm is essentially unchanged • Continuous space – Static HJ PDE no longer reduces to the Eikonal equation – Gradient of ϑ...bounded: ||·||1 • If action is bounded in ||·||p, then value function is solution of “ Eikonal ” equation ||ϑ(x)||p* = c(x) in the dual norm p* – p = 1

  14. Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

    Science.gov (United States)

    Wang, Xiaohu; Lu, Kening; Wang, Bixiang

    2018-01-01

    In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.

  15. Analysis of electromagnetic wave interactions on nonlinear scatterers using time domain volume integral equations

    KAUST Repository

    Ulku, Huseyin Arda; Sayed, Sadeed Bin; Bagci, Hakan

    2014-01-01

    solvers are the method of choice when it comes simulating these nonlinear effects. Oftentimes, finite difference time domain (FDTD) method is used for this purpose. This is simply due to the fact that explicitness of the FDTD renders the implementation

  16. Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6

    International Nuclear Information System (INIS)

    Mukminov, F Kh; Bikkulov, I M

    2004-01-01

    The behaviour as t→∞ of the solution of a mixed problem for parabolic equations in an unbounded domain with two exits to infinity is studied. A certain class of domains is distinguished, in which an estimate characterizing the stabilization of solutions and determined by the geometry of the domain is established. This estimate is proved to be sharp in a certain sense for a broad class of domains with two exits to infinity.

  17. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang; Sen, Mrinal K.

    2009-01-01

    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  18. A new time–space domain high-order finite-difference method for the acoustic wave equation

    KAUST Repository

    Liu, Yang

    2009-12-01

    A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D acoustic wave modeling using a plane wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2 M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the acoustic wave equation. However, under the same discretization, the new 1D method can reach (2 M)th-order accuracy and is always stable. The 2D method can reach (2 M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2 M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of acoustic wave equation for homogeneous and inhomogeneous acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D acoustic wave equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference equations arising in other fields of science and engineering. © 2009 Elsevier Inc.

  19. Contribution to the development of methods for nuclear reactor core calculations with APOLLO3 code: domain decomposition in transport theory with nonlinear diffusion acceleration for 2D and 3D geometries

    International Nuclear Information System (INIS)

    Lenain, Roland

    2015-01-01

    This thesis is devoted to the implementation of a domain decomposition method applied to the neutron transport equation. The objective of this work is to access high-fidelity deterministic solutions to properly handle heterogeneities located in nuclear reactor cores, for problems' size ranging from color-sets of assemblies to large reactor cores configurations in 2D and 3D. The innovative algorithm developed during the thesis intends to optimize the use of parallelism and memory. The approach also aims to minimize the influence of the parallel implementation on the performances. These goals match the needs of APOLLO3 project, developed at CEA and supported by EDF and AREVA, which must be a portable code (no optimization on a specific architecture) in order to achieve best estimate modeling with resources ranging from personal computer to compute cluster available for engineers analyses. The proposed algorithm is a Parallel Multigroup-Block Jacobi one. Each sub-domain is considered as a multi-group fixed-source problem with volume-sources (fission) and surface-sources (interface flux between the sub-domains). The multi-group problem is solved in each sub-domain and a single communication of the interface flux is required at each power iteration. The spectral radius of the resolution algorithm is made similar to the one of a classical resolution algorithm with a nonlinear diffusion acceleration method: the well-known Coarse Mesh Finite Difference. In this way an ideal scalability is achievable when the calculation is parallelized. The memory organization, taking advantage of shared memory parallelism, optimizes the resources by avoiding redundant copies of the data shared between the sub-domains. Distributed memory architectures are made available by a hybrid parallel method that combines both paradigms of shared memory parallelism and distributed memory parallelism. For large problems, these architectures provide a greater number of processors and the amount of

  20. Stabilization of the solution of a two-dimensional system of Navier-Stokes equations in an unbounded domain with several exits to infinity

    International Nuclear Information System (INIS)

    Khisamutdinova, N A

    2003-01-01

    The behaviour as t→∞ of the solution of the mixed problem for the system of Navier-Stokes equations with a Dirichlet condition at the boundary is studied in an unbounded two-dimensional domain with several exits to infinity. A class of domains is distinguished in which an estimate characterizing the decay of solutions in terms of the geometry of the domain is proved for exponentially decreasing initial velocities. A similar estimate of the solution of the first mixed problem for the heat equation is sharp in a broad class of domains with several exits to infinity

  1. Stability of a Jensen Type Logarithmic Functional Equation on Restricted Domains and Its Asymptotic Behaviors

    Directory of Open Access Journals (Sweden)

    Chung Jae-Young

    2010-01-01

    Full Text Available Let be the set of positive real numbers, a Banach space, and , with . We prove the Hyers-Ulam stability of the Jensen type logarithmic functional inequality in restricted domains of the form for fixed with or and . As consequences of the results we obtain asymptotic behaviors of the inequality as .

  2. A wavelet-based PWTD algorithm-accelerated time domain surface integral equation solver

    KAUST Repository

    Liu, Yang; Yucel, Abdulkadir C.; Gilbert, Anna C.; Bagci, Hakan; Michielssen, Eric

    2015-01-01

    © 2015 IEEE. The multilevel plane-wave time-domain (PWTD) algorithm allows for fast and accurate analysis of transient scattering from, and radiation by, electrically large and complex structures. When used in tandem with marching-on-in-time (MOT

  3. On the internal resonant modes in marching-on-in-time solution of the time domain electric field integral equation

    KAUST Repository

    Shi, Yifei

    2013-08-01

    Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although \\'relaxed initial conditions,\\' which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes\\' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made \\'invisible\\' by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. © 2013 IEEE.

  4. On the internal resonant modes in marching-on-in-time solution of the time domain electric field integral equation

    KAUST Repository

    Shi, Yifei; Bagci, Hakan; Lu, Mingyu

    2013-01-01

    Internal resonant modes are always observed in the marching-on-in-time (MOT) solution of the time domain electric field integral equation (EFIE), although 'relaxed initial conditions,' which are enforced at the beginning of time marching, should in theory prevent these spurious modes from appearing. It has been conjectured that, numerical errors built up during time marching establish the necessary initial conditions and induce the internal resonant modes. However, this conjecture has never been proved by systematic numerical experiments. Our numerical results in this communication demonstrate that, the internal resonant modes' amplitudes are indeed dictated by the numerical errors. Additionally, it is shown that in a few cases, the internal resonant modes can be made 'invisible' by significantly suppressing the numerical errors. These tests prove the conjecture that the internal resonant modes are induced by numerical errors when the time domain EFIE is solved by the MOT method. © 2013 IEEE.

  5. Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains II: The monotone case

    Science.gov (United States)

    Zhou, Feng; Sun, Chunyou; Cheng, Jiaqi

    2018-02-01

    In this article, we continue the study of the dynamics of the following complex Ginzburg-Landau equation ∂tu - (λ + iα)Δu + (κ + iβ)|u|p-2u - γu = f(t) on non-cylindrical domains. We assume that the spatial domains are bounded and increase with time, which is different from the diffeomorphism case presented in Zhou and Sun [Discrete Contin. Dyn. Syst., Ser. B 21, 3767-3792 (2016)]. We develop a new penalty function to establish the existence and uniqueness of a variational solution satisfying energy equality as well as some energy inequalities and prove the existence of a D -pullback attractor for the non-autonomous dynamical system generated by this class of solutions.

  6. Finite-difference time-domain modeling of curved material interfaces by using boundary condition equations method

    International Nuclear Information System (INIS)

    Lu Jia; Zhou Huaichun

    2016-01-01

    To deal with the staircase approximation problem in the standard finite-difference time-domain (FDTD) simulation, the two-dimensional boundary condition equations (BCE) method is proposed in this paper. In the BCE method, the standard FDTD algorithm can be used as usual, and the curved surface is treated by adding the boundary condition equations. Thus, while maintaining the simplicity and computational efficiency of the standard FDTD algorithm, the BCE method can solve the staircase approximation problem. The BCE method is validated by analyzing near field and far field scattering properties of the PEC and dielectric cylinders. The results show that the BCE method can maintain a second-order accuracy by eliminating the staircase approximation errors. Moreover, the results of the BCE method show good accuracy for cylinder scattering cases with different permittivities. (paper)

  7. Classical solutions of two dimensional Stokes problems on non smooth domains. 2: Collocation method for the Radon equation

    International Nuclear Information System (INIS)

    Lubuma, M.S.

    1991-05-01

    The non uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities. (author). 34 refs

  8. Marching on-in-time solution of the time domain magnetic field integral equation using a predictor-corrector scheme

    KAUST Repository

    Ulku, Huseyin Arda; Bagci, Hakan; Michielssen, Eric

    2013-01-01

    An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao-Wilton-Glisson basis functions for spatial discretization and a PE(CE)m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. © 1963-2012 IEEE.

  9. Marching on-in-time solution of the time domain magnetic field integral equation using a predictor-corrector scheme

    KAUST Repository

    Ulku, Huseyin Arda

    2013-08-01

    An explicit marching on-in-time (MOT) scheme for solving the time-domain magnetic field integral equation (TD-MFIE) is presented. The proposed MOT-TD-MFIE solver uses Rao-Wilton-Glisson basis functions for spatial discretization and a PE(CE)m-type linear multistep method for time marching. Unlike previous explicit MOT-TD-MFIE solvers, the time step size can be chosen as large as that of the implicit MOT-TD-MFIE solvers without adversely affecting accuracy or stability. An algebraic stability analysis demonstrates the stability of the proposed explicit solver; its accuracy and efficiency are established via numerical examples. © 1963-2012 IEEE.

  10. Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions.

    Science.gov (United States)

    Langlands, T A M; Henry, B I; Wearne, S L

    2009-12-01

    We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.

  11. Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

    Science.gov (United States)

    Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

    2018-01-01

    Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

  12. Incremental localized boundary-domain integro-differential equations of elastic damage mechanics for inhomogeneous body

    OpenAIRE

    Mikhailov, SE

    2006-01-01

    Copyright @ 2006 Tech Science Press A quasi-static mixed boundary value problem of elastic damage mechanics for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary homogeneous linear elasticity with frozen initial, secant or tangent elastic coe±cients, a boundary-domain integro-differential formulation of the elasto-plastic problem with respect to the displacement rates and their gradients is derived. Usin...

  13. Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains

    Czech Academy of Sciences Publication Activity Database

    Brzezniak, Z.; Motyl, E.; Ondreját, Martin

    2017-01-01

    Roč. 45, č. 5 (2017), s. 3145-3201 ISSN 0091-1798 R&D Projects: GA ČR(CZ) GA15-08819S Institutional support: RVO:67985556 Keywords : Invariant measure * bw-Feller semigroup * stochastic Navier–Stokes equation Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.940, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/ondrejat-0478383.pdf

  14. Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach

    Energy Technology Data Exchange (ETDEWEB)

    Hilger, T.; Krassnigg, A. [University of Graz, NAWI Graz, Institute of Physics, Graz (Austria); Gomez-Rocha, M. [ECT*, Villazzano, Trento (Italy)

    2017-09-15

    We investigate the light-quarkonium spectrum using a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach to QCD. We discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction. In particular, we predict the mass of anti ss exotic 1{sup -+} states, and identify orbital angular momentum content in the excitations of the ρ meson. Comparing our covariant model results, the ρ and its second excitation being predominantly S-wave, the first excitation being predominantly D-wave, to corresponding conflicting lattice-QCD studies, we investigate the pion-mass dependence of the orbital-angular-momentum assignment and find a crossing at a scale of m{sub π} ∝ 1.4 GeV. If this crossing turns out to be a feature of the spectrum generated by lattice-QCD studies as well, it may reconcile the different results, since they have been obtained at different values of m{sub π}. (orig.)

  15. A numerical method for solving the 3D unsteady incompressible Navier Stokes equations in curvilinear domains with complex immersed boundaries

    Science.gov (United States)

    Ge, Liang; Sotiropoulos, Fotis

    2007-08-01

    A novel numerical method is developed that integrates boundary-conforming grids with a sharp interface, immersed boundary methodology. The method is intended for simulating internal flows containing complex, moving immersed boundaries such as those encountered in several cardiovascular applications. The background domain (e.g. the empty aorta) is discretized efficiently with a curvilinear boundary-fitted mesh while the complex moving immersed boundary (say a prosthetic heart valve) is treated with the sharp-interface, hybrid Cartesian/immersed-boundary approach of Gilmanov and Sotiropoulos [A. Gilmanov, F. Sotiropoulos, A hybrid cartesian/immersed boundary method for simulating flows with 3d, geometrically complex, moving bodies, Journal of Computational Physics 207 (2005) 457-492.]. To facilitate the implementation of this novel modeling paradigm in complex flow simulations, an accurate and efficient numerical method is developed for solving the unsteady, incompressible Navier-Stokes equations in generalized curvilinear coordinates. The method employs a novel, fully-curvilinear staggered grid discretization approach, which does not require either the explicit evaluation of the Christoffel symbols or the discretization of all three momentum equations at cell interfaces as done in previous formulations. The equations are integrated in time using an efficient, second-order accurate fractional step methodology coupled with a Jacobian-free, Newton-Krylov solver for the momentum equations and a GMRES solver enhanced with multigrid as preconditioner for the Poisson equation. Several numerical experiments are carried out on fine computational meshes to demonstrate the accuracy and efficiency of the proposed method for standard benchmark problems as well as for unsteady, pulsatile flow through a curved, pipe bend. To demonstrate the ability of the method to simulate flows with complex, moving immersed boundaries we apply it to calculate pulsatile, physiological flow

  16. Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion

    Science.gov (United States)

    Fukao, Takeshi; Kurima, Shunsuke; Yokota, Tomomi

    2018-05-01

    This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as \\[ \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a growth condition for $\\beta$ even though the Stefan problem was excluded from examples of (P). This paper completely removes the growth condition for $\\beta$ by confirming Cauchy's criterion for solutions of the following approximate problem (P)$_{\\varepsilon}$ with approximate parameter $\\varepsilon>0$: \\[ \\frac{\\partial u_{\\varepsilon}}{\\partial t} + (-\\Delta+1)(\\varepsilon(-\\Delta+1)u_{\\varepsilon} + \\beta(u_{\\varepsilon}) + \\pi_{\\varepsilon}(u_{\\varepsilon})) = g \\quad \\mbox{in}\\ \\Omega\\times(0, T), \\] which is called the Cahn--Hilliard system, even if $\\Omega \\subset \\mathbb{R}^N$ ($N \\in \\mathbb{N}$) is an unbounded domain. Moreover, it can be seen that the Stefan problem is covered in the framework of this paper.

  17. Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains

    International Nuclear Information System (INIS)

    Shishkov, A E; Shchelkov, A G

    1999-01-01

    A new approach (not based on the techniques of barriers) to the study of asymptotic properties of the generalized solutions of parabolic initial boundary-value problems with finite-time blow-up of the boundary values is proposed. Precise conditions on the blow-up pattern are found that guarantee uniform localization of the solution for an arbitrary compactly supported initial function. The main result of the paper consists in obtaining precise sufficient conditions for the singular (or blow-up) set of an arbitrary solution to remain within the boundary of the domain

  18. Radiation Boundary Conditions for Maxwell’s Equations: A Review of Accurate Time-Domain Formulations

    Science.gov (United States)

    2007-01-01

    conditions have only been constructed for the case ne = 0. Lastly we note that exact reflection formulas have recently been derived by Diaz and Joly [20, 21...SIAM J. Numer. Anal. 41 (2003), 287–305. 6. E. Bécache and P. Joly , On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations...Computational Wave Propagation (M. Ainsworth, P. Davies, D. Duncan, P. Martin , and B. Rynne, eds.), Springer-Verlag, 2003, pp. 43–82. 13. O. Bruno and D. Hoch

  19. An explicit marching on-in-time solver for the time domain volume magnetic field integral equation

    KAUST Repository

    Sayed, Sadeed Bin

    2014-07-01

    Transient scattering from inhomogeneous dielectric objects can be modeled using time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marching on-in-time (MOT) techniques. Classical MOT-TDVIE solvers expand the field induced on the scatterer using local spatio-temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation in space and time yields a system of equations that is solved by time marching. Depending on the type of the basis and testing functions and the time step, the time marching scheme can be implicit (N. T. Gres, et al., Radio Sci., 36(3), 379-386, 2001) or explicit (A. Al-Jarro, et al., IEEE Trans. Antennas Propag., 60(11), 5203-5214, 2012). Implicit MOT schemes are known to be more stable and accurate. However, under low-frequency excitation, i.e., when the time step size is large, they call for inversion of a full matrix system at very time step.

  20. What Is the Validity Domain of Einstein’s Equations? Distributional Solutions over Singularities and Topological Links in Geometrodynamics

    Directory of Open Access Journals (Sweden)

    Elias Zafiris

    2016-08-01

    Full Text Available The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions.

  1. An explicit marching on-in-time solver for the time domain volume magnetic field integral equation

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin Arda; Bagci, Hakan

    2014-01-01

    Transient scattering from inhomogeneous dielectric objects can be modeled using time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marching on-in-time (MOT) techniques. Classical MOT-TDVIE solvers expand the field induced on the scatterer using local spatio-temporal basis functions. Inserting this expansion into the TDVIE and testing the resulting equation in space and time yields a system of equations that is solved by time marching. Depending on the type of the basis and testing functions and the time step, the time marching scheme can be implicit (N. T. Gres, et al., Radio Sci., 36(3), 379-386, 2001) or explicit (A. Al-Jarro, et al., IEEE Trans. Antennas Propag., 60(11), 5203-5214, 2012). Implicit MOT schemes are known to be more stable and accurate. However, under low-frequency excitation, i.e., when the time step size is large, they call for inversion of a full matrix system at very time step.

  2. A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

    Directory of Open Access Journals (Sweden)

    Zhuo Su

    2013-01-01

    Full Text Available Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

  3. Simulation of neutron transport equation using parallel Monte Carlo for deep penetration problems

    International Nuclear Information System (INIS)

    Bekar, K. K.; Tombakoglu, M.; Soekmen, C. N.

    2001-01-01

    Neutron transport equation is simulated using parallel Monte Carlo method for deep penetration neutron transport problem. Monte Carlo simulation is parallelized by using three different techniques; direct parallelization, domain decomposition and domain decomposition with load balancing, which are used with PVM (Parallel Virtual Machine) software on LAN (Local Area Network). The results of parallel simulation are given for various model problems. The performances of the parallelization techniques are compared with each other. Moreover, the effects of variance reduction techniques on parallelization are discussed

  4. A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

    Science.gov (United States)

    Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

    2017-11-01

    The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

  5. Regular growth of systems of functions and systems of non-homogeneous convolution equations in convex domains of the complex plane

    International Nuclear Information System (INIS)

    Krivosheev, A S

    2000-01-01

    In this paper we introduce the notion of regular growth for a system of entire functions of finite order and type. This is a direct and natural generalization of the classical completely regular growth of an entire function. We obtain sufficient and necessary conditions for the solubility of a system of non-homogeneous convolution equations in convex domains of the complex plane. These conditions depend on whether the system of Laplace transforms of the analytic functionals that generate the convolution equations has regular growth. In the case of smooth convex domains, these solubility conditions form a criterion

  6. A numerical algorithm to evaluate the transient response for a synchronous scanning streak camera using a time-domain Baum–Liu–Tesche equation

    Energy Technology Data Exchange (ETDEWEB)

    Pei, Chengquan [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China); Tian, Jinshou [Xi' an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi' an 710119 (China); Wu, Shengli, E-mail: slwu@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China); He, Jiai [School of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu 730050 (China); Liu, Zhen [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi’an 710049 (China)

    2016-10-01

    The transient response is of great influence on the electromagnetic compatibility of synchronous scanning streak cameras (SSSCs). In this paper we propose a numerical method to evaluate the transient response of the scanning deflection plate (SDP). First, we created a simplified circuit model for the SDP used in an SSSC, and then derived the Baum–Liu–Tesche (BLT) equation in the frequency domain. From the frequency-domain BLT equation, its transient counterpart was derived. These parameters, together with the transient-BLT equation, were used to compute the transient load voltage and load current, and then a novel numerical method to fulfill the continuity equation was used. Several numerical simulations were conducted to verify this proposed method. The computed results were then compared with transient responses obtained by a frequency-domain/fast Fourier transform (FFT) method, and the accordance was excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used with slight modifications to calculate the transient response and the error can be controlled by a computer program. The result showed that the transient voltage was up to 1000 V and the transient current was approximately 10 A, so some protective measures should be taken to improve the electromagnetic compatibility.

  7. A numerical algorithm to evaluate the transient response for a synchronous scanning streak camera using a time-domain Baum–Liu–Tesche equation

    International Nuclear Information System (INIS)

    Pei, Chengquan; Tian, Jinshou; Wu, Shengli; He, Jiai; Liu, Zhen

    2016-01-01

    The transient response is of great influence on the electromagnetic compatibility of synchronous scanning streak cameras (SSSCs). In this paper we propose a numerical method to evaluate the transient response of the scanning deflection plate (SDP). First, we created a simplified circuit model for the SDP used in an SSSC, and then derived the Baum–Liu–Tesche (BLT) equation in the frequency domain. From the frequency-domain BLT equation, its transient counterpart was derived. These parameters, together with the transient-BLT equation, were used to compute the transient load voltage and load current, and then a novel numerical method to fulfill the continuity equation was used. Several numerical simulations were conducted to verify this proposed method. The computed results were then compared with transient responses obtained by a frequency-domain/fast Fourier transform (FFT) method, and the accordance was excellent for highly conducting cables. The benefit of deriving the BLT equation in the time domain is that it may be used with slight modifications to calculate the transient response and the error can be controlled by a computer program. The result showed that the transient voltage was up to 1000 V and the transient current was approximately 10 A, so some protective measures should be taken to improve the electromagnetic compatibility.

  8. Using normalized equations to solve the indetermination problem in the Oaxaca-Blinder decomposition: an application to the gender wage gap in Brazil

    OpenAIRE

    Scorzafave,Luiz Guilherme; Pazello,Elaine Toldo

    2007-01-01

    There are hundreds of works that implement the Oaxaca-Blinder decomposition. However, this decomposition is not invariant to the choice of reference group when dummy variables are used. This paper applies the solution proposed by Yun (005a,b) for this identification problem to Brazilian gender wage gap estimation. Our principal finding is the increasing difference in part-time work coefficients between men and women, which contributes to narrow the gender wage gap. Other studies in Brazil not...

  9. A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer

    International Nuclear Information System (INIS)

    Kim, Hyun Keol; Charette, Andre

    2007-01-01

    The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved

  10. A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

    Science.gov (United States)

    Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

    2018-05-01

    The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

  11. Multi-GPU-based acceleration of the explicit time domain volume integral equation solver using MPI-OpenACC

    KAUST Repository

    Feki, Saber

    2013-07-01

    An explicit marching-on-in-time (MOT)-based time-domain volume integral equation (TDVIE) solver has recently been developed for characterizing transient electromagnetic wave interactions on arbitrarily shaped dielectric bodies (A. Al-Jarro et al., IEEE Trans. Antennas Propag., vol. 60, no. 11, 2012). The solver discretizes the spatio-temporal convolutions of the source fields with the background medium\\'s Green function using nodal discretization in space and linear interpolation in time. The Green tensor, which involves second order spatial and temporal derivatives, is computed using finite differences on the temporal and spatial grid. A predictor-corrector algorithm is used to maintain the stability of the MOT scheme. The simplicity of the discretization scheme permits the computation of the discretized spatio-temporal convolutions on the fly during time marching; no \\'interaction\\' matrices are pre-computed or stored resulting in a memory efficient scheme. As a result, most often the applicability of this solver to the characterization of wave interactions on electrically large structures is limited by the computation time but not the memory. © 2013 IEEE.

  12. Automatic sleep staging using empirical mode decomposition, discrete wavelet transform, time-domain, and nonlinear dynamics features of heart rate variability signals.

    Science.gov (United States)

    Ebrahimi, Farideh; Setarehdan, Seyed-Kamaledin; Ayala-Moyeda, Jose; Nazeran, Homer

    2013-10-01

    The conventional method for sleep staging is to analyze polysomnograms (PSGs) recorded in a sleep lab. The electroencephalogram (EEG) is one of the most important signals in PSGs but recording and analysis of this signal presents a number of technical challenges, especially at home. Instead, electrocardiograms (ECGs) are much easier to record and may offer an attractive alternative for home sleep monitoring. The heart rate variability (HRV) signal proves suitable for automatic sleep staging. Thirty PSGs from the Sleep Heart Health Study (SHHS) database were used. Three feature sets were extracted from 5- and 0.5-min HRV segments: time-domain features, nonlinear-dynamics features and time-frequency features. The latter was achieved by using empirical mode decomposition (EMD) and discrete wavelet transform (DWT) methods. Normalized energies in important frequency bands of HRV signals were computed using time-frequency methods. ANOVA and t-test were used for statistical evaluations. Automatic sleep staging was based on HRV signal features. The ANOVA followed by a post hoc Bonferroni was used for individual feature assessment. Most features were beneficial for sleep staging. A t-test was used to compare the means of extracted features in 5- and 0.5-min HRV segments. The results showed that the extracted features means were statistically similar for a small number of features. A separability measure showed that time-frequency features, especially EMD features, had larger separation than others. There was not a sizable difference in separability of linear features between 5- and 0.5-min HRV segments but separability of nonlinear features, especially EMD features, decreased in 0.5-min HRV segments. HRV signal features were classified by linear discriminant (LD) and quadratic discriminant (QD) methods. Classification results based on features from 5-min segments surpassed those obtained from 0.5-min segments. The best result was obtained from features using 5-min HRV

  13. A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain

    Energy Technology Data Exchange (ETDEWEB)

    Bazalii, B V; Degtyarev, S P [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

    2013-07-31

    An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.

  14. Symmetric Tensor Decomposition

    DEFF Research Database (Denmark)

    Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

    2010-01-01

    We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

  15. Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

    Science.gov (United States)

    Chen, Jing-Bo

    2014-06-01

    By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

  16. Ozone decomposition

    Directory of Open Access Journals (Sweden)

    Batakliev Todor

    2014-06-01

    Full Text Available Catalytic ozone decomposition is of great significance because ozone is a toxic substance commonly found or generated in human environments (aircraft cabins, offices with photocopiers, laser printers, sterilizers. Considerable work has been done on ozone decomposition reported in the literature. This review provides a comprehensive summary of the literature, concentrating on analysis of the physico-chemical properties, synthesis and catalytic decomposition of ozone. This is supplemented by a review on kinetics and catalyst characterization which ties together the previously reported results. Noble metals and oxides of transition metals have been found to be the most active substances for ozone decomposition. The high price of precious metals stimulated the use of metal oxide catalysts and particularly the catalysts based on manganese oxide. It has been determined that the kinetics of ozone decomposition is of first order importance. A mechanism of the reaction of catalytic ozone decomposition is discussed, based on detailed spectroscopic investigations of the catalytic surface, showing the existence of peroxide and superoxide surface intermediates

  17. Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico

    2014-12-15

    In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.

  18. Parallel algorithms for solving the diffusion equation by finite elements methods and by nodal methods

    International Nuclear Information System (INIS)

    Coulomb, F.

    1989-06-01

    The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr

  19. Decomposition techniques

    Science.gov (United States)

    Chao, T.T.; Sanzolone, R.F.

    1992-01-01

    Sample decomposition is a fundamental and integral step in the procedure of geochemical analysis. It is often the limiting factor to sample throughput, especially with the recent application of the fast and modern multi-element measurement instrumentation. The complexity of geological materials makes it necessary to choose the sample decomposition technique that is compatible with the specific objective of the analysis. When selecting a decomposition technique, consideration should be given to the chemical and mineralogical characteristics of the sample, elements to be determined, precision and accuracy requirements, sample throughput, technical capability of personnel, and time constraints. This paper addresses these concerns and discusses the attributes and limitations of many techniques of sample decomposition along with examples of their application to geochemical analysis. The chemical properties of reagents as to their function as decomposition agents are also reviewed. The section on acid dissolution techniques addresses the various inorganic acids that are used individually or in combination in both open and closed systems. Fluxes used in sample fusion are discussed. The promising microwave-oven technology and the emerging field of automation are also examined. A section on applications highlights the use of decomposition techniques for the determination of Au, platinum group elements (PGEs), Hg, U, hydride-forming elements, rare earth elements (REEs), and multi-elements in geological materials. Partial dissolution techniques used for geochemical exploration which have been treated in detail elsewhere are not discussed here; nor are fire-assaying for noble metals and decomposition techniques for X-ray fluorescence or nuclear methods be discussed. ?? 1992.

  20. Semiempirical equations for modeling solid-state kinetics based on a Maxwell-Boltzmann distribution of activation energies: applications to a polymorphic transformation under crystallization slurry conditions and to the thermal decomposition of AgMnO4 crystals.

    Science.gov (United States)

    Skrdla, Peter J; Robertson, Rebecca T

    2005-06-02

    Many solid-state reactions and phase transformations performed under isothermal conditions give rise to asymmetric, sigmoidally shaped conversion-time (x-t) profiles. The mathematical treatment of such curves, as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell-Boltzmann (M-B) distribution is used to describe the distribution of activation energies for the reagent solids, which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equation that may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equation is used to relate the distribution of activation energies to a corresponding distribution of rate constants for the individual molecules in the reagent solids. This distribution of molecular rate constants is then correlated to the (observable) reaction time in the derivation of the model equation. In addition to providing a versatile treatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other models is that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple, two-parameter equation to successfully model the experimental x-t data for the polymorphic transformation of a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, we use a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical (i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.

  1. Explicit Solutions for the (2 + 1-Dimensional Jaulent–Miodek Equation Using the Integrating Factors Method in an Unbounded Domain

    Directory of Open Access Journals (Sweden)

    Rahma Sadat

    2018-03-01

    Full Text Available In this work, we prove that the integrating factors can be used as a reduction method. Analytical solutions of the Jaulent–Miodek (JM equation are obtained using integrating factors as an extension of a recent work where, through hidden symmetries, the JM was reduced to ordinary differential equations (ODEs. Some of these ODEs had no quadrature. We here derive several new solutions for these non-solvable ODEs.

  2. Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

    Science.gov (United States)

    Tay, Wei Choon; Tan, Eng Leong

    2014-07-01

    In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

  3. Controllability and stabilization of parabolic equations

    CERN Document Server

    Barbu, Viorel

    2018-01-01

    This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear diff...

  4. A highly accurate spectral method for the Navier–Stokes equations in a semi-infinite domain with flexible boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Matsushima, Toshiki; Ishioka, Keiichi, E-mail: matsushima@kugi.kyoto-u.ac.jp, E-mail: ishioka@gfd-dennou.org [Graduate School of Science, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan)

    2017-04-15

    This paper presents a spectral method for numerically solving the Navier–Stokes equations in a semi-infinite domain bounded by a flat plane: the aim is to obtain high accuracy with flexible boundary conditions. The proposed use is for numerical simulations of small-scale atmospheric phenomena near the ground. We introduce basis functions that fit the semi-infinite domain, and an integral condition for vorticity is used to reduce the computational cost when solving the partial differential equations that appear when the viscosity term is treated implicitly. Furthermore, in order to ensure high accuracy, two iteration techniques are applied when solving the system of linear equations and in determining boundary values. This significantly reduces numerical errors, and the proposed method enables high-resolution numerical experiments. This is demonstrated by numerical experiments showing the collision of a vortex ring into a wall; these were performed using numerical models based on the proposed method. It is shown that the time evolution of the flow field is successfully obtained not only near the boundary, but also in a region far from the boundary. The applicability of the proposed method and the integral condition is discussed. (paper)

  5. A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

    KAUST Repository

    Sayed, Sadeed Bin

    2015-05-05

    A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

  6. A Stable Marching on-in-time Scheme for Solving the Time Domain Electric Field Volume Integral Equation on High-contrast Scatterers

    KAUST Repository

    Sayed, Sadeed Bin; Ulku, Huseyin; Bagci, Hakan

    2015-01-01

    A time domain electric field volume integral equation (TD-EFVIE) solver is proposed for characterizing transient electromagnetic wave interactions on high-contrast dielectric scatterers. The TD-EFVIE is discretized using the Schaubert- Wilton-Glisson (SWG) and approximate prolate spherical wave (APSW) functions in space and time, respectively. The resulting system of equations can not be solved by a straightforward application of the marching on-in-time (MOT) scheme since the two-sided APSW interpolation functions require the knowledge of unknown “future” field samples during time marching. Causality of the MOT scheme is restored using an extrapolation technique that predicts the future samples from known “past” ones. Unlike the extrapolation techniques developed for MOT schemes that are used in solving time domain surface integral equations, this scheme trains the extrapolation coefficients using samples of exponentials with exponents on the complex frequency plane. This increases the stability of the MOT-TD-EFVIE solver significantly, since the temporal behavior of decaying and oscillating electromagnetic modes induced inside the scatterers is very accurately taken into account by this new extrapolation scheme. Numerical results demonstrate that the proposed MOT solver maintains its stability even when applied to analyzing wave interactions on high-contrast scatterers.

  7. Using normalized equations to solve the indetermination problem in the Oaxaca-Blinder decomposition: an application to the gender wage gap in Brazil

    Directory of Open Access Journals (Sweden)

    Luiz Guilherme Scorzafave

    2007-12-01

    Full Text Available There are hundreds of works that implement the Oaxaca-Blinder decomposition. However, this decomposition is not invariant to the choice of reference group when dummy variables are used. This paper applies the solution proposed by Yun (005a,b for this identification problem to Brazilian gender wage gap estimation. Our principal finding is the increasing difference in part-time work coefficients between men and women, which contributes to narrow the gender wage gap. Other studies in Brazil not using any correction of the identification problem have found different results.Há centenas de trabalhos que implementam a decomposição de Oaxaca-Blinder. Entretanto, esta decomposição não é invariante à escolha dos grupos de referência quando variáveis binárias são utilizadas como regressores. Este artigo aplica a solução proposta por Yun (005a,b para este problema de identificação à estimação do diferencial de salários por sexo no Brasil. A crescente diferença entre homens e mulheres no coeficiente da regressão associado ao trabalho em meio período vem contribuindo para reduzir o diferencial de salários por sexo. Outros estudos já realizados no Brasil que não utilizaram qualquer correção do problema de identificação, encontraram resultados diferentes.

  8. Strong solutions for the Navier-Stokes equations on bounded and unbounded domains with a moving boundary

    Directory of Open Access Journals (Sweden)

    Juergen Saal

    2007-02-01

    Full Text Available It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.

  9. Convergence analysis of a class of massively parallel direction splitting algorithms for the Navier-Stokes equations in simple domains

    KAUST Repository

    Guermond, Jean-Luc; Minev, Peter D.; Salgado, Abner J.

    2012-01-01

    We provide a convergence analysis for a new fractional timestepping technique for the incompressible Navier-Stokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. © 2012 American Mathematical Society.

  10. On large-time energy concentration in solutions to the Navier-Stokes equations in general domains

    Czech Academy of Sciences Publication Activity Database

    Skalák, Zdeněk

    2011-01-01

    Roč. 91, č. 9 (2011), s. 724-732 ISSN 0044-2267 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z20600510 Keywords : Navier-Stokes equations * large-time behavior * energy concentration Subject RIV: BA - General Mathematics Impact factor: 0.863, year: 2011

  11. A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis.

    Science.gov (United States)

    MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H

    2016-03-15

    In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

  12. A surface-integral-equation approach to the propagation of waves in EBG-based devices

    NARCIS (Netherlands)

    Lancellotti, V.; Tijhuis, A.G.

    2012-01-01

    We combine surface integral equations with domain decomposition to formulate and (numerically) solve the problem of electromagnetic (EM) wave propagation inside finite-sized structures. The approach is of interest for (but not limited to) the analysis of devices based on the phenomenon of

  13. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Synthetic and field data examples

    KAUST Repository

    Zhang, Sanzong

    2015-05-26

    Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.

  14. Numerical experiments on the solution of the Holmholtz equation in the case of domains of complicated boundary shape

    International Nuclear Information System (INIS)

    Sarmiento, G.S.; Laura, P.A.A.

    1979-01-01

    Domains of complicated boundary shape are of great practical importance in several fields of technology and applied science; e.g. solid propellant rocket grains, electromagnetic and acoustic waveguides, and certain elements used in nuclear engineering. The technical literature contains very few comparative studies of analytical and numerical solutions when dealing with such rather complex geometries. The present study constitutes an effort in that direction. (Auth.)

  15. Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2005-10-01

    Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

  16. A space-time mixed galerkin marching-on-in-time scheme for the time-domain combined field integral equation

    KAUST Repository

    Beghein, Yves

    2013-03-01

    The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required. © 2012 IEEE.

  17. Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

    Science.gov (United States)

    Ryo, Ikehata

    Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

  18. Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl-von Kármán equation: energy decomposition analysis and energy budget.

    Science.gov (United States)

    Yokoyama, Naoto; Takaoka, Masanori

    2014-12-01

    A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

  19. A Wavelet-Enhanced PWTD-Accelerated Time-Domain Integral Equation Solver for Analysis of Transient Scattering from Electrically Large Conducting Objects

    KAUST Repository

    Liu, Yang

    2018-02-26

    A wavelet-enhanced plane-wave time-domain (PWTD) algorithm for efficiently and accurately solving time-domain surface integral equations (TD-SIEs) on electrically large conducting objects is presented. The proposed scheme reduces the memory requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD-accelerated TD-SIE solver, when applied to the analysis of transient scattering from smooth quasi-planar objects with near-normal incident pulses, scale nearly as O(Ns log Ns) and O(Ns 1.5 ), respectively. Here, Ns denotes the number of spatial unknowns. The efficiency and accuracy of the proposed scheme are demonstrated through its applications to the analysis of transient scattering from a 185 wave-length-long NASA almond and a 123-wavelength long Air-bus-A320 model.

  20. Students' Understanding of Quadratic Equations

    Science.gov (United States)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  1. A hybrid method combining the FDTD and a time domain boundary-integral equation marching-on-in-time algorithm

    Directory of Open Access Journals (Sweden)

    A. Becker

    2003-01-01

    Full Text Available In this paper a hybrid method combining the FDTD/FIT with a Time Domain Boundary-Integral Marching-on-in-Time Algorithm (TD-BIM is presented. Inhomogeneous regions are modelled with the FIT-method, an alternative formulation of the FDTD. Homogeneous regions (which is in the presented numerical example the open space are modelled using a TD-BIM with equivalent electric and magnetic currents flowing on the boundary between the inhomogeneous and the homogeneous regions. The regions are coupled by the tangential magnetic fields just outside the inhomogeneous regions. These fields are calculated by making use of a Mixed Potential Integral Formulation for the magnetic field. The latter consists of equivalent electric and magnetic currents on the boundary plane between the homogeneous and the inhomogeneous region. The magnetic currents result directly from the electric fields of the Yee lattice. Electric currents in the same plane are calculated by making use of the TD-BIM and using the electric field of the Yee lattice as boundary condition. The presented hybrid method only needs the interpolations inherent in FIT and no additional interpolation. A numerical result is compared to a calculation that models both regions with FDTD.

  2. Regularity for a clamped grid equation $u_{xxxx}+u_{yyyy}=f $ on a domain with a corner

    Directory of Open Access Journals (Sweden)

    Tymofiy Gerasimov

    2009-04-01

    Full Text Available The operator $L=frac{partial ^{4}}{partial x^{4}} +frac{partial ^{4}}{partial y^{4}}$ appears in a model for the vertical displacement of a two-dimensional grid that consists of two perpendicular sets of elastic fibers or rods. We are interested in the behaviour of such a grid that is clamped at the boundary and more specifically near a corner of the domain. Kondratiev supplied the appropriate setting in the sense of Sobolev type spaces tailored to find the optimal regularity. Inspired by the Laplacian and the Bilaplacian models one expect, except maybe for some special angles that the optimal regularity improves when angle decreases. For the homogeneous Dirichlet problem with this special non-isotropic fourth order operator such a result does not hold true. We will show the existence of an interval $( frac{1}{2}pi ,omega _{star }$, $omega _{star }/pi approx 0.528dots$ (in degrees $omega _{star }approx 95.1dots^{circ} $, in which the optimal regularity improves with increasing opening angle.

  3. Tracking techniques for the characteristics method applied to the resolution of the neutrons transport equation in multi scale domains

    International Nuclear Information System (INIS)

    Fevotte, F.

    2008-01-01

    At the various stages of a nuclear reactor's life, numerous studies are needed to guaranty the safety and efficiency of the design, analyse the fuel cycle, prepare the dismantlement, and so on. Due to the extreme difficulty to take extensive and accurate measurements in the reactor core, most of these studies are numerical simulations. The complete numerical simulation of a nuclear reactor involves many types of physics: neutronics, thermal hydraulics, materials, control engineering, Among these, the neutron transport simulation is one of the fundamental steps, since it allows computation - among other things - of various fundamental values such as the power density (used in thermal hydraulics computations) or fuel burn-up. The neutron transport simulation is based on the Boltzmann equation, which models the neutron population inside the reactor core. Among the various methods allowing its numerical solution, much interest has been devoted in the past few years to the Method of Characteristics in unstructured meshes (MOC), since it offers a good accuracy and operates in complicated geometries. The aim of this work is to propose improvements of the calculation scheme bound on the two dimensions MOC, in order to decrease the needed resources number. (A.L.B.)

  4. A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer

    International Nuclear Information System (INIS)

    Kim, Hyun Keol; Hielscher, Andreas H

    2009-01-01

    It is well acknowledged that transport-theory-based reconstruction algorithm can provide the most accurate reconstruction results especially when small tissue volumes or high absorbing media are considered. However, these codes have a high computational burden and are often only slowly converging. Therefore, methods that accelerate the computation are highly desirable. To this end, we introduce in this work a partial-differential-equation (PDE) constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and inverse variables independently, which makes it possible to update the radiation intensities and the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate the performance of the proposed scheme with numerical and experimental data, and find that the rSQP scheme can reduce the computation time by a factor of 10–25, as compared to the commonly employed limited memory BFGS method. At the same time accuracy and robustness even in the presence of noise are not compromised

  5. Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

    Science.gov (United States)

    White, Jeffery A.; Baurle, Robert A.; Passe, Bradley J.; Spiegel, Seth C.; Nishikawa, Hiroaki

    2017-01-01

    The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on

  6. Resolution of Maxwell equations within a 2D domain with inner corners. Part I: modelling with boundary conditions of the perfect conductor type

    International Nuclear Information System (INIS)

    Assous, F.; Ciarlet, P.; Sonnendruker, E.

    1996-01-01

    This study addresses the resolution of Maxwell equations in the case of a non-regular boundary and non-convex domain (presence of inner corners) which requires a notably locally refined mesh to obtain an acceptable numerical solution. The authors focus on a 2D problem which may physically correspond to a 3D problem, for example when the electromagnetic field is independent of one the three space variables (for example an infinite cylinder when the field does not depend on the variable associated with the cylinder axis). Model problems are presented: the steady problem, and the evolution problem. The solution is then decomposed into a regular part and a singular one. The authors report the solution calculation, and then the study of the model problems

  7. Thermal decomposition of γ-irradiated lead nitrate

    International Nuclear Information System (INIS)

    Nair, S.M.K.; Kumar, T.S.S.

    1990-01-01

    The thermal decomposition of unirradiated and γ-irradiated lead nitrate was studied by the gas evolution method. The decomposition proceeds through initial gas evolution, a short induction period, an acceleratory stage and a decay stage. The acceleratory and decay stages follow the Avrami-Erofeev equation. Irradiation enhances the decomposition but does not affect the shape of the decomposition curve. (author) 10 refs.; 7 figs.; 2 tabs

  8. Strongly \\'etale difference algebras and Babbitt's decomposition

    OpenAIRE

    Tomašić, Ivan; Wibmer, Michael

    2015-01-01

    We introduce a class of strongly \\'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \\'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.

  9. On the static loop modes in the marching-on-in-time solution of the time-domain electric field integral equation

    KAUST Repository

    Shi, Yifei; Bagci, Hakan; Lu, Mingyu

    2014-01-01

    When marching-on-in-time (MOT) method is applied to solve the time-domain electric field integral equation, spurious internal resonant and static loop modes are always observed in the solution. The internal resonant modes have recently been studied by the authors; this letter investigates the static loop modes. Like internal resonant modes, static loop modes, in theory, should not be observed in the MOT solution since they do not satisfy the zero initial conditions; their appearance is attributed to numerical errors. It is discussed in this letter that the dependence of spurious static loop modes on numerical errors is substantially different from that of spurious internal resonant modes. More specifically, when Rao-Wilton-Glisson functions and Lagrange interpolation functions are used as spatial and temporal basis functions, respectively, errors due to space-time discretization have no discernible impact on spurious static loop modes. Numerical experiments indeed support this discussion and demonstrate that the numerical errors due to the approximate solution of the MOT matrix system have dominant impact on spurious static loop modes in the MOT solution. © 2014 IEEE.

  10. Bregmanized Domain Decomposition for Image Restoration

    KAUST Repository

    Langer, Andreas; Osher, Stanley; Schö nlieb, Carola-Bibiane

    2012-01-01

    Computational problems of large-scale data are gaining attention recently due to better hardware and hence, higher dimensionality of images and data sets acquired in applications. In the last couple of years non-smooth minimization problems

  11. Non-equilibrium theory of arrested spinodal decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Olais-Govea, José Manuel; López-Flores, Leticia; Medina-Noyola, Magdaleno [Instituto de Física “Manuel Sandoval Vallarta,” Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP (Mexico)

    2015-11-07

    The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramŕez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.

  12. Open problems in CEM: Porting an explicit time-domain volume-integral- equation solver on GPUs with OpenACC

    KAUST Repository

    Ergül, Özgür

    2014-04-01

    Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart. © 2014 IEEE.

  13. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Slattery, S. R.; Wilson, P. P. H. [Engineering Physics Department, University of Wisconsin - Madison, 1500 Engineering Dr., Madison, WI 53706 (United States); Evans, T. M. [Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37830 (United States)

    2013-07-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  14. A spectral analysis of the domain decomposed Monte Carlo method for linear systems

    International Nuclear Information System (INIS)

    Slattery, S. R.; Wilson, P. P. H.; Evans, T. M.

    2013-01-01

    The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

  15. A thermodynamic definition of protein domains.

    Science.gov (United States)

    Porter, Lauren L; Rose, George D

    2012-06-12

    Protein domains are conspicuous structural units in globular proteins, and their identification has been a topic of intense biochemical interest dating back to the earliest crystal structures. Numerous disparate domain identification algorithms have been proposed, all involving some combination of visual intuition and/or structure-based decomposition. Instead, we present a rigorous, thermodynamically-based approach that redefines domains as cooperative chain segments. In greater detail, most small proteins fold with high cooperativity, meaning that the equilibrium population is dominated by completely folded and completely unfolded molecules, with a negligible subpopulation of partially folded intermediates. Here, we redefine structural domains in thermodynamic terms as cooperative folding units, based on m-values, which measure the cooperativity of a protein or its substructures. In our analysis, a domain is equated to a contiguous segment of the folded protein whose m-value is largely unaffected when that segment is excised from its parent structure. Defined in this way, a domain is a self-contained cooperative unit; i.e., its cooperativity depends primarily upon intrasegment interactions, not intersegment interactions. Implementing this concept computationally, the domains in a large representative set of proteins were identified; all exhibit consistency with experimental findings. Specifically, our domain divisions correspond to the experimentally determined equilibrium folding intermediates in a set of nine proteins. The approach was also proofed against a representative set of 71 additional proteins, again with confirmatory results. Our reframed interpretation of a protein domain transforms an indeterminate structural phenomenon into a quantifiable molecular property grounded in solution thermodynamics.

  16. A Wavelet-Enhanced PWTD-Accelerated Time-Domain Integral Equation Solver for Analysis of Transient Scattering from Electrically Large Conducting Objects

    KAUST Repository

    Liu, Yang; Yucel, Abdulkadir C.; Bagci, Hakan; Gilbert, Anna C.; Michielssen, Eric

    2018-01-01

    requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD

  17. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  18. Spectral Decomposition Algorithm (SDA)

    Data.gov (United States)

    National Aeronautics and Space Administration — Spectral Decomposition Algorithm (SDA) is an unsupervised feature extraction technique similar to PCA that was developed to better distinguish spectral features in...

  19. Thermal decomposition of pyrite

    International Nuclear Information System (INIS)

    Music, S.; Ristic, M.; Popovic, S.

    1992-01-01

    Thermal decomposition of natural pyrite (cubic, FeS 2 ) has been investigated using X-ray diffraction and 57 Fe Moessbauer spectroscopy. X-ray diffraction analysis of pyrite ore from different sources showed the presence of associated minerals, such as quartz, szomolnokite, stilbite or stellerite, micas and hematite. Hematite, maghemite and pyrrhotite were detected as thermal decomposition products of natural pyrite. The phase composition of the thermal decomposition products depends on the terature, time of heating and starting size of pyrite chrystals. Hematite is the end product of the thermal decomposition of natural pyrite. (author) 24 refs.; 6 figs.; 2 tabs

  20. Generalized decompositions of dynamic systems and vector Lyapunov functions

    Science.gov (United States)

    Ikeda, M.; Siljak, D. D.

    1981-10-01

    The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

  1. Survey of the status of finite element methods for partial differential equations

    Science.gov (United States)

    Temam, Roger

    1986-01-01

    The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

  2. Multiresolution signal decomposition schemes

    NARCIS (Netherlands)

    J. Goutsias (John); H.J.A.M. Heijmans (Henk)

    1998-01-01

    textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis

  3. Decomposition of Sodium Tetraphenylborate

    International Nuclear Information System (INIS)

    Barnes, M.J.

    1998-01-01

    The chemical decomposition of aqueous alkaline solutions of sodium tetraphenylborate (NaTPB) has been investigated. The focus of the investigation is on the determination of additives and/or variables which influence NaTBP decomposition. This document describes work aimed at providing better understanding into the relationship of copper (II), solution temperature, and solution pH to NaTPB stability

  4. 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.

  5. Azimuthal decomposition of optical modes

    CSIR Research Space (South Africa)

    Dudley, Angela L

    2012-07-01

    Full Text Available This presentation analyses the azimuthal decomposition of optical modes. Decomposition of azimuthal modes need two steps, namely generation and decomposition. An azimuthally-varying phase (bounded by a ring-slit) placed in the spatial frequency...

  6. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  7. The simplified spherical harmonics (SPL) methodology with space and moment decomposition in parallel environments

    International Nuclear Information System (INIS)

    Gianluca, Longoni; Alireza, Haghighat

    2003-01-01

    In recent years, the SP L (simplified spherical harmonics) equations have received renewed interest for the simulation of nuclear systems. We have derived the SP L equations starting from the even-parity form of the S N equations. The SP L equations form a system of (L+1)/2 second order partial differential equations that can be solved with standard iterative techniques such as the Conjugate Gradient (CG). We discretized the SP L equations with the finite-volume approach in a 3-D Cartesian space. We developed a new 3-D general code, Pensp L (Parallel Environment Neutral-particle SP L ). Pensp L solves both fixed source and criticality eigenvalue problems. In order to optimize the memory management, we implemented a Compressed Diagonal Storage (CDS) to store the SP L matrices. Pensp L includes parallel algorithms for space and moment domain decomposition. The computational load is distributed on different processors, using a mapping function, which maps the 3-D Cartesian space and moments onto processors. The code is written in Fortran 90 using the Message Passing Interface (MPI) libraries for the parallel implementation of the algorithm. The code has been tested on the Pcpen cluster and the parallel performance has been assessed in terms of speed-up and parallel efficiency. (author)

  8. Cellular decomposition in vikalloys

    International Nuclear Information System (INIS)

    Belyatskaya, I.S.; Vintajkin, E.Z.; Georgieva, I.Ya.; Golikov, V.A.; Udovenko, V.A.

    1981-01-01

    Austenite decomposition in Fe-Co-V and Fe-Co-V-Ni alloys at 475-600 deg C is investigated. The cellular decomposition in ternary alloys results in the formation of bcc (ordered) and fcc structures, and in quaternary alloys - bcc (ordered) and 12R structures. The cellular 12R structure results from the emergence of stacking faults in the fcc lattice with irregular spacing in four layers. The cellular decomposition results in a high-dispersion structure and magnetic properties approaching the level of well-known vikalloys [ru

  9. Decompositions of manifolds

    CERN Document Server

    Daverman, Robert J

    2007-01-01

    Decomposition theory studies decompositions, or partitions, of manifolds into simple pieces, usually cell-like sets. Since its inception in 1929, the subject has become an important tool in geometric topology. The main goal of the book is to help students interested in geometric topology to bridge the gap between entry-level graduate courses and research at the frontier as well as to demonstrate interrelations of decomposition theory with other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be strongly recommended to eve

  10. Three-dimensional decomposition models for carbon productivity

    International Nuclear Information System (INIS)

    Meng, Ming; Niu, Dongxiao

    2012-01-01

    This paper presents decomposition models for the change in carbon productivity, which is considered a key indicator that reflects the contributions to the control of greenhouse gases. Carbon productivity differential was used to indicate the beginning of decomposition. After integrating the differential equation and designing the Log Mean Divisia Index equations, a three-dimensional absolute decomposition model for carbon productivity was derived. Using this model, the absolute change of carbon productivity was decomposed into a summation of the absolute quantitative influences of each industrial sector, for each influence factor (technological innovation and industrial structure adjustment) in each year. Furthermore, the relative decomposition model was built using a similar process. Finally, these models were applied to demonstrate the decomposition process in China. The decomposition results reveal several important conclusions: (a) technological innovation plays a far more important role than industrial structure adjustment; (b) industry and export trade exhibit great influence; (c) assigning the responsibility for CO 2 emission control to local governments, optimizing the structure of exports, and eliminating backward industrial capacity are highly essential to further increase China's carbon productivity. -- Highlights: ► Using the change of carbon productivity to measure a country's contribution. ► Absolute and relative decomposition models for carbon productivity are built. ► The change is decomposed to the quantitative influence of three-dimension. ► Decomposition results can be used for improving a country's carbon productivity.

  11. Photochemical decomposition of catecholamines

    International Nuclear Information System (INIS)

    Mol, N.J. de; Henegouwen, G.M.J.B. van; Gerritsma, K.W.

    1979-01-01

    During photochemical decomposition (lambda=254 nm) adrenaline, isoprenaline and noradrenaline in aqueous solution were converted to the corresponding aminochrome for 65, 56 and 35% respectively. In determining this conversion, photochemical instability of the aminochromes was taken into account. Irradiations were performed in such dilute solutions that the neglect of the inner filter effect is permissible. Furthermore, quantum yields for the decomposition of the aminochromes in aqueous solution are given. (Author)

  12. Domains and domain loss

    DEFF Research Database (Denmark)

    Haberland, Hartmut

    2005-01-01

    politicians and in the media, especially in the discussion whether some languages undergo ‘domain loss’ vis-à-vis powerful international languages like English. An objection that has been raised here is that domains, as originally conceived, are parameters of language choice and not properties of languages...

  13. A Longitudinal Study on Human Outdoor Decomposition in Central Texas.

    Science.gov (United States)

    Suckling, Joanna K; Spradley, M Katherine; Godde, Kanya

    2016-01-01

    The development of a methodology that estimates the postmortem interval (PMI) from stages of decomposition is a goal for which forensic practitioners strive. A proposed equation (Megyesi et al. 2005) that utilizes total body score (TBS) and accumulated degree days (ADD) was tested using longitudinal data collected from human remains donated to the Forensic Anthropology Research Facility (FARF) at Texas State University-San Marcos. Exact binomial tests examined the rate of the equation to successfully predict ADD. Statistically significant differences were found between ADD estimated by the equation and the observed value for decomposition stage. Differences remained significant after carnivore scavenged donations were removed from analysis. Low success rates for the equation to predict ADD from TBS and the wide standard errors demonstrate the need to re-evaluate the use of this equation and methodology for PMI estimation in different environments; rather, multivariate methods and equations should be derived that are environmentally specific. © 2015 American Academy of Forensic Sciences.

  14. Decomposing Nekrasov decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Morozov, A. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); Institute for Information Transmission Problems,19-1 Bolshoy Karetniy, Moscow, 127051 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Zenkevich, Y. [ITEP,25 Bolshaya Cheremushkinskaya, Moscow, 117218 (Russian Federation); National Research Nuclear University MEPhI,31 Kashirskoe highway, Moscow, 115409 (Russian Federation); Institute for Nuclear Research of Russian Academy of Sciences,6a Prospekt 60-letiya Oktyabrya, Moscow, 117312 (Russian Federation)

    2016-02-16

    AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.

  15. Decomposing Nekrasov decomposition

    International Nuclear Information System (INIS)

    Morozov, A.; Zenkevich, Y.

    2016-01-01

    AGT relations imply that the four-point conformal block admits a decomposition into a sum over pairs of Young diagrams of essentially rational Nekrasov functions — this is immediately seen when conformal block is represented in the form of a matrix model. However, the q-deformation of the same block has a deeper decomposition — into a sum over a quadruple of Young diagrams of a product of four topological vertices. We analyze the interplay between these two decompositions, their properties and their generalization to multi-point conformal blocks. In the latter case we explain how Dotsenko-Fateev all-with-all (star) pair “interaction” is reduced to the quiver model nearest-neighbor (chain) one. We give new identities for q-Selberg averages of pairs of generalized Macdonald polynomials. We also translate the slicing invariance of refined topological strings into the language of conformal blocks and interpret it as abelianization of generalized Macdonald polynomials.

  16. Effect of dislocations on spinodal decomposition in Fe-Cr alloys

    International Nuclear Information System (INIS)

    Li Yongsheng; Li Shuxiao; Zhang Tongyi

    2009-01-01

    Phase-field simulations of spinodal decomposition in Fe-Cr alloys with dislocations were performed by using the Cahn-Hilliard diffusion equation. The stress field of dislocations was calculated in real space via Stroh's formalism, while the composition inhomogeneity-induced stress field and the diffusion equation were numerically calculated in Fourier space. The simulation results indicate that dislocation stress field facilitates, energetically and kinetically, spinodal decomposition, making the phase separation faster and the separated phase particles bigger at and near the dislocation core regions. A tilt grain boundary is thus a favorable place for spinodal decomposition, resulting in a special microstructure morphology, especially at the early stage of decomposition.

  17. FDG decomposition products

    International Nuclear Information System (INIS)

    Macasek, F.; Buriova, E.

    2004-01-01

    In this presentation authors present the results of analysis of decomposition products of [ 18 ]fluorodexyglucose. It is concluded that the coupling of liquid chromatography - mass spectrometry with electrospray ionisation is a suitable tool for quantitative analysis of FDG radiopharmaceutical, i.e. assay of basic components (FDG, glucose), impurities (Kryptofix) and decomposition products (gluconic and glucuronic acids etc.); 2-[ 18 F]fluoro-deoxyglucose (FDG) is sufficiently stable and resistant towards autoradiolysis; the content of radiochemical impurities (2-[ 18 F]fluoro-gluconic and 2-[ 18 F]fluoro-glucuronic acids in expired FDG did not exceed 1%

  18. Thermal decomposition and reaction of confined explosives

    International Nuclear Information System (INIS)

    Catalano, E.; McGuire, R.; Lee, E.; Wrenn, E.; Ornellas, D.; Walton, J.

    1976-01-01

    Some new experiments designed to accurately determine the time interval required to produce a reactive event in confined explosives subjected to temperatures which will cause decomposition are described. Geometry and boundary conditions were both well defined so that these experiments on the rapid thermal decomposition of HE are amenable to predictive modelling. Experiments have been carried out on TNT, TATB and on two plastic-bonded HMX-based high explosives, LX-04 and LX-10. When the results of these experiments are plotted as the logarithm of the time to explosion versus 1/T K (Arrhenius plot), the curves produced are remarkably linear. This is in contradiction to the results obtained by an iterative solution of the Laplace equation for a system with a first order rate heat source. Such calculations produce plots which display considerable curvature. The experiments have also shown that the time to explosion is strongly influenced by the void volume in the containment vessel. Results of the experiments with calculations based on the heat flow equations coupled with first-order models of chemical decomposition are compared. The comparisons demonstrate the need for a more realistic reaction model

  19. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  20. The simplified spherical harmonics (SP{sub L}) methodology with space and moment decomposition in parallel environments

    Energy Technology Data Exchange (ETDEWEB)

    Gianluca, Longoni; Alireza, Haghighat [Florida University, Nuclear and Radiological Engineering Department, Gainesville, FL (United States)

    2003-07-01

    In recent years, the SP{sub L} (simplified spherical harmonics) equations have received renewed interest for the simulation of nuclear systems. We have derived the SP{sub L} equations starting from the even-parity form of the S{sub N} equations. The SP{sub L} equations form a system of (L+1)/2 second order partial differential equations that can be solved with standard iterative techniques such as the Conjugate Gradient (CG). We discretized the SP{sub L} equations with the finite-volume approach in a 3-D Cartesian space. We developed a new 3-D general code, Pensp{sub L} (Parallel Environment Neutral-particle SP{sub L}). Pensp{sub L} solves both fixed source and criticality eigenvalue problems. In order to optimize the memory management, we implemented a Compressed Diagonal Storage (CDS) to store the SP{sub L} matrices. Pensp{sub L} includes parallel algorithms for space and moment domain decomposition. The computational load is distributed on different processors, using a mapping function, which maps the 3-D Cartesian space and moments onto processors. The code is written in Fortran 90 using the Message Passing Interface (MPI) libraries for the parallel implementation of the algorithm. The code has been tested on the Pcpen cluster and the parallel performance has been assessed in terms of speed-up and parallel efficiency. (author)

  1. An iterative algorithm for solving the multidimensional neutron diffusion nodal method equations on parallel computers

    International Nuclear Information System (INIS)

    Kirk, B.L.; Azmy, Y.Y.

    1992-01-01

    In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines

  2. Inverse scale space decomposition

    DEFF Research Database (Denmark)

    Schmidt, Marie Foged; Benning, Martin; Schönlieb, Carola-Bibiane

    2018-01-01

    We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and even and positively one-homogeneous regularisation functionals, can decompose data represented...... by the application of a forward operator to a linear combination of generalised singular vectors into its individual singular vectors. We verify that for this decomposition to hold true, two additional conditions on the singular vectors are sufficient: orthogonality in the data space and inclusion of partial sums...... of the subgradients of the singular vectors in the subdifferential of the regularisation functional at zero. We also address the converse question of when the inverse scale space flow returns a generalised singular vector given that the initial data is arbitrary (and therefore not necessarily in the range...

  3. Magic Coset Decompositions

    CERN Document Server

    Cacciatori, Sergio L; Marrani, Alessio

    2013-01-01

    By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special K\\"ahler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.

  4. Wood decomposition as influenced by invertebrates.

    Science.gov (United States)

    Ulyshen, Michael D

    2016-02-01

    The diversity and habitat requirements of invertebrates associated with dead wood have been the subjects of hundreds of studies in recent years but we still know very little about the ecological or economic importance of these organisms. The purpose of this review is to examine whether, how and to what extent invertebrates affect wood decomposition in terrestrial ecosystems. Three broad conclusions can be reached from the available literature. First, wood decomposition is largely driven by microbial activity but invertebrates also play a significant role in both temperate and tropical environments. Primary mechanisms include enzymatic digestion (involving both endogenous enzymes and those produced by endo- and ectosymbionts), substrate alteration (tunnelling and fragmentation), biotic interactions and nitrogen fertilization (i.e. promoting nitrogen fixation by endosymbiotic and free-living bacteria). Second, the effects of individual invertebrate taxa or functional groups can be accelerative or inhibitory but the cumulative effect of the entire community is generally to accelerate wood decomposition, at least during the early stages of the process (most studies are limited to the first 2-3 years). Although methodological differences and design limitations preclude meta-analysis, studies aimed at quantifying the contributions of invertebrates to wood decomposition commonly attribute 10-20% of wood loss to these organisms. Finally, some taxa appear to be particularly influential with respect to promoting wood decomposition. These include large wood-boring beetles (Coleoptera) and termites (Termitoidae), especially fungus-farming macrotermitines. The presence or absence of these species may be more consequential than species richness and the influence of invertebrates is likely to vary biogeographically. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

  5. Kinetics of the decomposition reaction of phosphorite concentrate

    Directory of Open Access Journals (Sweden)

    Huang Run

    2014-01-01

    Full Text Available Apatite is the raw material, which is mainly used in phosphate fertilizer, and part are used in yellow phosphorus, red phosphorus, and phosphoric acid in the industry. With the decrease of the high grade phosphorite lump, the agglomeration process is necessary for the phosphorite concentrate after beneficiation process. The decomposition behavior and the phase transformation are of vital importance for the agglomeration process of phosphorite. In this study, the thermal kinetic analysis method was used to study the kinetics of the decomposition of phosphorite concentrate. The phosphorite concentrate was heated under various heating rate, and the phases in the sample heated were examined by the X-ray diffraction method. It was found that the main phases in the phosphorite are fluorapatiteCa5(PO43F, quartz SiO2,and dolomite CaMg(CO32.The endothermic DSC peak corresponding to the mass loss caused by the decomposition of dolomite covers from 600°C to 850°C. The activation energy of the decomposition of dolomite, which increases with the increase in the extent of conversion, is about 71.6~123.6kJ/mol. The mechanism equation for the decomposition of dolomite agrees with the Valensi equation and G-B equation.

  6. Thermal decomposition of potassium metaperiodate doped with trivalent ions

    Energy Technology Data Exchange (ETDEWEB)

    Muraleedharan, K., E-mail: kmuralika@gmail.com [Department of Chemistry, University of Calicut, Calicut, Kerala 673 635 (India); Kannan, M.P.; Gangadevi, T. [Department of Chemistry, University of Calicut, Calicut, Kerala 673 635 (India)

    2010-04-20

    The kinetics of isothermal decomposition of potassium metaperiodate (KIO{sub 4}), doped with phosphate and aluminium has been studied by thermogravimetry (TG). We introduced a custom-made thermobalance that is able to record weight decrease with time under pure isothermal conditions. The decomposition proceeds mainly through two stages: an acceleratory stages up to {alpha} = 0.50 and the decay stage beyond. The decomposition data for aluminium and phosphate doped KIO{sub 4} were found to be best described by the Prout-Tompkins equation. Separate kinetic analyses of the {alpha}-t data corresponding to the acceleratory region and decay region showed that the acceleratory stage gave the best fit with Prout-Tompkins equation itself whereas the decay stage fitted better to the contracting area equation. The rate of decomposition of phosphate doped KIO{sub 4} increases approximately linearly with an increase in the dopant concentration. In the case of aluminium doped KIO{sub 4}, the rate passes through a maximum with increase in the dopant concentration. The {alpha}-t data of pure and doped KIO{sub 4} were also subjected to isoconversional studies for the determination of activation energy values. Doping did not change the activation energy of the reaction. The results favour an electron-transfer mechanism for the isothermal decomposition of KIO{sub 4}, agreeing well with our earlier observations.

  7. Optimization and kinetics decomposition of monazite using NaOH

    International Nuclear Information System (INIS)

    MV Purwani; Suyanti; Deddy Husnurrofiq

    2015-01-01

    Decomposition of monazite with NaOH has been done. Decomposition performed at high temperature on furnace. The parameters studied were the comparison NaOH / monazite, temperature and time decomposition. From the research decomposition for 100 grams of monazite with NaOH, it can be concluded that the greater the ratio of NaOH / monazite, the greater the conversion. In the temperature influences decomposition 400 - 700°C, the greater the reaction rate constant with increasing temperature greater decomposition. Comparison NaOH / monazite optimum was 1.5 and the optimum time of 3 hours. Relations ratio NaOH / monazite with conversion (x) following the polynomial equation y = 0.1579x 2 – 0.2855x + 0.8301 (y = conversion and x = ratio of NaOH/monazite). Decomposition reaction of monazite with NaOH was second orde reaction, the relationship between temperature (T) with a reaction rate constant (k), k = 6.106.e - 1006.8 /T or ln k = - 1006.8/T + 6.106, frequency factor A = 448.541, activation energy E = 8.371 kJ/mol. (author)

  8. Toeplitz quantization and asymptotic expansions : Peter Weyl decomposition

    Czech Academy of Sciences Publication Activity Database

    Engliš, Miroslav; Upmeier, H.

    2010-01-01

    Roč. 68, č. 3 (2010), s. 427-449 ISSN 0378-620X R&D Projects: GA ČR GA201/09/0473 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded symmetric domain * real symmetric domain * star product * Toeplitz operator * Peter-Weyl decomposition Subject RIV: BA - General Mathematics Impact factor: 0.521, year: 2010 http://link.springer.com/article/10.1007%2Fs00020-010-1808-5

  9. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  10. Memory effect and fast spinodal decomposition

    International Nuclear Information System (INIS)

    Koide, T.; Krein, G.; Ramos, Rudnei O.

    2007-01-01

    We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and have the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region. (author)

  11. Domain analysis

    DEFF Research Database (Denmark)

    Hjørland, Birger

    2017-01-01

    The domain-analytic approach to knowledge organization (KO) (and to the broader field of library and information science, LIS) is outlined. The article reviews the discussions and proposals on the definition of domains, and provides an example of a domain-analytic study in the field of art studies....... Varieties of domain analysis as well as criticism and controversies are presented and discussed....

  12. Clustering via Kernel Decomposition

    DEFF Research Database (Denmark)

    Have, Anna Szynkowiak; Girolami, Mark A.; Larsen, Jan

    2006-01-01

    Methods for spectral clustering have been proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this work it is proposed that the affinity matrix is created based on the elements of a non-parametric density estimator. This matrix is then decomposed to obtain...... posterior probabilities of class membership using an appropriate form of nonnegative matrix factorization. The troublesome selection of hyperparameters such as kernel width and number of clusters can be obtained using standard cross-validation methods as is demonstrated on a number of diverse data sets....

  13. Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

    Science.gov (United States)

    Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

    2013-09-01

    Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

  14. Danburite decomposition by sulfuric acid

    International Nuclear Information System (INIS)

    Mirsaidov, U.; Mamatov, E.D.; Ashurov, N.A.

    2011-01-01

    Present article is devoted to decomposition of danburite of Ak-Arkhar Deposit of Tajikistan by sulfuric acid. The process of decomposition of danburite concentrate by sulfuric acid was studied. The chemical nature of decomposition process of boron containing ore was determined. The influence of temperature on the rate of extraction of boron and iron oxides was defined. The dependence of decomposition of boron and iron oxides on process duration, dosage of H 2 SO 4 , acid concentration and size of danburite particles was determined. The kinetics of danburite decomposition by sulfuric acid was studied as well. The apparent activation energy of the process of danburite decomposition by sulfuric acid was calculated. The flowsheet of danburite processing by sulfuric acid was elaborated.

  15. Thermal decomposition of lutetium propionate

    DEFF Research Database (Denmark)

    Grivel, Jean-Claude

    2010-01-01

    The thermal decomposition of lutetium(III) propionate monohydrate (Lu(C2H5CO2)3·H2O) in argon was studied by means of thermogravimetry, differential thermal analysis, IR-spectroscopy and X-ray diffraction. Dehydration takes place around 90 °C. It is followed by the decomposition of the anhydrous...... °C. Full conversion to Lu2O3 is achieved at about 1000 °C. Whereas the temperatures and solid reaction products of the first two decomposition steps are similar to those previously reported for the thermal decomposition of lanthanum(III) propionate monohydrate, the final decomposition...... of the oxycarbonate to the rare-earth oxide proceeds in a different way, which is here reminiscent of the thermal decomposition path of Lu(C3H5O2)·2CO(NH2)2·2H2O...

  16. Decomposition and reduction of AUC in hydrogen

    International Nuclear Information System (INIS)

    Ge Qingren; Kang Shifang; Zhou Meng

    1987-01-01

    AUC (Ammonium Uranyl Carbonate) conversion processes have been adopted extensively in nuclear fuel cycle. The kinetics investigation of these processes, however, has not yet been reported in detail at the published literatures. In the present work, the decomposition kinetics of AUC in hydrogen has been determined by non-isothermal method. DSC curves are solved with computer by Ge Qingren method. The results show that the kinetics obeys Avrami-Erofeev equation within 90% conversion. The apparent activation energy and preexponent are found to be 113.0 kJ/mol and 7.11 x 10 11 s -1 respectively. The reduction kinetics of AUC decomposition product in hydrogen at the range of 450 - 600 deg C has been determined by isothermal thermogravimetric method. The results show that good linear relationship can be obtained from the plot of conversion vs time, and that the apparent activation energy is found to be 113.9 kJ/mol. The effects of particle size and partial pressure of hydrogen are examined in reduction of AUC decomposition product. The reduction mechanism and the structure of particle are discussed according to the kinetics behaviour and SEM (scanning electron microscope) photograph

  17. Tensor gauge condition and tensor field decomposition

    Science.gov (United States)

    Zhu, Ben-Chao; Chen, Xiang-Song

    2015-10-01

    We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

  18. N3S project of fluid mechanics. High order in time methods by operator splitting. Application to Navier-Stokes equations; Projet N3S. Methode en temps d`ordre eleve par decomposition d`operateurs. Application aux equations de Navier-Stokes

    Energy Technology Data Exchange (ETDEWEB)

    Boukir, K

    1994-06-01

    This thesis deals with the extension to higher order in time of two splitting methods for the Navier-Stokes equations: the characteristics method and the projection one. The first consists in decoupling the convection operator from the Stokes one. The second decomposes this latter into a diffusion problem and a pressure-continuity one. Concerning the characteristics method, numerical and theoretical study is developed for the second order scheme together with a finite element spatial discretization. The case of a spectral spatial discretization is also treated and theoretical analysis are given respectively for second and third order schemes. For both spatial discretizations, we obtain good error estimates, unconditionally or under non stringent stability conditions, for both velocity and pressure. Numerical results illustrate the interest of the second order scheme comparing to the first order one. Extensions of the second order scheme to the K-epsilon turbulence model are proposed and tested, in the case of a finite element spatial discretization. Concerning the projection method, we define the order schemes. The theoretical study deals with stability and convergence of first and second order projection schemes, for the incompressible Navier-Stokes equations and with a finite element spatial discretization. The numerical study concerns mainly the second order scheme applied to the Navier-Stokes equations with varying density. (authors). 63 refs., figs.

  19. Tracking techniques for the characteristics method applied to the resolution of the neutrons transport equation in multi scale domains; Techniques de tracage pour la methode des caracteristiques appliquee a la resolution de l'equation du transport des neutrons en domaines multi-dimensionnels

    Energy Technology Data Exchange (ETDEWEB)

    Fevotte, F. [CEA Saclay, Dept. Modelisation de Systemes et Structures (DEN/DANS/DM2S/SERMA), 91 - Gif sur Yvette (France)

    2008-07-01

    At the various stages of a nuclear reactor's life, numerous studies are needed to guaranty the safety and efficiency of the design, analyse the fuel cycle, prepare the dismantlement, and so on. Due to the extreme difficulty to take extensive and accurate measurements in the reactor core, most of these studies are numerical simulations. The complete numerical simulation of a nuclear reactor involves many types of physics: neutronics, thermal hydraulics, materials, control engineering, Among these, the neutron transport simulation is one of the fundamental steps, since it allows computation - among other things - of various fundamental values such as the power density (used in thermal hydraulics computations) or fuel burn-up. The neutron transport simulation is based on the Boltzmann equation, which models the neutron population inside the reactor core. Among the various methods allowing its numerical solution, much interest has been devoted in the past few years to the Method of Characteristics in unstructured meshes (MOC), since it offers a good accuracy and operates in complicated geometries. The aim of this work is to propose improvements of the calculation scheme bound on the two dimensions MOC, in order to decrease the needed resources number. (A.L.B.)

  20. Texture of lipid bilayer domains

    DEFF Research Database (Denmark)

    Jensen, Uffe Bernchou; Brewer, Jonathan R.; Midtiby, Henrik Skov

    2009-01-01

    We investigate the texture of gel (g) domains in binary lipid membranes composed of the phospholipids DPPC and DOPC. Lateral organization of lipid bilayer membranes is a topic of fundamental and biological importance. Whereas questions related to size and composition of fluid membrane domain...... are well studied, the possibility of texture in gel domains has so far not been examined. When using polarized light for two-photon excitation of the fluorescent lipid probe Laurdan, the emission intensity is highly sensitive to the angle between the polarization and the tilt orientation of lipid acyl...... chains. By imaging the intensity variations as a function of the polarization angle, we map the lateral variations of the lipid tilt within domains. Results reveal that gel domains are composed of subdomains with different lipid tilt directions. We have applied a Fourier decomposition method...

  1. A High Temperature Kinetic Study for the Thermal Unimolecular Decomposition of Diethyl Carbonate

    KAUST Repository

    Alabbad, Mohammed

    2017-07-08

    Thermal unimolecular decomposition of diethyl carbonate (DEC) was investigated in a shock tube by measuring ethylene concentration with a CO2 gas laser over 900 - 1200 K and 1.2 – 2.8 bar. Rate coefficients were extracted using a simple kinetic scheme comprising of thermal decomposition of DEC as initial step followed by rapid thermal decomposition of the intermediate ethyl-hydrogen-carbonate. Our results were further analysed using ab initio and master equation calculations to obtain pressure- and temperature- dependence of rate coefficients. Similar to alkyl esters, unimolecular decomposition of DEC is found to undergo six-center retro-ene elimination of ethylene in a concerted manner.

  2. A High Temperature Kinetic Study for the Thermal Unimolecular Decomposition of Diethyl Carbonate

    KAUST Repository

    Alabbad, Mohammed; Giri, Binod; Szőri, Milan; Viskolcz, Bé la; Farooq, Aamir

    2017-01-01

    Thermal unimolecular decomposition of diethyl carbonate (DEC) was investigated in a shock tube by measuring ethylene concentration with a CO2 gas laser over 900 - 1200 K and 1.2 – 2.8 bar. Rate coefficients were extracted using a simple kinetic scheme comprising of thermal decomposition of DEC as initial step followed by rapid thermal decomposition of the intermediate ethyl-hydrogen-carbonate. Our results were further analysed using ab initio and master equation calculations to obtain pressure- and temperature- dependence of rate coefficients. Similar to alkyl esters, unimolecular decomposition of DEC is found to undergo six-center retro-ene elimination of ethylene in a concerted manner.

  3. SVD compression for magnetic resonance fingerprinting in the time domain.

    Science.gov (United States)

    McGivney, Debra F; Pierre, Eric; Ma, Dan; Jiang, Yun; Saybasili, Haris; Gulani, Vikas; Griswold, Mark A

    2014-12-01

    Magnetic resonance (MR) fingerprinting is a technique for acquiring and processing MR data that simultaneously provides quantitative maps of different tissue parameters through a pattern recognition algorithm. A predefined dictionary models the possible signal evolutions simulated using the Bloch equations with different combinations of various MR parameters and pattern recognition is completed by computing the inner product between the observed signal and each of the predicted signals within the dictionary. Though this matching algorithm has been shown to accurately predict the MR parameters of interest, one desires a more efficient method to obtain the quantitative images. We propose to compress the dictionary using the singular value decomposition, which will provide a low-rank approximation. By compressing the size of the dictionary in the time domain, we are able to speed up the pattern recognition algorithm, by a factor of between 3.4-4.8, without sacrificing the high signal-to-noise ratio of the original scheme presented previously.

  4. Darboux transformation and explicit solutions for some (2+1)-dimensional equations

    International Nuclear Information System (INIS)

    Wang Yan; Shen Lijuan; Du Dianlou

    2007-01-01

    Three systems of (2+1)-dimensional soliton equations and their decompositions into the (1+1)-dimensional soliton equations are proposed. These equations include KPI, CKP, MKPI. With the help of Darboux transformation of (1+1)-dimensional equations, we get the explicit solutions of the (2+1)-dimensional equations

  5. Concrete domains

    OpenAIRE

    Kahn, G.; Plotkin, G.D.

    1993-01-01

    This paper introduces the theory of a particular kind of computation domains called concrete domains. The purpose of this theory is to find a satisfactory framework for the notions of coroutine computation and sequentiality of evaluation.

  6. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  7. Proton mass decomposition

    Science.gov (United States)

    Yang, Yi-Bo; Chen, Ying; Draper, Terrence; Liang, Jian; Liu, Keh-Fei

    2018-03-01

    We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of Nf = 2 + 1 DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop pertur-bative calculation and proper normalization of the glue operator, we find that the u, d, and s quark masses contribute 9(2)% to the proton mass. The quark energy and glue field energy contribute 31(5)% and 37(5)% respectively in the MS scheme at µ = 2 GeV. The trace anomaly gives the remaining 23(1)% contribution. The u, d, s and glue momentum fractions in the MS scheme are consistent with the global analysis at µ = 2 GeV.

  8. Erbium hydride decomposition kinetics.

    Energy Technology Data Exchange (ETDEWEB)

    Ferrizz, Robert Matthew

    2006-11-01

    Thermal desorption spectroscopy (TDS) is used to study the decomposition kinetics of erbium hydride thin films. The TDS results presented in this report are analyzed quantitatively using Redhead's method to yield kinetic parameters (E{sub A} {approx} 54.2 kcal/mol), which are then utilized to predict hydrogen outgassing in vacuum for a variety of thermal treatments. Interestingly, it was found that the activation energy for desorption can vary by more than 7 kcal/mol (0.30 eV) for seemingly similar samples. In addition, small amounts of less-stable hydrogen were observed for all erbium dihydride films. A detailed explanation of several approaches for analyzing thermal desorption spectra to obtain kinetic information is included as an appendix.

  9. Art of spin decomposition

    International Nuclear Information System (INIS)

    Chen Xiangsong; Sun Weimin; Wang Fan; Goldman, T.

    2011-01-01

    We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular-momentum eigenstates. We split, from the total angular-momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular-momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.

  10. Domain Engineering

    Science.gov (United States)

    Bjørner, Dines

    Before software can be designed we must know its requirements. Before requirements can be expressed we must understand the domain. So it follows, from our dogma, that we must first establish precise descriptions of domains; then, from such descriptions, “derive” at least domain and interface requirements; and from those and machine requirements design the software, or, more generally, the computing systems.

  11. Thermal decomposition studies of CuInS2

    Institute of Scientific and Technical Information of China (English)

    Sunil H. CHAKI

    2008-01-01

    Single crystals of copper indium disulphide (CuInS2) have been successfully grown by the chemical vapour transport (CVT) technique using iodine as the transporting agent. Thermogravimetric analysis (TGA) and differential thermal analysis (DTA) were carried out for the CVT grown CuInS2 single crystals. It was revealed that the crystals are thermally stable between the ambient temperature (300 K) and 845 K and that the decomposi-tion occurs sequentially in three steps. The kinetic para-meters, e.g., activation energy, order of reaction, and frequency factor were evaluated using non-mechanistic equations for thermal decomposition.

  12. Decomposition methods for unsupervised learning

    DEFF Research Database (Denmark)

    Mørup, Morten

    2008-01-01

    This thesis presents the application and development of decomposition methods for Unsupervised Learning. It covers topics from classical factor analysis based decomposition and its variants such as Independent Component Analysis, Non-negative Matrix Factorization and Sparse Coding...... methods and clustering problems is derived both in terms of classical point clustering but also in terms of community detection in complex networks. A guiding principle throughout this thesis is the principle of parsimony. Hence, the goal of Unsupervised Learning is here posed as striving for simplicity...... in the decompositions. Thus, it is demonstrated how a wide range of decomposition methods explicitly or implicitly strive to attain this goal. Applications of the derived decompositions are given ranging from multi-media analysis of image and sound data, analysis of biomedical data such as electroencephalography...

  13. Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn

    Science.gov (United States)

    Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han

    2018-06-01

    We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.

  14. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  15. Danburite decomposition by hydrochloric acid

    International Nuclear Information System (INIS)

    Mamatov, E.D.; Ashurov, N.A.; Mirsaidov, U.

    2011-01-01

    Present article is devoted to decomposition of danburite of Ak-Arkhar Deposit of Tajikistan by hydrochloric acid. The interaction of boron containing ores of Ak-Arkhar Deposit of Tajikistan with mineral acids, including hydrochloric acid was studied. The optimal conditions of extraction of valuable components from danburite composition were determined. The chemical composition of danburite of Ak-Arkhar Deposit was determined as well. The kinetics of decomposition of calcined danburite by hydrochloric acid was studied. The apparent activation energy of the process of danburite decomposition by hydrochloric acid was calculated.

  16. AUTONOMOUS GAUSSIAN DECOMPOSITION

    Energy Technology Data Exchange (ETDEWEB)

    Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian [Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706 (United States); Heiles, Carl [Radio Astronomy Lab, UC Berkeley, 601 Campbell Hall, Berkeley, CA 94720 (United States); Hennebelle, Patrick [Laboratoire AIM, Paris-Saclay, CEA/IRFU/SAp-CNRS-Université Paris Diderot, F-91191 Gif-sur Yvette Cedex (France); Goss, W. M. [National Radio Astronomy Observatory, P.O. Box O, 1003 Lopezville, Socorro, NM 87801 (United States); Dickey, John, E-mail: rlindner@astro.wisc.edu [University of Tasmania, School of Maths and Physics, Private Bag 37, Hobart, TAS 7001 (Australia)

    2015-04-15

    We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes.

  17. AUTONOMOUS GAUSSIAN DECOMPOSITION

    International Nuclear Information System (INIS)

    Lindner, Robert R.; Vera-Ciro, Carlos; Murray, Claire E.; Stanimirović, Snežana; Babler, Brian; Heiles, Carl; Hennebelle, Patrick; Goss, W. M.; Dickey, John

    2015-01-01

    We present a new algorithm, named Autonomous Gaussian Decomposition (AGD), for automatically decomposing spectra into Gaussian components. AGD uses derivative spectroscopy and machine learning to provide optimized guesses for the number of Gaussian components in the data, and also their locations, widths, and amplitudes. We test AGD and find that it produces results comparable to human-derived solutions on 21 cm absorption spectra from the 21 cm SPectral line Observations of Neutral Gas with the EVLA (21-SPONGE) survey. We use AGD with Monte Carlo methods to derive the H i line completeness as a function of peak optical depth and velocity width for the 21-SPONGE data, and also show that the results of AGD are stable against varying observational noise intensity. The autonomy and computational efficiency of the method over traditional manual Gaussian fits allow for truly unbiased comparisons between observations and simulations, and for the ability to scale up and interpret the very large data volumes from the upcoming Square Kilometer Array and pathfinder telescopes

  18. NRSA enzyme decomposition model data

    Data.gov (United States)

    U.S. Environmental Protection Agency — Microbial enzyme activities measured at more than 2000 US streams and rivers. These enzyme data were then used to predict organic matter decomposition and microbial...

  19. Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

    Science.gov (United States)

    Man, Yiu-Kwong

    2012-01-01

    Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

  20. Spectral decomposition of nonlinear systems with memory

    Science.gov (United States)

    Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.

    2016-02-01

    We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.

  1. Separating Cognitive and Content Domains in Mathematical Competence

    Science.gov (United States)

    Harks, Birgit; Klieme, Eckhard; Hartig, Johannes; Leiss, Dominik

    2014-01-01

    The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

  2. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  3. Accelerating solutions of one-dimensional unsteady PDEs with GPU-based swept time-space decomposition

    Science.gov (United States)

    Magee, Daniel J.; Niemeyer, Kyle E.

    2018-03-01

    The expedient design of precision components in aerospace and other high-tech industries requires simulations of physical phenomena often described by partial differential equations (PDEs) without exact solutions. Modern design problems require simulations with a level of resolution difficult to achieve in reasonable amounts of time-even in effectively parallelized solvers. Though the scale of the problem relative to available computing power is the greatest impediment to accelerating these applications, significant performance gains can be achieved through careful attention to the details of memory communication and access. The swept time-space decomposition rule reduces communication between sub-domains by exhausting the domain of influence before communicating boundary values. Here we present a GPU implementation of the swept rule, which modifies the algorithm for improved performance on this processing architecture by prioritizing use of private (shared) memory, avoiding interblock communication, and overwriting unnecessary values. It shows significant improvement in the execution time of finite-difference solvers for one-dimensional unsteady PDEs, producing speedups of 2 - 9 × for a range of problem sizes, respectively, compared with simple GPU versions and 7 - 300 × compared with parallel CPU versions. However, for a more sophisticated one-dimensional system of equations discretized with a second-order finite-volume scheme, the swept rule performs 1.2 - 1.9 × worse than a standard implementation for all problem sizes.

  4. Faddeev wave function decomposition using bipolar harmonics

    International Nuclear Information System (INIS)

    Friar, J.L.; Tomusiak, E.L.; Gibson, B.F.; Payne, G.L.

    1981-01-01

    The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the 3 He Coulomb energy

  5. Speckle imaging using the principle value decomposition method

    International Nuclear Information System (INIS)

    Sherman, J.W.

    1978-01-01

    Obtaining diffraction-limited images in the presence of atmospheric turbulence is a topic of current interest. Two types of approaches have evolved: real-time correction and speckle imaging. A speckle imaging reconstruction method was developed by use of an ''optimal'' filtering approach. This method is based on a nonlinear integral equation which is solved by principle value decomposition. The method was implemented on a CDC 7600 for study. The restoration algorithm is discussed and its performance is illustrated. 7 figures

  6. Time characteristics for the spinodal decomposition in nuclear matter

    Energy Technology Data Exchange (ETDEWEB)

    Idier, D.; Farine, M.; Benhassine, B.; Remaud, B.; Sebille, F.

    1992-12-31

    Dynamics of the fluctuation growth are studied. Time characteristics are key quantities to determine the conditions under which spinodal decomposition could be observed. Dynamical instabilities arising from fluctuations in spinodal zone for nuclear matter are studied using Skyrme type interactions within a pseudo-particle model. Typical times for cluster formation are extracted. The numerical treatment is based on the Vlasov phase space transport equation. (K.A.) 11 refs.; 7 figs.

  7. Time characteristics for the spinodal decomposition in nuclear matter

    International Nuclear Information System (INIS)

    Idier, D.; Farine, M.; Benhassine, B.; Remaud, B.; Sebille, F.

    1992-01-01

    Dynamics of the fluctuation growth are studied. Time characteristics are key quantities to determine the conditions under which spinodal decomposition could be observed. Dynamical instabilities arising from fluctuations in spinodal zone for nuclear matter are studied using Skyrme type interactions within a pseudo-particle model. Typical times for cluster formation are extracted. The numerical treatment is based on the Vlasov phase space transport equation. (K.A.) 11 refs.; 7 figs

  8. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  9. Real interest parity decomposition

    Directory of Open Access Journals (Sweden)

    Alex Luiz Ferreira

    2009-09-01

    Full Text Available The aim of this paper is to investigate the general causes of real interest rate differentials (rids for a sample of emerging markets for the period of January 1996 to August 2007. To this end, two methods are applied. The first consists of breaking the variance of rids down into relative purchasing power pariety and uncovered interest rate parity and shows that inflation differentials are the main source of rids variation; while the second method breaks down the rids and nominal interest rate differentials (nids into nominal and real shocks. Bivariate autoregressive models are estimated under particular identification conditions, having been adequately treated for the identified structural breaks. Impulse response functions and error variance decomposition result in real shocks as being the likely cause of rids.O objetivo deste artigo é investigar as causas gerais dos diferenciais da taxa de juros real (rids para um conjunto de países emergentes, para o período de janeiro de 1996 a agosto de 2007. Para tanto, duas metodologias são aplicadas. A primeira consiste em decompor a variância dos rids entre a paridade do poder de compra relativa e a paridade de juros a descoberto e mostra que os diferenciais de inflação são a fonte predominante da variabilidade dos rids; a segunda decompõe os rids e os diferenciais de juros nominais (nids em choques nominais e reais. Sob certas condições de identificação, modelos autorregressivos bivariados são estimados com tratamento adequado para as quebras estruturais identificadas e as funções de resposta ao impulso e a decomposição da variância dos erros de previsão são obtidas, resultando em evidências favoráveis a que os choques reais são a causa mais provável dos rids.

  10. The influence of temperature on the decomposition kinetics of peracetic acid in solutions

    Directory of Open Access Journals (Sweden)

    Kunigk L.

    2001-01-01

    Full Text Available Peracetic acid is a powerful sanitizer that has only recently been introduced in the Brazilian food industry. The main disadvantage of this sanitizer is its decomposition rate. The main purpose of this paper is to present results obtained in experiments carried out to study the decomposition kinetics of peracetic acid in aqueous solutions at 25, 35, 40 and 45 °C. The decompositon of peracetic acid is a first-order reaction. The decomposition rate constants are between 1.71x10-3 h -1 for 25 °C and 9.64x10-3 h-1 for 45 °C. The decomposition rate constant is affected by temperature according to the Arrhenius equation, and the activation energy for the decomposition of peracetic acid in aqueous solutions prepared from the commercial formulation used in this work is 66.20 kJ/mol.

  11. Detailed RIF decomposition with selection : the gender pay gap in Italy

    OpenAIRE

    Töpfer, Marina

    2017-01-01

    In this paper, we estimate the gender pay gap along the wage distribution using a detailed decomposition approach based on unconditional quantile regressions. Non-randomness of the sample leads to biased and inconsistent estimates of the wage equation as well as of the components of the wage gap. Therefore, the method is extended to account for sample selection problems. The decomposition is conducted by using Italian microdata. Accounting for labor market selection may be particularly rele...

  12. The Numerical Solution of an Abelian Ordinary Differential Equation ...

    African Journals Online (AJOL)

    In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

  13. Exact Solutions of the Harry-Dym Equation

    International Nuclear Information System (INIS)

    Mokhtari, Reza

    2011-01-01

    The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation. (general)

  14. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  15. Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2007-01-01

    In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established

  16. On the hadron mass decomposition

    Science.gov (United States)

    Lorcé, Cédric

    2018-02-01

    We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force.

  17. On the hadron mass decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Lorce, Cedric [Universite Paris-Saclay, Centre de Physique Theorique, Ecole Polytechnique, CNRS, Palaiseau (France)

    2018-02-15

    We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force. (orig.)

  18. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  19. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  20. 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)

  1. Abstract decomposition theorem and applications

    CERN Document Server

    Grossberg, R; Grossberg, Rami; Lessmann, Olivier

    2005-01-01

    Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).

  2. An inherently parallel method for solving discretized diffusion equations

    International Nuclear Information System (INIS)

    Eccleston, B.R.; Palmer, T.S.

    1999-01-01

    A Monte Carlo approach to solving linear systems of equations is being investigated in the context of the solution of discretized diffusion equations. While the technique was originally devised decades ago, changes in computer architectures (namely, massively parallel machines) have driven the authors to revisit this technique. There are a number of potential advantages to this approach: (1) Analog Monte Carlo techniques are inherently parallel; this is not necessarily true to today's more advanced linear equation solvers (multigrid, conjugate gradient, etc.); (2) Some forms of this technique are adaptive in that they allow the user to specify locations in the problem where resolution is of particular importance and to concentrate the work at those locations; and (3) These techniques permit the solution of very large systems of equations in that matrix elements need not be stored. The user could trade calculational speed for storage if elements of the matrix are calculated on the fly. The goal of this study is to compare the parallel performance of Monte Carlo linear solvers to that of a more traditional parallelized linear solver. The authors observe the linear speedup that they expect from the Monte Carlo algorithm, given that there is no domain decomposition to cause significant communication overhead. Overall, PETSc outperforms the Monte Carlo solver for the test problem. The PETSc parallel performance improves with larger numbers of unknowns for a given number of processors. Parallel performance of the Monte Carlo technique is independent of the size of the matrix and the number of processes. They are investigating modifications to the scheme to accommodate matrix problems with positive off-diagonal elements. They are also currently coding an on-the-fly version of the algorithm to investigate the solution of very large linear systems

  3. Empirical projection-based basis-component decomposition method

    Science.gov (United States)

    Brendel, Bernhard; Roessl, Ewald; Schlomka, Jens-Peter; Proksa, Roland

    2009-02-01

    Advances in the development of semiconductor based, photon-counting x-ray detectors stimulate research in the domain of energy-resolving pre-clinical and clinical computed tomography (CT). For counting detectors acquiring x-ray attenuation in at least three different energy windows, an extended basis component decomposition can be performed in which in addition to the conventional approach of Alvarez and Macovski a third basis component is introduced, e.g., a gadolinium based CT contrast material. After the decomposition of the measured projection data into the basis component projections, conventional filtered-backprojection reconstruction is performed to obtain the basis-component images. In recent work, this basis component decomposition was obtained by maximizing the likelihood-function of the measurements. This procedure is time consuming and often unstable for excessively noisy data or low intrinsic energy resolution of the detector. Therefore, alternative procedures are of interest. Here, we introduce a generalization of the idea of empirical dual-energy processing published by Stenner et al. to multi-energy, photon-counting CT raw data. Instead of working in the image-domain, we use prior spectral knowledge about the acquisition system (tube spectra, bin sensitivities) to parameterize the line-integrals of the basis component decomposition directly in the projection domain. We compare this empirical approach with the maximum-likelihood (ML) approach considering image noise and image bias (artifacts) and see that only moderate noise increase is to be expected for small bias in the empirical approach. Given the drastic reduction of pre-processing time, the empirical approach is considered a viable alternative to the ML approach.

  4. Thermal decomposition of biphenyl (1963); Decomposition thermique du biphenyle (1963)

    Energy Technology Data Exchange (ETDEWEB)

    Clerc, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1962-06-15

    The rates of formation of the decomposition products of biphenyl; hydrogen, methane, ethane, ethylene, as well as triphenyl have been measured in the vapour and liquid phases at 460 deg. C. The study of the decomposition products of biphenyl at different temperatures between 400 and 460 deg. C has provided values of the activation energies of the reactions yielding the main products of pyrolysis in the vapour phase. Product and Activation energy: Hydrogen 73 {+-} 2 kCal/Mole; Benzene 76 {+-} 2 kCal/Mole; Meta-triphenyl 53 {+-} 2 kCal/Mole; Biphenyl decomposition 64 {+-} 2 kCal/Mole; The rate of disappearance of biphenyl is only very approximately first order. These results show the major role played at the start of the decomposition by organic impurities which are not detectable by conventional physico-chemical analysis methods and the presence of which accelerates noticeably the decomposition rate. It was possible to eliminate these impurities by zone-melting carried out until the initial gradient of the formation curves for the products became constant. The composition of the high-molecular weight products (over 250) was deduced from the mean molecular weight and the dosage of the aromatic C - H bonds by infrared spectrophotometry. As a result the existence in tars of hydrogenated tetra, penta and hexaphenyl has been demonstrated. (author) [French] Les vitesses de formation des produits de decomposition du biphenyle: hydrogene, methane, ethane, ethylene, ainsi que des triphenyles, ont ete mesurees en phase vapeur et en phase liquide a 460 deg. C. L'etude des produits de decomposition du biphenyle a differentes temperatures comprises entre 400 et 460 deg. C, a fourni les valeurs des energies d'activation des reactions conduisant aux principaux produits de la pyrolyse en phase vapeur. Produit et Energie d'activation: Hydrogene 73 {+-} 2 kcal/Mole; Benzene 76 {+-} 2 kcal/Mole; Metatriphenyle, 53 {+-} 2 kcal/Mole; Decomposition du biphenyle 64 {+-} 2 kcal/Mole; La

  5. Simulation and Domain Identification of Sea Ice Thermodynamic System

    Directory of Open Access Journals (Sweden)

    Bing Tan

    2012-01-01

    Full Text Available Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers with a time-dependent domain and its parameter identification problem. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as parametric variables and the deviation between the calculated and measured sea ice temperatures as the performance criterion. The unique existence of the weak solution of the thermodynamic system is proved. The properties of the identification problem and the existence of the optimal parameter are discussed, and the one-order necessary condition is derived. Finally, based on the nonoverlapping domain decomposition method and semi-implicit difference scheme, an optimization algorithm is proposed for the numerical simulation. Results show that the simulated temperature of sea ice fit well with the measured data, and the better fit is corresponding to the deeper sea ice.

  6. Direct solution of the biharmonic equation on rectangular regions and the Poisson equation on irregular regions

    International Nuclear Information System (INIS)

    Buzbee, B.L.; Dorr, F.W.

    1974-01-01

    The discrete biharmonic equation on a rectangular region and the discrete Poisson equation on an irregular region can be treated as modifications to matrix problems with very special structure. It is shown how to use the direct method of matrix decomposition to formulate an effective numerical algorithm for these problems. For typical applications the operation count is O(N 3 ) for an N x N grid. Numerical comparisons with other techniques are included. (U.S.)

  7. Bernoulli's Equation

    Indian Academy of Sciences (India)

    regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.

  8. Relativistic equations

    International Nuclear Information System (INIS)

    Gross, F.

    1986-01-01

    Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs

  9. Lie bialgebras with triangular decomposition

    International Nuclear Information System (INIS)

    Andruskiewitsch, N.; Levstein, F.

    1992-06-01

    Lie bialgebras originated in a triangular decomposition of the underlying Lie algebra are discussed. The explicit formulas for the quantization of the Heisenberg Lie algebra and some motion Lie algebras are given, as well as the algebra of rational functions on the quantum Heisenberg group and the formula for the universal R-matrix. (author). 17 refs

  10. Decomposition of metal nitrate solutions

    International Nuclear Information System (INIS)

    Haas, P.A.; Stines, W.B.

    1982-01-01

    Oxides in powder form are obtained from aqueous solutions of one or more heavy metal nitrates (e.g. U, Pu, Th, Ce) by thermal decomposition at 300 to 800 deg C in the presence of about 50 to 500% molar concentration of ammonium nitrate to total metal. (author)

  11. Probability inequalities for decomposition integrals

    Czech Academy of Sciences Publication Activity Database

    Agahi, H.; Mesiar, Radko

    2017-01-01

    Roč. 315, č. 1 (2017), s. 240-248 ISSN 0377-0427 Institutional support: RVO:67985556 Keywords : Decomposition integral * Superdecomposition integral * Probability inequalities Subject RIV: BA - General Mathematics OBOR OECD: Statistics and probability Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2017/E/mesiar-0470959.pdf

  12. Thermal decomposition of ammonium hexachloroosmate

    DEFF Research Database (Denmark)

    Asanova, T I; Kantor, Innokenty; Asanov, I. P.

    2016-01-01

    Structural changes of (NH4)2[OsCl6] occurring during thermal decomposition in a reduction atmosphere have been studied in situ using combined energy-dispersive X-ray absorption spectroscopy (ED-XAFS) and powder X-ray diffraction (PXRD). According to PXRD, (NH4)2[OsCl6] transforms directly to meta...

  13. Limited-memory adaptive snapshot selection for proper orthogonal decomposition

    Energy Technology Data Exchange (ETDEWEB)

    Oxberry, Geoffrey M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kostova-Vassilevska, Tanya [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Arrighi, Bill [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Chand, Kyle [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2015-04-02

    Reduced order models are useful for accelerating simulations in many-query contexts, such as optimization, uncertainty quantification, and sensitivity analysis. However, offline training of reduced order models can have prohibitively expensive memory and floating-point operation costs in high-performance computing applications, where memory per core is limited. To overcome this limitation for proper orthogonal decomposition, we propose a novel adaptive selection method for snapshots in time that limits offline training costs by selecting snapshots according an error control mechanism similar to that found in adaptive time-stepping ordinary differential equation solvers. The error estimator used in this work is related to theory bounding the approximation error in time of proper orthogonal decomposition-based reduced order models, and memory usage is minimized by computing the singular value decomposition using a single-pass incremental algorithm. Results for a viscous Burgers’ test problem demonstrate convergence in the limit as the algorithm error tolerances go to zero; in this limit, the full order model is recovered to within discretization error. The resulting method can be used on supercomputers to generate proper orthogonal decomposition-based reduced order models, or as a subroutine within hyperreduction algorithms that require taking snapshots in time, or within greedy algorithms for sampling parameter space.

  14. Domain crossing

    DEFF Research Database (Denmark)

    Schraefel, M. C.; Rouncefield, Mark; Kellogg, Wendy

    2012-01-01

    In CSCW, how much do we need to know about another domain/culture before we observe, intersect and intervene with designs. What optimally would that other culture need to know about us? Is this a “how long is a piece of string” question, or an inquiry where we can consider a variety of contexts a...

  15. Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method

    Directory of Open Access Journals (Sweden)

    Hooman Fatoorehchi

    2014-10-01

    Full Text Available In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial equation through the Adomian decomposition method equipped with a number of developed theorems from matrix algebra. These auxiliary theorems are associated with eigenvalues of matrices and enable convergence of the Adomian decomposition method toward different real roots of the target polynomial equation. To further improve the computational speed of our technique, a nonlinear convergence accelerator known as the Shanks transform has optionally been employed. For the sake of illustration, a number of numerical examples are given.

  16. Investigating hydrogel dosimeter decomposition by chemical methods

    International Nuclear Information System (INIS)

    Jordan, Kevin

    2015-01-01

    The chemical oxidative decomposition of leucocrystal violet micelle hydrogel dosimeters was investigated using the reaction of ferrous ions with hydrogen peroxide or sodium bicarbonate with hydrogen peroxide. The second reaction is more effective at dye decomposition in gelatin hydrogels. Additional chemical analysis is required to determine the decomposition products

  17. KEJAHATAN NAMA DOMAIN BERKAITAN DENGAN MEREK

    Directory of Open Access Journals (Sweden)

    Muhammad Nizar

    2018-02-01

    Full Text Available Indonesia already has an ITE Law governing domain names in general terms and on certain provisions in chapter VI, but the regulation of domain name crimes is not regulated in the ITE Law as mandated in the academic draft of the ITE Bill. The absence of regulation of domain name norm in the ITE Law creates problems with registrant of domain name (registrant which deliberately register the domain name is bad faith. The characteristic of a crime in a domain name relating to the mark is that the registered domain name has an equation in essence with another party’s well-known brand, the act of doing so by exploiting a reputation for well-known or previously commercially valuable names as domain names for addresses for sites (websites it manages. The Prosecutor may include articles of the KUHP in filing his indictment before the Court during the absence of special regulatory provisions concerning domain name crime.

  18. Systems of Inhomogeneous Linear Equations

    Science.gov (United States)

    Scherer, Philipp O. J.

    Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

  19. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    Science.gov (United States)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  20. Development of an object oriented nodal code using the refined AFEN derived from the method of component decomposition

    International Nuclear Information System (INIS)

    Noh, J. M.; Yoo, J. W.; Joo, H. K.

    2004-01-01

    In this study, we invented a method of component decomposition to derive the systematic inter-nodal coupled equations of the refined AFEN method and developed an object oriented nodal code to solve the derived coupled equations. The method of component decomposition decomposes the intra-nodal flux expansion of a nodal method into even and odd components in three dimensions to reduce the large coupled linear system equation into several small single equations. This method requires no additional technique to accelerate the iteration process to solve the inter-nodal coupled equations, since the derived equations can automatically act as the coarse mesh re-balance equations. By utilizing the object oriented programming concepts such as abstraction, encapsulation, inheritance and polymorphism, dynamic memory allocation, and operator overloading, we developed an object oriented nodal code that can facilitate the input/output and the dynamic control of the memories, and can make the maintenance easy. (authors)

  1. Trusted Domain

    DEFF Research Database (Denmark)

    Hjorth, Theis Solberg; Torbensen, Rune

    2012-01-01

    remote access via IP-based devices such as smartphones. The Trusted Domain platform fits existing legacy technologies by managing their interoperability and access controls, and it seeks to avoid the security issues of relying on third-party servers outside the home. It is a distributed system...... of wireless standards, limited resources of embedded systems, etc. Taking these challenges into account, we present a Trusted Domain home automation platform, which dynamically and securely connects heterogeneous networks of Short-Range Wireless devices via simple non-expert user. interactions, and allows......In the digital age of home automation and with the proliferation of mobile Internet access, the intelligent home and its devices should be accessible at any time from anywhere. There are many challenges such as security, privacy, ease of configuration, incompatible legacy devices, a wealth...

  2. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  3. Compression of magnetohydrodynamic simulation data using singular value decomposition

    International Nuclear Information System (INIS)

    Castillo Negrete, D. del; Hirshman, S.P.; Spong, D.A.; D'Azevedo, E.F.

    2007-01-01

    Numerical calculations of magnetic and flow fields in magnetohydrodynamic (MHD) simulations can result in extensive data sets. Particle-based calculations in these MHD fields, needed to provide closure relations for the MHD equations, will require communication of this data to multiple processors and rapid interpolation at numerous particle orbit positions. To facilitate this analysis it is advantageous to compress the data using singular value decomposition (SVD, or principal orthogonal decomposition, POD) methods. As an example of the compression technique, SVD is applied to magnetic field data arising from a dynamic nonlinear MHD code. The performance of the SVD compression algorithm is analyzed by calculating Poincare plots for electron orbits in a three-dimensional magnetic field and comparing the results with uncompressed data

  4. Dictionary-Based Tensor Canonical Polyadic Decomposition

    Science.gov (United States)

    Cohen, Jeremy Emile; Gillis, Nicolas

    2018-04-01

    To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

  5. Decomposition of diesel oil by various microorganisms

    Energy Technology Data Exchange (ETDEWEB)

    Suess, A; Netzsch-Lehner, A

    1969-01-01

    Previous experiments demonstrated the decomposition of diesel oil in different soils. In this experiment the decomposition of /sup 14/C-n-Hexadecane labelled diesel oil by special microorganisms was studied. The results were as follows: (1) In the experimental soils the microorganisms Mycoccus ruber, Mycobacterium luteum and Trichoderma hamatum are responsible for the diesel oil decomposition. (2) By adding microorganisms to the soil an increase of the decomposition rate was found only in the beginning of the experiments. (3) Maximum decomposition of diesel oil was reached 2-3 weeks after incubation.

  6. Variance decomposition in stochastic simulators.

    Science.gov (United States)

    Le Maître, O P; Knio, O M; Moraes, A

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  7. Variance decomposition in stochastic simulators

    Science.gov (United States)

    Le Maître, O. P.; Knio, O. M.; Moraes, A.

    2015-06-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  8. Variance decomposition in stochastic simulators

    Energy Technology Data Exchange (ETDEWEB)

    Le Maître, O. P., E-mail: olm@limsi.fr [LIMSI-CNRS, UPR 3251, Orsay (France); Knio, O. M., E-mail: knio@duke.edu [Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States); Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa [King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

    2015-06-28

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  9. Variance decomposition in stochastic simulators

    KAUST Repository

    Le Maî tre, O. P.; Knio, O. M.; Moraes, Alvaro

    2015-01-01

    This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

  10. Numerical solutions of diffusive logistic equation

    International Nuclear Information System (INIS)

    Afrouzi, G.A.; Khademloo, S.

    2007-01-01

    In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

  11. A domian Decomposition Method for Transient Neutron Transport with Pomrning-Eddington Approximation

    International Nuclear Information System (INIS)

    Hendi, A.A.; Abulwafa, E.E.

    2008-01-01

    The time-dependent neutron transport problem is approximated using the Pomraning-Eddington approximation. This approximation is two-flux approximation that expands the angular intensity in terms of the energy density and the net flux. This approximation converts the integro-differential Boltzmann equation into two first order differential equations. The A domian decomposition method that used to solve the linear or nonlinear differential equations is used to solve the resultant two differential equations to find the neutron energy density and net flux, which can be used to calculate the neutron angular intensity through the Pomraning-Eddington approximation

  12. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    International Nuclear Information System (INIS)

    Lee, Yoon Hee; Cho, Nam Zin

    2016-01-01

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  13. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)

    2016-05-15

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  14. Excimer laser decomposition of silicone

    International Nuclear Information System (INIS)

    Laude, L.D.; Cochrane, C.; Dicara, Cl.; Dupas-Bruzek, C.; Kolev, K.

    2003-01-01

    Excimer laser irradiation of silicone foils is shown in this work to induce decomposition, ablation and activation of such materials. Thin (100 μm) laminated silicone foils are irradiated at 248 nm as a function of impacting laser fluence and number of pulsed irradiations at 1 s intervals. Above a threshold fluence of 0.7 J/cm 2 , material starts decomposing. At higher fluences, this decomposition develops and gives rise to (i) swelling of the irradiated surface and then (ii) emission of matter (ablation) at a rate that is not proportioned to the number of pulses. Taking into consideration the polymer structure and the foil lamination process, these results help defining the phenomenology of silicone ablation. The polymer decomposition results in two parts: one which is organic and volatile, and another part which is inorganic and remains, forming an ever thickening screen to light penetration as the number of light pulses increases. A mathematical model is developed that accounts successfully for this physical screening effect

  15. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  16. Fast heap transform-based QR-decomposition of real and complex matrices: algorithms and codes

    Science.gov (United States)

    Grigoryan, Artyom M.

    2015-03-01

    In this paper, we describe a new look on the application of Givens rotations to the QR-decomposition problem, which is similar to the method of Householder transformations. We apply the concept of the discrete heap transform, or signal-induced unitary transforms which had been introduced by Grigoryan (2006) and used in signal and image processing. Both cases of real and complex nonsingular matrices are considered and examples of performing QR-decomposition of square matrices are given. The proposed method of QR-decomposition for the complex matrix is novel and differs from the known method of complex Givens rotation and is based on analytical equations for the heap transforms. Many examples illustrated the proposed heap transform method of QR-decomposition are given, algorithms are described in detail, and MATLAB-based codes are included.

  17. Decomposition of benzidine, α-naphthylamine, and p-toluidine in soils

    International Nuclear Information System (INIS)

    Graveel, J.G.; Sommers, L.E.; Nelson, D.W.

    1986-01-01

    Decomposition of 14 C-labeled benzidine, α-naphthylamine, and p-toluidine in soil was studied in laboratory experiments by monitoring CO 2 production during a 308- to 365-d incubation period. The importance of microbial activity in decomposition of all three aromatic amines was shown by decreased 14 CO 2 evolution in 60 Co treated soils. After 365 d of incubation, 8.4 to 12% of added benzidine (54.3 μmol kg -1 ) was evolved as CO 2 while 17 to 31% of added α-naphthylamine (69.8 μmol kg -1 ) and 19 to 35% of added p-toluidine (93.3 μmol kg -1 ) were evolved as CO 2 in 308 d. Decomposition was enhanced by increasing the temperature from 12 to 30 0 C. For benzidine, both the amount and proportion decomposed increased with an increase in application rate. Decomposition of aromatic amines was not enhanced by the addition of decomposable substrates. Differences in decomposition of aromatic amines occurred among soils, but consistent relationships between decomposition of amines and soil properties were not observed. In batch equilibration studies, the Freundlich equation described aromatic amine sorption. Isotherms were nonlinear for benzidine and 1 -naphthylamine and linear for p-toluidine. Desorption of sorbed amines followed the order: benzidine < p-toluidine < α-naphthylamine and was inversely related to the extent of decomposition

  18. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  19. Resolution of the neutron transport equation by massively parallel computer in the Cronos code

    International Nuclear Information System (INIS)

    Zardini, D.M.

    1996-01-01

    The feasibility of neutron transport problems parallel resolution by CRONOS code's SN module is here studied. In this report we give the first data about the parallel resolution by angular variable decomposition of the transport equation. Problems about parallel resolution by spatial variable decomposition and memory stage limits are also explained here. (author)

  20. Parabolized stability equations

    Science.gov (United States)

    Herbert, Thorwald

    1994-01-01

    The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.