WorldWideScience
 
 
1

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence  

CERN Document Server

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.

Chalupecký, Vladimír

2011-01-01

2

Discretization of convection-diffusion equations with finite-difference scheme derived from simplified analytical solutions  

International Nuclear Information System (INIS)

Most of thermal hydraulic processes in nuclear engineering can be described by general convection-diffusion equations that are often can be simulated numerically with finite-difference method (FDM). An effective scheme for finite-difference discretization of such equations is presented in this report. The derivation of this scheme is based on analytical solutions of a simplified one-dimensional equation written for every control volume of the finite-difference mesh. These analytical solutions are constructed using linearized representations of both diffusion coefficient and source term. As a result, the Efficient Finite-Differencing (EFD) scheme makes it possible to significantly improve the accuracy of numerical method even using mesh systems with fewer grid nodes that, in turn, allows to speed-up numerical simulation. EFD has been carefully verified on the series of sample problems for which either analytical or very precise numerical solutions can be found. EFD has been compared with other popular FDM schemes including novel, accurate (as well as sophisticated) methods. Among the methods compared were well-known central difference scheme, upwind scheme, exponential differencing and hybrid schemes of Spalding. Also, newly developed finite-difference schemes, such as the the quadratic upstream (QUICK) scheme of Leonard, the locally analytic differencing (LOAD) scheme of Wong and Raithby, the flux-spline scheme proposed by Varejago and Patankar as well as the latest LENS discretization of Sakai have been compared. Detailed results of this comparison are given in this report. These tests have shown a high efficiency of the EFD scheme. For most of sample problems considered EFD has demonstrated the numerical error that appeared to be in orders of magnitude lower than that of other discretization methods. Or, in other words, EFD has predicted numerical solution with the same given numerical error but using much fewer grid nodes. In this report, the detailed description of EFD is given. It includes basic assumptions, the detailed derivation, the verification procedure, as well verification and comparisons. Conclusion summarizes results and highlights the problems to be solved. (author)

2000-01-01

3

On second-order mimetic and conservative finite-difference discretization schemes  

Scientific Electronic Library Online (English)

Full Text Available SciELO Mexico | Language: English Abstract in spanish Aunque la derivación del esquema se puede realizar usando la reciente metodología de discretización numérica conocida como Diferencias Finitas Miméticas, estaremos presentando la derivación de un esquema de discretización mimético en diferencias finitas de segundo orden en una forma mas intuitiva, m [...] ediante el uso de expansiones de Taylor. Considerando que los estudiantes se familiarizan con expansiones de Taylor en los primeros cursos de cálculo y métodos matemáticos para físicos, pensamos que la presente alternativa de presentar este nuevo esquema de discretización es más favorable de ser asimilada en cursos de computación numérica tanto de pregrado como de postgrado. La robusticidad del esquema será ilustrada encontrando la solución numérica de un problema unidimensional del tipo capa límite difícil de resolver en forma numérica y que se basa en la ecuación de difusión estacionaria. Más aun, dado que el esquema de discretización alcanza segundo orden de precisión en todo el dominio computacional (incluyendo las fronteras), como ejercicio comparativo el mismo puede ser rápidamente aplicado para resolver ejemplos comúnmente encontrados en textos sobre métodos numéricos aplicados y que se resuelven usando otras metodologías numéricas (incluyendo algunos esquemas de discretización en diferencias finitas) Abstract in english Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as Mimetic Finite-Difference Approach, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansion [...] s. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries), as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite-diffence discretization schemes)

S, Rojas; J.M, Guevara-Jordan.

4

Upwind Compact Finite Difference Schemes  

Science.gov (United States)

It was shown by Ciment, Leventhal, and Weinberg ( J. Comput. Phys.28 (1978), 135) that the standard compact finite difference scheme may break down in convection dominated problems. An upwinding of the method, which maintains the fourth order accuracy, is suggested and favorable numerical results are found for a number of test problems.

Christie, I.

1985-07-01

5

THEORETICAL OPTIMIZATION OF FINITE DIFFERENCE SCHEMES  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the numerical error is taken into account. The theoretical study of a related linear algebraic problem gives general results which can lead to the determination of the optimal scheme.

2006-01-01

6

Applications of nonstandard finite difference schemes  

CERN Multimedia

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain

Mickens, Ronald E

2000-01-01

7

Finite Element, Discontinuous Galerkin, and Finite Difference evolution schemes in spacetime  

CERN Multimedia

Numerical schemes for the vacuum Einstein equations are developed. The Einstein equation in harmonic gauge is second order symmetric hyperbolic. It is discretized in four-dimensional spacetime by Finite Differences, Finite Elements, and Interior Penalty Discontinuous Galerkin methods, the latter related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and non-linear test problems of the Apples-with-Apples collection.

Zumbusch, Gerhard

2009-01-01

8

Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime  

International Nuclear Information System (INIS)

Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.

2009-09-07

9

Semigroup stability of finite difference schemes for multidimensional hyperbolic initial-boundary value problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We develop a simple energy method to prove the stability of finite difference schemes for multidimensional hyperbolic initial boundary value problems. In particular we extend to several space dimensions a crucial result by Goldberg and Tadmor. This allows us to give two conditions on the discretized operator that ensure that stability estimates for zero initial data imply a semigroup stability estimate for general initial data. We then apply this criterion to several numerical schemes in two ...

Coulombel, Jean-franc?ois; Gloria, Antoine

2011-01-01

10

An explicit finite difference scheme for the Camassa-Holm equation  

CERN Document Server

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general $H^1$ initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in $H^1$ towards a dissipative weak solution of Camassa-Holm equation.

Coclite, Giuseppe Maria; Risebro, Nils Henrik

2008-01-01

11

Finite element, discontinuous Galerkin, and finite difference evolution schemes in spacetime  

Energy Technology Data Exchange (ETDEWEB)

Numerical schemes for Einstein's vacuum equation are developed. Einstein's equation in harmonic gauge is second-order symmetric hyperbolic. It is discretized in four-dimensional spacetime by finite differences, finite elements and interior penalty discontinuous Galerkin methods, the latter being related to Regge calculus. The schemes are split into space and time and new time-stepping schemes for wave equations are derived. The methods are evaluated for linear and nonlinear test problems of the Apples-with-Apples collection.

Zumbusch, G, E-mail: gerhard.zumbusch@uni-jena.d [Institut fuer Angewandte Mathematik, Friedrich-Schiller-Universitaet Jena, 07743 Jena (Germany)

2009-09-07

12

Approximation of systems of partial differential equations by finite difference schemes  

International Nuclear Information System (INIS)

The approximation of Friedrichs' symmetric systems by a finite difference scheme with second order accuracy with respect to the step of discretization is studied. Unconditional stability of such a scheme is proved by the method of energy increase. This implicit scheme is then solved by three iterative methods: the first one, of the gradient type, converges slowly, the second one, of the Gauss-Seidel type, converges only if the system has been regularized to the first order with respect to the step of discretization by an elliptic operator, the last one, of the under-relaxation type, converges rapidly to a second order accurate solution. Explicit schemes for the integration of linear hyperbolic systems of evolution are considered. Conditional stability is proved for different schemes: Crank Nicolson, Leap-frog, Explicit, Predictor-corrector. Results relative to the explicit scheme are generalized to a quasi-linear, monotone system. Finally, stability and convergence in the solution of a finite difference scheme approximating an elliptic-parabolic equation, and an iterative method of relaxation for solving this scheme are studied. (author)

1971-01-01

13

On standard finite difference discretizations of the elliptic Monge-Ampere equation  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Given an orthogonal lattice with mesh length h on a bounded convex domain, we show that the Aleksandrov solution of the Monge-Ampere equation is the limit in a discrete L2 norm of mesh functions which solve discrete Monge-Ampere equations with the Hessian discretized using the standard finite difference method. The result provides the mathematical foundation of methods based on the standard finite difference method and designed to numerically converge to non-smooth solutions.

Awanou, Gerard

2013-01-01

14

Single-cone real-space finite difference scheme for the time-dependent Dirac equation  

CERN Document Server

A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme and its properties are presented for the two-component (2+1)D Dirac equation.

Hammer, René; Arnold, Anton

2013-01-01

15

A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations  

CERN Multimedia

In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent and discuss the applicability of them to nonlinear PDE's as well as to the case of variable coefficients. Moreover, we systematically use another symbolic technique, namely the cylindrical algebraic decomposition, in order to derive the conditions on the von Neumann stability of a difference s cheme for a linear PDE with constant coefficients. For stable schemes we demonst rate algorithmic and symbolic approach to handle both continuous and discrete di spersion. We present an implementation of tools for generation of schemes, which rely on Gr\\"obner basis, in the system SINGULAR and present numerous e xamples, computed with our implementation. In the stability analysis, we use the system MATHEMATICA for cylindrical algebraic decomposition.

Levandovskyy, Viktor

2010-01-01

16

High-Order Finite Difference GLM-MHD Schemes for Cell-Centered MHD  

CERN Multimedia

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting...

Mignone, A; Bodo, G

2010-01-01

17

Converged accelerated finite difference scheme for the multigroup neutron diffusion equation  

Energy Technology Data Exchange (ETDEWEB)

Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)

Terranova, N.; Mostacci, D. [DIENCA - Dipartimento di Ingegneria Energetica Nucleare e del Controllo Ambientale, Universita Alma Mater Studiorum, Bologna (Italy); Ganapol, B. D. [Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson AZ (United States)

2013-07-01

18

Spurious lattice solitons for linear finite difference schemes  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The goal of this work is to show that lattice traveling solitary wave are solution of the general linear finite-differenced version of the linear advection equation. The occurance of such a spurious solitary waves, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to has a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasse...

David, Claire

2010-01-01

19

Finite Difference Weighted Essentially Non-Oscillatory Schemes with Constrained Transport for Ideal Magnetohydrodynamics  

CERN Multimedia

In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vecto...

Christlieb, Andrew J; Tang, Qi

2013-01-01

20

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations  

Science.gov (United States)

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Abramopoulos, Frank

1988-01-01

 
 
 
 
21

A comparison of some implicit finite difference schemes used in flow boiling analysis  

International Nuclear Information System (INIS)

This study has been limited to low order schemes which are already used in some system codes. We have tested them on the simplest two-phase flow model, i.e. the three equations homogeneous model. The main objective of the paper is to prove that the need for further comparisons is doubtless. We review briefly the difficulties which must be overcome for the comparisons to be valid. First of all, the discretization of the three conservation equations yields to non linear dicrete systems. The types of linearization used in codes such as RAMA, K. FIX and CLYSTERE are not equivalent at all and this might have a non-negligible infuence on the results and on the computer-time used to solve a particular problem. Secondly, for implicit schemes, the method to solve the linearized system should be the same, for instance Gaussian elimination with pivoting. Thirdly, special treatments for dealing with discontinuities such as the Boiling Boundary, the breech, if any, must be the same. If has been proven that some schemes can handle discontinuities much better than other and that's also an important point of comparison. These restrictions have convinced ourselves that a good comparison should be made with a unique code, specially designed to be very flexible with respect to the Finite Difference Scheme used

1981-02-01

22

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES  

Science.gov (United States)

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

23

Development and application of a third order scheme of finite differences centered in mesh  

International Nuclear Information System (INIS)

In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)

2003-09-10

24

A finite difference scheme for a degenerated diffusion equation arising in microbial ecology  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first property leads to a finite speed of interface propagation if the initial data have compact support, while the second one introduces counter-acting super diffusion. This squeezing property of this model leads to steep gradients at the interface. Moving interface problems of this kind are known to be problematic for classical numerical methods and introduce non-physical and non-mathematical solutions. The proposed method is developed to address this observation. The central idea is a non-local (in time representation of the diffusion operator. It can be shown that the proposed method is free of oscillations at the interface, that the discrete interface satisfies a discrete version of the continuous interface condition and that the effect of interface smearing is quantitatively small.

Hermann J. Eberl

2007-02-01

25

Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics  

Science.gov (United States)

In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.

Christlieb, Andrew J.; Rossmanith, James A.; Tang, Qi

2014-07-01

26

Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems  

Science.gov (United States)

Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

Skollermo, G.

1979-01-01

27

Construction of finite difference schemes having special properties for ordinary and partial differential equations  

Science.gov (United States)

Work on the construction of finite difference models of differential equations having zero truncation errors is summarized. Both linear and nonlinear unidirectional wave equations are discussed. Results regarding the construction of zero truncation error schemes for the full wave equation and Burger's equation are also briefly reported.

Mickens, R. E.

1984-01-01

28

On the effective accuracy of spectral-like optimized finite-difference schemes for computational aeroacoustics  

Science.gov (United States)

The present article aims at highlighting the strengths and weaknesses of the so-called spectral-like optimized (explicit central) finite-difference schemes, when the latter are used for numerically approximating spatial derivatives in aeroacoustics evolution problems. With that view, we first remind how differential operators can be approximated using explicit central finite-difference schemes. The possible spectral-like optimization of the latter is then discussed, the advantages and drawbacks of such an optimization being theoretically studied, before they are numerically quantified. For doing so, two popular spectral-like optimized schemes are assessed via a direct comparison against their standard counterparts, such a comparative exercise being conducted for several academic test cases. At the end, general conclusions are drawn, which allows us discussing the way spectral-like optimized schemes shall be preferred (or not) to standard ones, when it comes to simulate real-life aeroacoustics problems.

Cunha, G.; Redonnet, S.

2014-04-01

29

Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We investigate asymptotic convergence in the~$\\Delta x \\!\\rightarrow\\! 0$ limit as a tool for determining whether numerical computations involving shocks are accurate. We use one-dimensional operator-split finite-difference schemes for hydrodynamics with a von Neumann artificial viscosity. An internal-energy scheme converges to demonstrably wrong solutions. We associate this failure with the presence of discontinuities in the limiting solution. Our extension of the Lax-Wendr...

Kimoto, Paul A.; Chernoff, David F.

1993-01-01

30

Spurious solitons and structural stability of finite-difference schemes for non-linear wave equations  

International Nuclear Information System (INIS)

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a finite-difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of non-linear wave equation. The occurrence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to has a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solution of the original continuous equations.

2009-07-30

31

Lie group invariant finite difference schemes for the neutron diffusion equation  

Energy Technology Data Exchange (ETDEWEB)

Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.

Jaegers, P.J.

1994-06-01

32

A new finite difference scheme for a dissipative cubic nonlinear Schrödinger equation  

International Nuclear Information System (INIS)

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient. (general)

2011-03-01

33

Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation  

Science.gov (United States)

We present a new approach for the construction of stochastic subgrid scale parameterizations. Starting from a high-resolution finite-difference discretization of some model equations, the new approach is based on splitting the model variables into fast, small-scale and slow, large-scale modes by averaging the model discretization over neighboring grid cells. After that, the fast modes are eliminated by applying a stochastic mode reduction procedure. This procedure is a generalization of the mode reduction strategy proposed by Majda, Timofeyev & Vanden-Eijnden, in that it allows for oscillations in the closure assumption. The new parameterization is applied to the forced Burgers equation and is compared with a Smagorinsky-type subgrid scale closure.

Dolaptchiev, S. I.; Achatz, U.; Timofeyev, I.

2013-06-01

34

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws  

Science.gov (United States)

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( ?) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

35

Finite difference schemes for incompressible flows in the velocity-impulse density formulation  

International Nuclear Information System (INIS)

We consider finite difference schemes based on the impulse density variable. We show that the original velocity-impulse density formulation of Oseledets is marginally ill-posed for the inviscid flow, and this has the consequence that some ordinarily stable numerical methods in other formulations become unstable in the velocity-impulse density formulation. We present numerical evidence of this instability. We then discuss the construction of stable finite difference schemes by requiring that at the numerical level the nonlinear terms be convertible to similar terms in the primitive variable formulation. Finally we give a simplified velocity-impulse density formulation which is free of these complications and yet retains the nice features of the original velocity-impulse density formulation with regard to the treatment of boundary. We present numerical results on this simplified formulation for the driven cavity flow on both the staggered and non-staggered grids. 21 refs., 11 figs

1997-01-01

36

A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent and discuss the applicability of them to nonlinear PDE's as well as to the case of variable coefficients. Moreover, we systematically use another symbolic technique, namely the cylindrical algebraic decomposition, in order to derive the con...

Levandovskyy, Viktor; Martin, Bernd

2010-01-01

37

A finite difference scheme for a degenerated diffusion equation arising in microbial ecology  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A finite difference scheme is presented for a density-dependent diffusion equation that arises in the mathematical modelling of bacterial biofilms. The peculiarity of the underlying model is that it shows degeneracy as the dependent variable vanishes, as well as a singularity as the dependent variable approaches its a priori known upper bound. The first property leads to a finite speed of interface propagation if the initial data have compact support, while the second one introduces counter...

2007-01-01

38

Discrete level schemes  

International Nuclear Information System (INIS)

An entirely new discrete levels segment has been created by the Budapest group according to the recommended principles, using the Evaluated Nuclear Structure Data File, ENSDF as a source. The resulting segment contains 96,834 levels and 105,423 gamma rays for 2,585 nuclei, with their characteristics such as energy, spin, parity, half-life as well as gamma-ray energy and branching percentage. Isomer flags for half-lives longer than 1 s have been introduced. For those 1,277 nuclei having at least ten known levels the cutoff level numbers Nm have been determined from fits to the cumulative number of levels. The level numbers Nc associated with the cutoff energies Uc, corresponding to the upper energy limit of levels with unique spin and parity, have been included for each nuclide. The segment has the form of an ASCII file which follows the extended ENEA Bologna convention. For the RIPL Starter File the new Budapest file is recommended as a Discrete Level Schemes Segment because it is most complete, up-to-date, and also well documented. Moreover, the cutoff energies have been determined in a consistent way, giving also hints about basic level density parameters. The recommended files are budapest-levels.dat and budapest-cumulative.dat. As alternative choices, the libraries from Beijing, Bologna, JAERI, Obninsk and Livermore may also be used for special applications. (author)

1998-08-01

39

A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics  

International Nuclear Information System (INIS)

The authors present a high-order accurate weighted essentially non-oscillatory (WENO) finite difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This scheme is a direct extension of a WENO scheme, which has been successfully applied to hydrodynamic problems. The WENO scheme follows the same idea of an essentially non-oscillatory (ENO) scheme with an advantage of achieving higher-order accuracy with fewer computations. Both ENO and WENO can be easily applied to two and three spatial dimensions by evaluating the fluxes dimension-by-dimension. Details of the WENO scheme as well as the construction of a suitable eigen-system, which can properly decompose various families of MHD waves and handle the degenerate situations, are presented. Numerical results are shown to perform well for the one-dimensional Brio-Wu Riemann problems, the two-dimensional Kelvin-Helmholtz instability problems, and the two-dimensional Orszag-Tang MHD vortex system. They also demonstrate the importance of maintaining the divergence free condition for the magnetic field in achieving numerical stability. The tests also show the advantages of using the higher-order scheme. The new 5th-order WENO MHD code can attain an accuracy comparable with that of the second-order schemes with many fewer grid points

1999-04-10

40

a Two-Level Second-Order Finite Difference Scheme for the Single Term Structure Equation  

Science.gov (United States)

In the paper [6] the classical single factor term structure equation for models that predict non-negative interest rates is numerically studied. For these models the authors proposed a second order accurate three-level finite difference scheme (FDs) using the appropriate boundary conditions at zero. For the same problem we propose a two-level second-order accurate FDs. We also propose an effective algorithm for solving the difference schemes, for which also follows the positivity of the numerical solution. The flexibility of our FDs makes it easy to change the drift and diffusion terms in the model. The numerical experiments confirm the second-order of accuracy of the scheme and the positivity-convexity property.

Chernogorova, T.; Valkov, R.

2011-12-01

 
 
 
 
41

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves  

CERN Multimedia

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid ...

Lombard, Bruno; Gélis, Céline; Virieux, Jean

2007-01-01

42

Optimally Accurate Second-Order Time-Domain Finite-Difference Scheme for Acoustic, Electromagnetic, and Elastic Wave Modeling  

Directory of Open Access Journals (Sweden)

Full Text Available Numerical methods are extremely useful in solving real-life problems with complex materials and geometries. However, numerical methods in the time domain suffer from artificial numerical dispersion. Standard numerical techniques which are second-order in space and time, like the conventional Finite Difference 3-point (FD3 method, Finite-Difference Time-Domain (FDTD method, and Finite Integration Technique (FIT provide estimates of the error of discretized numerical operators rather than the error of the numerical solutions computed using these operators. Here optimally accurate time-domain FD operators which are second-order in time as well as in space are derived. Optimal accuracy means the greatest attainable accuracy for a particular type of scheme, e.g., second-order FD, for some particular grid spacing. The modified operators lead to an implicit scheme. Using the first order Born approximation, this implicit scheme is transformed into a two step explicit scheme, namely predictor-corrector scheme. The stability condition (maximum time step for a given spatial grid interval for the various modified schemes is roughly equal to that for the corresponding conventional scheme. The modified FD scheme (FDM attains reduction of numerical dispersion almost by a factor of 40 in 1-D case, compared to the FD3, FDTD, and FIT. The CPU time for the FDM scheme is twice of that required by the FD3 method. The simulated synthetic data for a 2-D P-SV (elastodynamics problem computed using the modified scheme are 30 times more accurate than synthetics computed using a conventional scheme, at a cost of only 3.5 times as much CPU time. The FDM is of particular interest in the modeling of large scale (spatial dimension is more or equal to one thousand wave lengths or observation time interval is very high compared to reference time step wave propagation and scattering problems, for instance, in ultrasonic antenna and synthetic scattering data modeling for Non-Destructive Testing (NDT applications, where other standard numerical methods fail due to numerical dispersion effects. The possibility of extending this method to staggered grid approach is also discussed. The numerical FD3, FDTD, FIT, and FDM results are compared against analytical solutions.

C. Bommaraju

2005-01-01

43

Optimized explicit finite-difference schemes for spatial derivatives using maximum norm  

Science.gov (United States)

Conventional explicit finite-difference methods have difficulties in handling high-frequency components due to strong numerical dispersions. One can reduce the numerical dispersions by optimizing the constant coefficients of the finite-difference operator. Different from traditional optimized schemes that use the 2-norm and the least squares, we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing algorithm. Both theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three aspects. First, it provides us with much more flexibility when designing the objective functions; thus we can use various possible forms and contents to make the objective functions more reasonable. Second, it allows for tighter error limitation, which is shown to be necessary to avoid rapid error accumulations for simulations on large-scale models with long travel times. Finally, it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits, which means greater savings in computational efforts and memory demand.

Zhang, Jin-Hai; Yao, Zhen-Xing

2013-10-01

44

Finite difference scheme for semiconductor Boltzmann equation with nonlinear collision operator  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper the Boltzmann equation describing electron flow ina semiconductor device is considered. The doping profile and the selfconsistent electric field are related by the Poisson equation. Time dependentsolutions to the Boltzmann-Poisson system are obtained byusing a finite difference numerical scheme. The collision operator ofthe Boltzmann equation models the scattering processes between electronsand phonons which are assumed in thermal equilibrium, and takesinto account the Pauli’s exclusion principle. Numerical results for onedimensional n+ ? n ? n+ silicon device are shown.

C. L. R. Milazzo

2013-01-01

45

A fourth-order finite difference scheme for the numerical solution of 1D linear hyperbolic equation  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, a high-order and unconditionally stable difference method is proposed for the numerical solution of one-space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivative of this equation and a Pade approximation of fifth-order for the resulting system of ordinary differential equations. It is shown through analysis that the proposed scheme is unconditionally stable. This new method is easy to implement, produces very accurate results and needs short CPU time. Some numerical examples are included to demonstrate the validity and applicability of the technique. We compare the numerical results of this paper with the numerical results of some methods in the literature.

Akbar Mohebbi

2013-10-01

46

Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme  

CERN Multimedia

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\\it i.e.}, all terms in the Bianchi identities (which all vary as $\\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\\partial g\\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $...

Meier, D L

2003-01-01

47

Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations  

DEFF Research Database (Denmark)

This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local nonlinear analysis. The various methods of analysis combine to provide significant insight into into the numerical behavior of this rather complicated system of nonlinear PDEs.

Fuhrmann, David R.; Bingham, Harry B.

2004-01-01

48

A finite difference scheme for magneto-thermo analysis of an infinite cylinder  

Directory of Open Access Journals (Sweden)

Full Text Available A finite different scheme as well as least-square method is presented for the magneto-thermo analysis of an infinite functionally graded hollow cylinder. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are investigated along the radial direction of the cylinder. Material properties are assumed to be graded in the radial direction according to a novel exponential-law distribution in terms of the volume fractions of the metal and ceramic constituents. The governing second-order differential equations are derived from the equations of motion and the heat-conduction equation. The system of differential equations is solved numerically and some plots for displacement, radial stress, and temperature are presented.

Daoud S. Mashat

2010-11-01

49

Fuzzy logic to improve efficiency of finite element and finite difference schemes  

Energy Technology Data Exchange (ETDEWEB)

This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.

Garcia, M.D. [Los Alamos National Lab., NM (United States); Heger, A.S. [New Mexico Univ., Albuquerque, NM (United States)

1994-05-01

50

A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates  

Energy Technology Data Exchange (ETDEWEB)

A finite-difference scheme for the direct simulation of the incompressible time-dependent three-dimensional Navier-Stokes equations in cylindrical coordinates is presented. The equations in primitive variables (v{sub r}, v{sub H}, v{sub 2} and p) are solved by a fractional-step method together with an approximate-factorization technique. Cylindrical coordinates are singular at the axis; the introduction of the radial flux q{sub r} = r{center_dot}v{sub r} on a staggered grid simplifies the treatment of the region at r = 0. The method is tested by comparing the evolution of a free vortex ring and its collision with a wall with the theory, experiments, and other numerical results. The formation of a tripolar vortex, where the highest vorticity is at r = 0, is also considered. Finally to emphasize the accurate treatment near the axis, the motion of a Lamb dipole crossing the origin is simulated. 28 refs., 13 figs.

Verzicco, R.; Orlandi, P. [Universita di Roma (Italy)

1996-02-01

51

A nonlocal finite difference scheme for simulation of wave propagation in 2D models with reduced numerical dispersion  

Science.gov (United States)

The work deals with the reduction of numerical dispersion in simulations of wave propagation in solids. The phenomenon of numerical dispersion naturally results from time and spatial discretization present in a numerical model of mechanical continuum. Although discretization itself makes possible to model wave propagation in structures with complicated geometries and made of different materials, it inevitably causes simulation errors when improper time and length scales are chosen for the simulations domains. Therefore, by definition, any characteristic parameter for spatial and time resolution must create limitations on maximal wavenumber and frequency for a numerical model. It should be however noted that expected increase of the model quality and its functionality in terms of affordable wavenumbers, frequencies and speeds should not be achieved merely by denser mesh and reduced time integration step. The computational cost would be simply unacceptable. The authors present a nonlocal finite difference scheme with the coefficients calculated applying a Fourier series, which allows for considerable reduction of numerical dispersion. There are presented the results of analyses for 2D models, with isotropic and anisotropic materials, fulfilling the planar stress state. Reduced numerical dispersion is shown in the dispersion surfaces for longitudinal and shear waves propagating for different directions with respect to the mesh orientation and without dramatic increase of required number of nonlocal interactions. A case with the propagation of longitudinal wave in composite material is studied with given referential solution of the initial value problem for verification of the time-domain outcomes. The work gives a perspective of modeling of any type of real material dispersion according to measurements and with assumed accuracy.

Martowicz, A.; Ruzzene, M.; Staszewski, W. J.; Rimoli, J. J.; Uhl, T.

2014-03-01

52

On the validity of "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences"  

CERN Document Server

A few families of counterexamples are provided to "A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences", Journal of Computational Physics, 214, 538-549 (2006).

Wei, G W; Zhao, Shan

2006-01-01

53

Conservative high-order finite-difference schemes for low-Mach number flows  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Three finite-difference algorithms are proposed to solve a low-Mach number approximation for the Navier-Stokes equations. These algorithms exhibit fourth-order spatial and second-order temporal accuracy. They are dissipation-free, and thus well suited for DNS and LES of turbulent flows. The key ingredient common to each of the methods presented is a Poisson equation with variable coefficient that is solved for the hydrodynamic pressure. This feature ensures that the velocity field is constrai...

Nicoud, Franck

2000-01-01

54

An analysis of the hybrid finite-difference time-domain scheme for modeling the propagation of electromagnetic waves in cold magnetized toroidal plasma  

Science.gov (United States)

To explore the behavior of electromagnetic waves in cold magnetized plasma, a three-dimensional cylindrical hybrid finite-difference time-domain model is developed. The full discrete dispersion relation is derived and compared with the exact solutions. We establish an analytical proof of stability in the case of nonmagnetized plasma. We demonstrate that in the case of nonmagnetized cold plasma the maximum stable Courant number of the hybrid method coincides with the vacuum Courant condition. In the case of magnetized plasma the stability of the applied numerical scheme is investigated by numerical simulation. In order to determine the utility of the applied difference scheme we complete the analysis of the numerical method demonstrating the limit of the reliability of the numerical results.

Surkova, Maryna; Pavlenko, Yvan; Van Oost, Guido; Van Eester, Dirk; De Zutter, Daniël

2014-05-01

55

On the Equivalence of the Digital Waveguide and FDTD Finite Difference Schemes  

CERN Multimedia

It is known that the digital waveguide (DW) method for solving the wave equation numerically on a grid can be manipulated into the form of the standard finite-difference time-domain (FDTD) method (also known as the ``leapfrog'' recursion). This paper derives a simple rule for going in the other direction, that is, converting the state variables of the FDTD recursion to corresponding wave variables in a DW simulation. Since boundary conditions and initial values are more intuitively transparent in the DW formulation, the simple means of converting back and forth can be useful in initializing and constructing boundaries for FDTD simulations.

Smith, J O

2004-01-01

56

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene  

International Nuclear Information System (INIS)

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses

2014-01-15

57

A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene  

Science.gov (United States)

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac-Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac-Poisson system where potentials act as beam splitters or Veselago lenses.

Brinkman, D.; Heitzinger, C.; Markowich, P. A.

2014-01-01

58

A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene  

Energy Technology Data Exchange (ETDEWEB)

We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.

Brinkman, D., E-mail: Daniel.Brinkman@asu.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 (United States); Heitzinger, C., E-mail: Clemens.Heitzinger@asu.edu [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); AIT Austrian Institute of Technology, A-1220 Vienna (Austria); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287 (United States); Markowich, P.A., E-mail: Peter.Markowich@kaust.edu.sa [Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900 (Saudi Arabia); Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2014-01-15

59

3D acoustic wave modelling with time-space domain dispersion-relation-based finite-difference schemes and hybrid absorbing boundary conditions  

Science.gov (United States)

Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations. Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of Geoscientists and Engineers salt models demonstrate that this modelling scheme has greater accuracy than a conventional scheme and has better absorbing effects than Clayton-Engquist absorbing boundary conditions.

Liu, Yang; Sen, Mrinal K.

2011-09-01

60

Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes  

Directory of Open Access Journals (Sweden)

Full Text Available We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced-order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order and implicit compact-difference (fourth-order formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.

Carlos Duque-Daza

2011-12-01

 
 
 
 
61

Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes  

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in english We present a computational study of the solution of the Falkner-Skan equation (a thirdorder boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes. There are a number of previously reported solution approaches that adopt a reduced- [...] order system of equations, and numerical methods such as: shooting, Taylor series, Runge-Kutta and other semi-analytic methods. Interestingly, though, methods that solve the original non-reduced third-order equation directly are absent from the literature. Two high-order schemes are presented using both explicit (third-order) and implicit compact-difference (fourth-order) formulations on a semi-infinite domain; to our knowledge this is the first time that high-order finite difference schemes are presented to find numerical solutions to the non-reduced-order Falkner-Skan equation directly. This approach maintains the simplicity of Taylor-series coefficient matching methods, avoiding complicated numerical algorithms, and in turn presents valuable information about the numerical behaviour of the equation. The accuracy and effectiveness of this approach is established by comparison with published data for accelerating, constant and decelerating flows; excellent agreement is observed. In general, the numerical behaviour of formulations that seek an optimum physical domain size (for a given computational grid) is discussed. Based on new insight into such methods, an alternative optimisation procedure is proposed that should increase the range of initial seed points for which convergence can be achieved.

Carlos, Duque-Daza; Duncan, Lockerby; Carlos, Galeano.

62

A note on the leap-frog scheme in two and three dimensions. [finite difference method for partial differential equations  

Science.gov (United States)

The paper considers the leap-frog finite-difference method (Kreiss and Oliger, 1973) for systems of partial differential equations of the form du/dt = dF/dx + dG/dy + dH/dz, where d denotes partial derivative, u is a q-component vector and a function of x, y, z, and t, and the vectors F, G, and H are functions of u only. The original leap-frog algorithm is shown to admit a modification that improves on the stability conditions for two and three dimensions by factors of 2 and 2.8, respectively, thereby permitting larger time steps. The scheme for three dimensions is considered optimal in the sense that it combines simple averaging and large time steps.

Abarbanel, S.; Gottlieb, D.

1976-01-01

63

An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation  

International Nuclear Information System (INIS)

The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward–backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. (paper)

2013-04-01

64

Dynamics of the wave turbulence spectrum in vibrating plates: A numerical investigation using a conservative finite difference scheme  

Science.gov (United States)

The dynamics of the local kinetic energy spectrum of an elastic plate vibrating in a wave turbulence (WT) regime is investigated with a finite difference, energy-conserving scheme. The numerical method allows the simulation of pointwise forcing together with realistic boundary conditions, a set-up which is close to experimental conditions. In the absence of damping, the framework of non-stationary wave turbulence is used. Numerical simulations show the presence of a front propagating to high frequencies, leaving a steady spectrum in its wake. Self-similar dynamics of the spectra are found with and without periodic external forcing. For the periodic forcing, the mean injected power is found to be constant, and the frequency at the cascade front evolves linearly with time resulting in a increase of the total energy. For the free turbulence, the energy contained in the cascade remains constant while the frequency front increases as t. These self-similar solutions are found to be in accordance with the kinetic equation derived from the von Kármán plate equations. The effect of the pointwise forcing is observable and introduces a steeper slope at low frequencies, as compared to the unforced case. The presence of a realistic geometric imperfection of the plate is found to have no effect on the global properties of the spectra dynamics. The steeper slope brought by the external forcing is shown to be still observable in a more realistic case where damping is added.

Ducceschi, Michele; Cadot, Olivier; Touzé, Cyril; Bilbao, Stefan

2014-07-01

65

An analysis of discretization for solutions of the diffusion equation using mesh centered finite differences (I) XYZ geometry  

Energy Technology Data Exchange (ETDEWEB)

In this paper eigenvalue mesh dependence is investigated for mesh centered finite difference approximations to the diffusion equation. The well known mesh squared variation of eigenvalue is quantified for XYZ geometry. The second part of the paper describes a method of significantly reducing mesh errors in diffusion theory finite difference codes. Essentially approximations to higher derivatives involving flux values at mesh points are used to generate a source which eliminates second order errors. The approach has been implemented in XYZ geometry and after a description of the technique results are presented for a series of test problems showing that almost zero mesh values can be obtained with the correction process. (author)

Fletcher, J.K. [Power Reactor and Nuclear Fuel Development Corp., Oarai, Ibaraki (Japan). Oarai Engineering Center

1998-11-01

66

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes  

Science.gov (United States)

In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( ? 0) and the scaling factor ( ? 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

2013-12-01

67

Intercomparison of the finite difference and nodal discrete ordinates and surface flux transport methods for a LWR pool-reactor benchmark problem in X-Y geometry  

Energy Technology Data Exchange (ETDEWEB)

The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included.

O' Dell, R.D.; Stepanek, J.; Wagner, M.R.

1983-01-01

68

Discrete schemes for Gaussian curvature and their convergence  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, several discrete schemes for Gaussian curvature are surveyed. The convergence property of a modified discrete scheme for the Gaussian curvature is considered. Furthermore, a new discrete scheme for Gaussian curvature is resented. We prove that the new scheme converges at the regular vertex with valence not less than 5. By constructing a counterexample, we also show that it is impossible for building a discrete scheme for Gaussian curvature which converges over...

Xu, Zhiqiang; Xu, Guoliang

2008-01-01

69

Improved finite-difference scheme for the solution of convection-diffusion problems with the SIMPLEN algorithm  

Energy Technology Data Exchange (ETDEWEB)

An improved version of the differencing scheme used in the SIMPLEN algorithm is presented. In the original scheme, source terms are upwinded in the modeled equations. The method is shown to be superior in accuracy compared to the original method.

Thiart, G.D. (Bureau for Mechanical Engineering, Univ. of Stellenbosch, Stellenbosch (ZA))

1990-01-01

70

Numerical solution of the space-time fractional diffusion equation: Alternatives to finite differences  

Digital Repository Infrastructure Vision for European Research (DRIVER)

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference method to discretize both the fractional-order space and time derivatives. While the finite difference method is simple and straightforward to solve integer-order differential equations, its appeal is reduced for fractional-order differential equations as it leads to systems of ...

2012-01-01

71

Development and application of a third order scheme of finite differences centered in mesh; Desarrollo y aplicacion de un esquema de tercer orden de diferencias finitas centradas en malla  

Energy Technology Data Exchange (ETDEWEB)

In this work the development of a third order scheme of finite differences centered in mesh is presented and it is applied in the numerical solution of those diffusion equations in multi groups in stationary state and X Y geometry. Originally this scheme was developed by Hennart and del Valle for the monoenergetic diffusion equation with a well-known source and they show that the one scheme is of third order when comparing the numerical solution with the analytical solution of a model problem using several mesh refinements and boundary conditions. The scheme by them developed it also introduces the application of numeric quadratures to evaluate the rigidity matrices and of mass that its appear when making use of the finite elements method of Galerkin. One of the used quadratures is the open quadrature of 4 points, no-standard, of Newton-Cotes to evaluate in approximate form the elements of the rigidity matrices. The other quadrature is that of 3 points of Radau that it is used to evaluate the elements of all the mass matrices. One of the objectives of these quadratures are to eliminate the couplings among the Legendre moments 0 and 1 associated to the left and right faces as those associated to the inferior and superior faces of each cell of the discretization. The other objective is to satisfy the particles balance in weighed form in each cell. In this work it expands such development to multiplicative means considering several energy groups. There are described diverse details inherent to the technique, particularly those that refer to the simplification of the algebraic systems that appear due to the space discretization. Numerical results for several test problems are presented and are compared with those obtained with other nodal techniques. (Author)

Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico); Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: adl@nuclear.inin.mx

2003-07-01

72

Mimetic finite difference method  

Science.gov (United States)

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

73

Explicit finite difference methods for the delay pseudoparabolic equations.  

Science.gov (United States)

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392

Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E

2014-01-01

74

Weighted average finite difference methods for fractional diffusion equations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Weighted averaged finite difference methods for solving fractional diffusion equations are discussed and different formulae of the discretization of the Riemann-Liouville derivative are considered. The stability analysis of the different numerical schemes is carried out by means of a procedure close to the well-known von Neumann method of ordinary diffusion equations. The stability bounds are easily found and checked in some representative examples.

Yuste, Santos B.

2004-01-01

75

Dual consistency and functional accuracy: a finite-difference perspective  

Science.gov (United States)

Consider the discretization of a partial differential equation (PDE) and an integral functional that depends on the PDE solution. The discretization is dual consistent if it leads to a discrete dual problem that is a consistent approximation of the corresponding continuous dual problem. Consequently, a dual-consistent discretization is a synthesis of the so-called discrete-adjoint and continuous-adjoint approaches. We highlight the impact of dual consistency on summation-by-parts (SBP) finite-difference discretizations of steady-state PDEs; specifically, superconvergent functionals and accurate functional error estimates. In the case of functional superconvergence, the discrete-adjoint variables do not need to be computed, since dual consistency on its own is sufficient. Numerical examples demonstrate that dual-consistent schemes significantly outperform dual-inconsistent schemes in terms of functional accuracy and error-estimate effectiveness. The dual-consistent and dual-inconsistent discretizations have similar computational costs, so dual consistency leads to improved efficiency. To illustrate the dual consistency analysis of SBP schemes, we thoroughly examine a discretization of the Euler equations of gas dynamics, including the treatment of the boundary conditions, numerical dissipation, interface penalties, and quadrature by SBP norms.

Hicken, J. E.; Zingg, D. W.

2014-01-01

76

Slab geometry spatial discretization schemes with infinite-order convergence  

International Nuclear Information System (INIS)

Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence

1985-11-01

77

A Transport Acceleration Scheme for Multigroup Discrete Ordinates with Upscattering  

International Nuclear Information System (INIS)

We have developed a modification of the two-grid upscatter acceleration scheme of Adams and Morel. The modified scheme uses a low-angular-order discrete ordinates equation to accelerate Gauss-Seidel multigroup iteration. This modification ensures that the scheme does not suffer from consistency problems that can affect diffusion-accelerated methods in multidimensional, multimaterial problems. The new transport two-grid scheme is very simple to implement for different spatial discretizations because it uses the same transport operator. The scheme has also been demonstrated to be very effective on three-dimensional, multimaterial problems. On simple one-dimensional graphite and heavy-water slabs modeled in three dimensions with reflecting boundary conditions, we see reductions in the number of Gauss-Seidel iterations by factors of 75 to 1000. We have also demonstrated the effectiveness of the new method on neutron well-logging problems. For forward problems, the new acceleration scheme reduces the number of Gauss-Seidel iterations by more than an order of magnitude with a corresponding reduction in the run time. For adjoint problems, the speedup is not as dramatic, but the new method still reduces the run time by greater than a factor of 6.

2010-07-01

78

A Transport Acceleration Scheme for Multigroup Discrete Ordinates with Upscattering  

Energy Technology Data Exchange (ETDEWEB)

We have developed a modification of the two-grid upscatter acceleration scheme of Adams and Morel. The modified scheme uses a low-angular-order discrete ordinates equation to accelerate Gauss-Seidel multigroup iteration. This modification ensures that the scheme does not suffer from consistency problems that can affect diffusion-accelerated methods in multidimensional, multimaterial problems. The new transport two-grid scheme is very simple to implement for different spatial discretizations because it uses the same transport operator. The scheme has also been demonstrated to be very effective on three-dimensional, multimaterial problems. On simple one-dimensional graphite and heavy-water slabs modeled in three dimensions with reflecting boundary conditions, we see reductions in the number of Gauss-Seidel iterations by factors of 75 to 1000. We have also demonstrated the effectiveness of the new method on neutron well-logging problems. For forward problems, the new acceleration scheme reduces the number of Gauss-Seidel iterations by more than an order of magnitude with a corresponding reduction in the run time. For adjoint problems, the speedup is not as dramatic, but the new method still reduces the run time by greater than a factor of 6.

Evans, Thomas M [ORNL; Clarno, Kevin T [ORNL; Morel, Jim E. [Texas A& M University

2010-01-01

79

Novel discretization schemes for the numerical simulation of membrane dynamics  

Science.gov (United States)

Motivated by the demands of simulating flapping wings of Micro Air Vehicles, novel numerical methods were developed and evaluated for the dynamic simulation of membranes. For linear membranes, a mixed-form time-continuous Galerkin method was employed using trilinear space-time elements. Rather than time-marching, the entire space-time domain was discretized and solved simultaneously. Second-order rates of convergence in both space and time were observed in numerical studies. Slight high-frequency noise was filtered during post-processing. For geometrically nonlinear membranes, the model incorporated two new schemes that were independently developed and evaluated. Time marching was performed using quintic Hermite polynomials uniquely determined by end-point jerk constraints. The single-step, implicit scheme was significantly more accurate than the most common Newmark schemes. For a simple harmonic oscillator, the scheme was found to be symplectic, frequency-preserving, and conditionally stable. Time step size was limited by accuracy requirements rather than stability. The spatial discretization scheme employed a staggered grid, grouping of nonlinear terms, and polygon shape functions in a strong-form point collocation formulation. The observed rate of convergence was two for both displacement and strain. Validation against existing experimental data showed the method to be accurate until hyperelastic effects dominate.

Kolsti, Kyle F.

80

Mimetic finite difference methods in image processing  

Directory of Open Access Journals (Sweden)

Full Text Available We introduce the use of mimetic methods to the imaging community, for the solution of the initial-value problems ubiquitous in the machine vision and image processing and analysis fields. PDE-based image processing and analysis techniques comprise a host of applications such as noise removal and restoration, deblurring and enhancement, segmentation, edge detection, inpainting, registration, motion analysis, etc. Because of their favorable stability and efficiency properties, semi-implicit finite difference and finite element schemes have been the methods of choice (in that order of preference. We propose a new approach for the numerical solution of these problems based on mimetic methods. The mimetic discretization scheme preserves the continuum properties of the mathematical operators often encountered in the image processing and analysis equations. This is the main contributing factor to the improved performance of the mimetic method approach, as compared to both of the aforementioned popular numerical solution techniques. To assess the performance of the proposed approach, we employ the Catté-Lions-Morel-Coll model to restore noisy images, by solving the PDE with the three numerical solution schemes. For all of the benchmark images employed in our experiments, and for every level of noise applied, we observe that the best image restored by using the mimetic method is closer to the noise-free image than the best images restored by the other two methods tested. These results motivate further studies of the application of the mimetic methods to other imaging problems. Mathematical subject classification: Primary: 68U10; Secondary: 65L12.

C. Bazan

2011-01-01

 
 
 
 
81

Numerical Solution of the Space-time Fractional Diffusion Equation: Alternataives to Finite Differences  

Digital Repository Infrastructure Vision for European Research (DRIVER)

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference (FD) method to discretize both the fractional-order space and time derivatives. Some numerical schemes using low-order finite elements (FE) have also been proposed. Both the FD and FE methods have long been used to solve integer-order partial differential equations. These low-or...

2013-01-01

82

Numerical stability for finite difference approximations of Einstein's equations  

International Nuclear Information System (INIS)

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in numerical relativity and, more generally, in Hamiltonian formulations of field theories. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy-Ortiz-Reula formulation of Einstein's equations. We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems

2006-11-01

83

New single-carrier transceiver scheme based on the discrete sine transform  

Directory of Open Access Journals (Sweden)

Full Text Available A discrete sine transform (DST-based single-carrier transceiver scheme for broadband wireless communications is proposed and investigated. The proposed scheme uses a DST rather than the conventional discrete Fourier transform (DFT as a basis function to implement the single-carrier system. The performance of the proposed scheme is studied and compared with the DFT-based single-carrier transceiver scheme and the discrete cosine transform based single-carrier transceiver scheme. Simulation results for single-carrier frequency division multiple access system are presented to demonstrate the effectiveness of the proposed scheme for broadband wireless communications.

Faisal Al-kamali

2014-05-01

84

Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography (Revised).  

Science.gov (United States)

This Recommendation specifies key establishment schemes using discrete logarithm cryptography, based on standards developed by the Accredited Standards Committee (ASC) X9, Inc.: ANS X9.42 (Agreement of Symmetric Keys Using Discrete Logarithm Cryptography)...

D. Johnson E. Barker M. Smid

2007-01-01

85

Research of stability and spectral properties explicit finite difference schemes with variable steps on time at modeling 3D flow in the pipe at large Reynolds numbers  

International Nuclear Information System (INIS)

There dimensional hydrodynamical calculations with heat transfer for nuclear reactors are complicated and actual tasks, their singularity is high numbers of Reynolds Re ? 106. The offered paper is one of initial development stages programs for problem solving the similar class. Operation contains exposition: mathematical setting of the task for the equations of Navier-Stokes with heat transfer compiling of space difference schemes by a method of check sizes, deriving of difference equations for pressure. The steady explicit methods of a solution of rigid tasks included in DUMKA program, and research of areas of their stability are used. Outcomes of numerical experiments of current of liquid in channels of rectangular cut are reduced. The complete spectrum analysis of the considered task is done (Authors)

2005-11-01

86

Finite difference methods for the time fractional diffusion equation on non-uniform meshes  

Science.gov (United States)

Since fractional derivatives are integrals with weakly singular kernel, the discretization on the uniform mesh may lead to poor accuracy. The finite difference approximation of Caputo derivative on non-uniform meshes is investigated in this paper. The method is applied to solve the fractional diffusion equation and a semi-discrete scheme is obtained. The unconditional stability and H1 norm convergence are proved. A fully discrete difference scheme is constructed with space discretization by compact difference method. The error estimates are established for two kinds of nonuniform meshes. Numerical tests are carried out to support the theoretical results and comparing with the method on uniform grid shows the efficiency of our methods. Moreover, a moving local refinement technique is introduced to improve the temporal accuracy of numerical solution.

Zhang, Ya-nan; Sun, Zhi-zhong; Liao, Hong-lin

2014-05-01

87

Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation  

Science.gov (United States)

The elliptic Monge-Ampère equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampère equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three-dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.

Froese, B. D.; Oberman, A. M.

2011-02-01

88

A semi-discrete scheme for the stochastic Landau-Lifshitz equation  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the scheme up to a subsequence.

2014-01-01

89

Finite Difference Time Domain (FDTD) Simulations Using Graphics Processors.  

Science.gov (United States)

This paper presents a graphics processor based implementation of the Finite Difference Time Domain (FDTD), which uses a central finite differencing scheme for solving Maxwell's equations for electromagnetics. FDTD simulations can be very computationally e...

J. Payne R. Boppana S. Adams

2007-01-01

90

On a space discretization scheme for the Fractional Stochastic Heat Equations  

CERN Multimedia

In this work, we introduce a new discretization to the fractional Laplacian and use it to elaborate an approximation scheme for fractional heat equations perturbed by a multiplicative cylindrical white noise. In particular, we estimate the rate of convergence.

Debbi, Latifa

2011-01-01

91

Stability of a Crank-Nicolson Pressure Correction Scheme Based on Staggered Discretizations  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In the context of Large Eddy Simulation of turbulent flows, the control of kinetic energy seems to be an essential requirement for the numerical scheme. Designing such an algorithm, ie as less dissipative as possible while being simple, for the resolution of variable density Navier-Stokes equations is the aim of the present work.The developed numerical scheme, based on a pressure correction technique, uses a Crank-Nicolson time discretization and a staggered space discretization relying on th...

Boyer, Franck; Dardalhon, Fanny; Lapuerta, Ce?line; Latche?, Jean-claude

2012-01-01

92

A 2D/3D Discrete Duality Finite Volume Scheme. Application to ECG simulation  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper presents a 2D/3D discrete duality finite volume method for solving heterogeneous and anisotropic elliptic equations on very general unstructured meshes. The scheme is based on the definition of discrete divergence and gradient operators that fulfill a duality property mimicking the Green formula. As a consequence, the discrete problem is proved to be well-posed, symmetric and positive-definite. Standard numerical tests are performed in 2D and 3D and the results are discussed and co...

Coudiere, Yves; Pierre, Charles; Rousseau, Olivier; Turpault, Rodolphe

2009-01-01

93

$H_{\\infty}$ Control Design for Novel Teleoperation System Scheme: A Discrete Approach  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper addresses the problem that, the discretization of stabilizing the continuous bilateral teleoperation controllers for digital implementation may lead to instable teleoperation or poor performance. With this problem, a discrete approach for the novel proxy teleoperation control scheme under time-varying delays is considered in the paper. The principle results involve sufficient conditions in terms of discrete Lyapunov-Krasovskii functionals (LKF) and $H_{\\infty}$ control theory, whic...

Zhang, Bo; Kruszewski, Alexandre; Richard, Jean-pierre

2012-01-01

94

Double Discretization Difference Schemes for Partial Integrodifferential Option Pricing Jump Diffusion Models  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A new discretization strategy is introduced for the numerical solution of partial integrodifferential equations appearing in option pricing jump diffusion models. In order to consider the unknown behaviour of the solution in the unbounded part of the spatial domain, a double discretization is proposed. Stability, consistency, and positivity of the resulting explicit scheme are analyzed. Advantages of the method are illustrated with several examples.

Casaba?n Bartual, Mª Consuelo; Company Rossi, Rafael; Jo?dar Sa?nchez, Lucas Antonio; Romero Bauset, Jose? Vicente

2012-01-01

95

A splitting higher order scheme with discrete transparent boundary conditions for the Schr\\"odinger equation in a semi-infinite parallelepiped  

CERN Document Server

An initial-boundary value problem for the $n$-dimensional ($n\\geq 2$) time-dependent Schr\\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we first construct higher order scheme with splitting space averages having much better spectral properties for $n\\geq 3$. Next we apply the Strang-type splitting with respect to the potential and, third, construct discrete transparent boundary conditions (TBC). For the resulting method, the uniqueness of solution and the unconditional uniform in time $L^2$-stability (in particular, $L^2$-conservativeness) are proved. Owing to the splitting, an effective direct algorithm using FFT (in the coordinate directions perpendicular to the leading axis of the parallelepiped) is applicable for general potential. Numerical results on the 2D tunnel effect for a P\\"{o}schl-Teller-like potential-barrier and a rectangular potential-well are also included.

Ducomet, Bernard; Romanova, Alla

2013-01-01

96

Discrete level schemes sublibrary. Progress report by Budapest group  

International Nuclear Information System (INIS)

An entirely new discrete levels file has been created by the Budapest group according to the recommended principles, using the Evaluated Nuclear Structure Data File, ENSDF as a source. The resulting library contains 96,834 levels and 105,423 gamma rays for 2,585 nuclei, with their characteristics such as energy, spin, parity, half-life as well gamma-ray energy and branching percentage

1997-09-01

97

A group signature scheme based on the integer factorization and the subgroup discrete logarithm problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Group signature schemes allow a user, belonging to a speci c group of users, to sign a message in an anonymous way on behalf of the group. In general, these schemes need the collaboration of a Trusted Third Party which, in case of a dispute, can reveal the identity of the real signer. A new group signature scheme is presented whose security is based on the Integer Factorization Problem (IFP) and on the Subgroup Discrete Logarithm Problem (SDLP).

Dura?n Di?az, Rau?l; Herna?ndez Encinas, Luis; Mun?oz Masque?, Jaime

2011-01-01

98

Propagation Characteristics of Rectangular Waveguides at Terahertz Frequencies with Finite-Difference Frequency-Domain Method  

Science.gov (United States)

The 2-D finite-difference frequency-domain method (FDFD) combined with the surface impedance boundary condition (SIBC) was employed to analyze the propagation characteristics of hollow rectangular waveguides at Terahertz (THz) frequencies. The electromagnetic field components, in the interior of the waveguide, were discretized using central finite-difference schemes. Considering the hollow rectangular waveguide surrounded by a medium of finite conductivity, the electric and magnetic tangential field components on the metal surface were related by the SIBC. The surface impedance was calculated by the Drude dispersion model at THz frequencies, which was used to characterize the conductivity of the metal. By solving the Eigen equations, the propagation constants, including the attenuation constant and the phase constant, were obtained for a given frequency. The proposed method shows good applicability for full-wave analysis of THz waveguides with complex boundaries.

Huang, Binke; Zhao, Chongfeng

2014-01-01

99

An error estimate for the finite difference approximation to degenerate convection -diffusion equations  

CERN Document Server

We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection-diffusion equations in one space dimension, and prove an L1 error estimate. Precisely, we show that the L1 loc difference between the approximate solution and the unique entropy solution converges at a rate O(\\Deltax 1/11), where \\Deltax is the spatial mesh size. If the diffusion is linear, we get the convergence rate O(\\Deltax 1/2), the point being that the O is independent of the size of the diffusion

Karlsen, K H; Risebro, And N H

2011-01-01

100

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions  

Science.gov (United States)

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

 
 
 
 
101

COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY  

Energy Technology Data Exchange (ETDEWEB)

We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.

Sebastian Schunert; Yousry Y. Azmy; Damien Fournier

2011-05-01

102

A mimetic finite difference method for the Stokes problem with elected edge bubbles  

Energy Technology Data Exchange (ETDEWEB)

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.

Lipnikov, K [Los Alamos National Laboratory; Berirao, L [DIPARTMENTO DI MATERMATICA

2009-01-01

103

A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra  

International Nuclear Information System (INIS)

In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a coarsely discretized problem that contains sharp boundary layers. We also examine eigenvalue and fixed source problems with mixed-shape meshes, anisotropic scattering and multi-group cross sections. Finally, we simulate the MOX fuel assembly in the Advance Test Reactor

2000-01-01

104

A three-dimensional SN high-order diamond differencing discretization with a consistent acceleration scheme  

International Nuclear Information System (INIS)

The extension of the diamond differencing scheme to high-order spatial approximation is described in the context of a regular, three-dimensional (3D) discrete ordinates method. This spatial discretization keeps the advantages of the well-known linear diamond differencing (DD) scheme in terms of rigorousness and simplicity of derivation, while extending it to high-order solutions. Along with the implementation of high-order diamond differencing comes the search for a consistent acceleration method for the SN source iteration. The proposed method relies on a Diffusion Synthetic Acceleration (DSA) scheme, combined with a Krylov Subspace Algorithm, GMRES. This two-level acceleration scheme has been proven efficient in case of realistic problems at any order. Numerical results are provided on 2D/3D legacy benchmarks and establish good properties of our solver.

2009-01-01

105

Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case.  

Science.gov (United States)

Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well. PMID:24125383

Guo, Zhaoli; Xu, Kun; Wang, Ruijie

2013-09-01

106

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes  

Science.gov (United States)

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Diskin, Boris; Thomas, James L.

2012-01-01

107

Total internal reflection microscopy: examination of competitive schemes via discrete sources method  

International Nuclear Information System (INIS)

The discrete sources method has been applied to perform a computer simulation analysis of different total internal reflection microscopy schemes. It has been found that the positioning of the objective lens beneath a glass prism can provide a considerable advantage for determination of the particle–film distance

2010-09-01

108

Accurate convergent finite difference approximations for viscosity solutions of the elliptic Monge-Amp\\`ere partial differential equation  

CERN Multimedia

The theory of viscosity solutions has been effective for representing and approximating weak solutions to fully nonlinear Partial Differential Equations (PDEs) such as the elliptic Monge-Amp\\`ere equation. The approximation theory of Barles-Souganidis [Barles and Souganidis, Asymptotic Anal., 4 (1999) 271-283] requires that numerical schemes be monotone (or elliptic in the sense of [Oberman, SIAM J. Numer. Anal, 44 (2006) 879-895]. But such schemes have limited accuracy. In this article, we establish a convergence result for nearly monotone schemes. This allows us to construct finite difference discretizations of arbitrarily high-order. We demonstrate that the higher accuracy is achieved when solutions are sufficiently smooth. In addition, the filtered scheme provides a natural detection principle for singularities. We employ this framework to construct a formally second-order scheme for the Monge-Amp\\`ere equation and present computational results on smooth and singular solutions.

Froese, Brittany D

2012-01-01

109

A free energy satisfying finite difference method for Poisson–Nernst–Planck equations  

Science.gov (United States)

In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three desired properties: i) mass conservation, ii) positivity preserving, and iii) free energy satisfying in the sense that these schemes satisfy a discrete free energy dissipation inequality. These ensure that the computed solution is a probability density, and the schemes are energy stable and preserve the equilibrium solutions. Both one- and two-dimensional numerical results are provided to demonstrate the good qualities of the algorithm, as well as effects of relative size of the data given.

Liu, Hailiang; Wang, Zhongming

2014-07-01

110

The mimetic finite difference method for elliptic problems  

CERN Document Server

This book describes the theoretical and computational aspects of the mimetic finite difference method for a wide class of multidimensional elliptic problems, which includes diffusion, advection-diffusion, Stokes, elasticity, magnetostatics and plate bending problems. The modern mimetic discretization technology developed in part by the Authors allows one to solve these equations on unstructured polygonal, polyhedral and generalized polyhedral meshes. The book provides a practical guide for those scientists and engineers that are interested in the computational properties of the mimetic finite difference method such as the accuracy, stability, robustness, and efficiency. Many examples are provided to help the reader to understand and implement this method. This monograph also provides the essential background material and describes basic mathematical tools required to develop further the mimetic discretization technology and to extend it to various applications.

Veiga, Lourenço Beirão; Manzini, Gianmarco

2014-01-01

111

On some fundamental finite difference inequalities  

Directory of Open Access Journals (Sweden)

Full Text Available The main object of this paper is to establish some new finite difference inequalities which can be used as tools in the study of various problems in the theory of certain classes of finite difference and sum-difference equations.

B. G. Pachpatte

2001-09-01

112

A parallel adaptive finite difference algorithm for petroleum reservoir simulation  

Energy Technology Data Exchange (ETDEWEB)

Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

Hoang, Hai Minh

2005-07-01

113

2D/3D Discrete Duality Finite Volume (DDFV) scheme for anisotropic- heterogeneous elliptic equations, application to the electrocardiogram simulation.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper is presented a finite volume (DDFV) scheme for solving elliptic equations with heterogeneous anisotropic conductivity tensor. That method is based on the definition of a discrete divergence and a discrete gradient operator. These discrete operators have close relationships with the continuous ones, in particulat they fulfil a duality property related with the Green formula. The operators are defined in dimension 2 and 3, their duality property is stated and used to establish the...

Coudiere, Yves; Pierre, Charles; Rousseau, Olivier; Turpault, Rodolphe

2008-01-01

114

Digital Waveguides versus Finite Difference Structures: Equivalence and Mixed Modeling  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Digital waveguides and finite difference time domain schemes have been used in physical modeling of spatially distributed systems. Both of them are known to provide exact modeling of ideal one-dimensional (1D) band-limited wave propagation, and both of them can be composed to approximate two-dimensional (2D) and three-dimensional (3D) mesh structures. Their equal capabilities in physical modeling have been shown for special cases and have been assumed to cover generalized cases as wel...

Cumhur Erkut; Matti Karjalainen

2004-01-01

115

An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs  

Science.gov (United States)

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L (sub 2) stability on a finite domain.

Warming, Robert F.; Beam, Richard M.

1990-01-01

116

Optimization of Dengue Epidemics: A Test Case with Different Discretization Schemes  

Science.gov (United States)

The incidence of Dengue epidemiologic disease has grown in recent decades. In this paper an application of optimal control in Dengue epidemics is presented. The mathematical model includes the dynamic of Dengue mosquito, the affected persons, the people's motivation to combat the mosquito and the inherent social cost of the disease, such as cost with ill individuals, educations and sanitary campaigns. The dynamic model presents a set of nonlinear ordinary differential equations. The problem was discretized through Euler and Runge Kutta schemes, and solved using nonlinear optimization packages. The computational results as well as the main conclusions are shown.

Rodrigues, Helena Sofia; Monteiro, M. Teresa T.; Torres, Delfim F. M.

2009-09-01

117

A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs  

CERN Multimedia

We consider the numerical approximation of a general second order semi-linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new scheme using in time a linear functional of the noise with a semi-implicit Euler-Maruyama method and in space we analyse a finite element method although extension to finite differences or finite volumes would be possible. We consider noise that is white in time and either in $H^1$ or $H^2$ in space. We give the convergence proofs in the root mean square $L^{2}$ norm for a diffusion reaction equation and in root mean square $H^{1}$ norm in the presence of advection. We examine the regularity of the initial data, the regularity of the noise and errors from projecting the noise. We present numerical results for a linear reaction diffusion equatio in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We see from both the analysis and numerics that we have bette...

Lord, Gabriel J

2010-01-01

118

A discrete ordinates scheme for void fraction evaluation with nonstandard reflective conditions and weakly divergent beams  

International Nuclear Information System (INIS)

In this article, a number of due changes in both a discrete ordinates neutron transport model and a companion void fraction evaluation scheme are introduced. These changes are due to the explicit consideration of a weakly divergent neutron beam, i.e. a neutron beam consisting of a monodirectional component with normal incidence, which is modeled by a Dirac delta distribution, and an angularly continuous component, which is modeled by a smooth function of the angular variable. Computational tests are performed in order to illustrate the numerical consistency of the evaluation scheme for weakly divergent beams with respect to the order of angular quadrature, as well as its low sensitivity to experimental inaccuracies in the detector responses. (orig.)

2009-04-01

119

Lifting scheme of biorthogonal wavelet transform based on discrete interpolatory splines  

Science.gov (United States)

In this paper, we present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction we used the interpolatory discrete splices which enabled us to design a library of perfect reconstruction filter banks. These filter banks are related to Buttersworth filters. The construction is performed in a 'lifting' manner. The difference from the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform. Two ways to choose the control filters are suggested. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. These filters have linear phase property and the basic waveforms are symmetric. In addition, these filters yield perfect frequency resolution.

Averbuch, Amir Z.; Pevnyi, Alexander B.; Zheludev, Valery A.

2000-12-01

120

An induced charge readout scheme incorporating image charge splitting on discrete pixels  

International Nuclear Information System (INIS)

Top hat electrostatic analysers used in space plasma instruments typically use microchannel plates (MCPs) followed by discrete pixel anode readout for the angular definition of the incoming particles. Better angular definition requires more pixels/readout electronics channels but with stringent mass and power budgets common in space applications, the number of channels is restricted. We describe here a technique that improves the angular definition using induced charge and an interleaved anode pattern. The technique adopts the readout philosophy used on the CRRES and CLUSTER I instruments but has the advantages of the induced charge scheme and significantly reduced capacitance. Charge from the MCP collected by an anode pixel is inductively split onto discrete pixels whose geometry can be tailored to suit the scientific requirements of the instrument. For our application, the charge is induced over two pixels. One of them is used for a coarse angular definition but is read out by a single channel of electronics, allowing a higher rate handling. The other provides a finer angular definition but is interleaved and hence carries the expense of lower rate handling. Using the technique and adding four channels of electronics, a four-fold increase in the angular resolution is obtained. Details of the scheme and performance results are presented

2003-11-01

 
 
 
 
121

A Finite Difference-Based Modeling Approach for Prediction of Steel Hardenability  

Science.gov (United States)

In this research work an independent finite difference-based modeling approach was adopted for determination of the hardenability of steels. In this model, at first, cooling curves were generated by solving transient heat transfer equation through discretization with pure explicit finite difference scheme coupled with MATLAB-based programing in view of variable thermo-physical properties of 1080 steel. The cooling curves were solved against 50% transformation nose of TTT diagram in order to predict hardening behavior of 1080 steel in terms of hardenability parameters (Grossmann critical diameter, D C; and ideal critical diameter, D I) and the variation of the unhardened core diameter ( D u) to diameter of steel bar ( D) ratio with diameter of steel bar ( D). The experiments were also performed to determine actual D C value of 1080 steel for still water quenching. The D C value obtained by the developed model was found to match the experimental D C value with only 6% deviation. Therefore, the model developed in the present work can be used for direct determination of D I, D C, and D u without resorting to any rigorous experimentation.

Sushanthi, Neethi; Maity, Joydeep

2014-06-01

122

A Discrete It\\^o Calculus Approach to He's Framework for Multi-Factor Discrete Markets  

CERN Multimedia

In the present paper, a discrete version of It\\^o's formula for a class of multi-dimensional random walk is introduced and applied to the study of a discrete-time complete market model which we call He's framework. The formula unifies continuous-time and discrete-time settings and by regarding the latter as the finite difference scheme of the former, the order of convergence is obtained. The result shows that He's framework cannot be of order 1 scheme except for the one dimensional case.

Akahori, J

2006-01-01

123

Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case  

CERN Document Server

This paper is a continuation of our earlier work [Z.L. Guo {\\it et al.}, Phys. Rev. E {\\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the fluxes at cell interfaces, so that the nice asymptotic preserving (AP) property is retained, such that the time step is limited only by the CFL number, the distribution function at cell interface recovers to the Chapman-Enskog one in the continuum limit while reduces to that of free-transport for free-molecular flow, and the time and spatial accuracy is of second-order accuracy in smooth region. These features make the DUGK...

Guo, Zhaoli; Xu, Kun

2014-01-01

124

Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation  

Directory of Open Access Journals (Sweden)

Full Text Available The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integral identities is more likely to produce better approximations. Recently, one of the authors developed a systematic approach to obtain mimetic finite difference discretizations for divergence and gradient operators, which achieves the same order of accuracy on the boundary and inner grid points. This paper uses the second-order version of those operators to develop a new mimetic finite difference method for the steady-state diffusion equation. A complete theoretical and numerical analysis of this new method is presented, including an original and nonstandard proof of the quadratic convergence rate of this new method. The numerical results agree in all cases with our theoretical analysis, providing strong evidence that the new method is a better choice than the standard finite difference method.

Rojas S

2007-01-01

125

Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation  

Directory of Open Access Journals (Sweden)

Full Text Available The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integral identities is more likely to produce better approximations. Recently, one of the authors developed a systematic approach to obtain mimetic finite difference discretizations for divergence and gradient operators, which achieves the same order of accuracy on the boundary and inner grid points. This paper uses the second-order version of those operators to develop a new mimetic finite difference method for the steady-state diffusion equation. A complete theoretical and numerical analysis of this new method is presented, including an original and nonstandard proof of the quadratic convergence rate of this new method. The numerical results agree in all cases with our theoretical analysis, providing strong evidence that the new method is a better choice than the standard finite difference method.

J. M. Guevara-Jordan

2007-06-01

126

Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic  

CERN Document Server

Let p be a prime. Let V be a discrete valuation ring of mixed characteristic (0,p) and index of ramification e. Let f: G \\to H be a homomorphism of finite flat commutative group schemes of p power order over V whose generic fiber is an isomorphism. We bound the kernel and the cokernel of the special fiber of f in terms of e. For e < p-1 this reproves a result of Raynaud. As an application we obtain an extension theorem for homomorphisms of truncated Barsotti--Tate groups which strengthens Tate's extension theorem for homomorphisms of p-divisible groups. In particular, our method provides short new proofs of the theorems of Tate and Raynaud.

Vasiu, Adrian

2009-01-01

127

A Novel Robust Zero-Watermarking Scheme Based on Discrete Wavelet Transform  

Directory of Open Access Journals (Sweden)

Full Text Available In traditional watermarking algorithms, the insertion of watermark into the original signal inevitably introduces some perceptible quality degradation. Another problem is the inherent conflict between imperceptibility and robustness. Zero-watermarking technique can solve these problems successfully. But most existing zero-watermarking algorithm for audio and image cannot resist against some signal processing manipulations or malicious attacks. In the paper, a novel audio zero-watermarking scheme based on discrete wavelet transform (DWT is proposed, which is more efficient and robust. The experiments show that the algorithm is robust against the common audio signal processing operations such as MP3 compression, re-quantization, re-sampling, low-pass filtering, cutting-replacement, additive white Gaussian noise and so on. These results demonstrate that the proposed watermarking method can be a suitable candidate for audio copyright protection.

Yu Yang

2012-08-01

128

Robust Multiple Image Watermarking Scheme using Discrete Cosine Transform with Multiple Descriptions  

Directory of Open Access Journals (Sweden)

Full Text Available A novel oblivious and robust multiple imagewatermarking scheme using Multiple Descriptions (MD andQuantization Index Modulation (QIM of the host image ispresented in this paper. Watermark embedding is done at twostages. In the first stage, Discrete Cosine Transform (DCT ofodd description of the host image is computed. The watermarkimage is embedded in the resulting DC coefficients. In thesecond stage, a copy of the watermark image is embedded in thewatermarked image generated at the first stage. This enablesus to achieve robustness to both local and global attacks. Thisalgorithm is highly robust for different attacks on thewatermarked image and superior in terms of Peak Signal toNoise Ratio (PSNR and Normalized Cross correlation (NC.

Mohan B. Chandra

2009-01-01

129

Wave Equation Simulation on Manifold using Discrete Exterior Calculus  

CERN Multimedia

Numerical simulation provides a effective tool for studying both the spatial and temporal nature of acoustic field on 3D or 4D timespace. The paper deals with the description of discrete exterior calculus scheme for the wave equation. This method can be directly implemented on manifold, which is the generation of finite difference time domain method from flat space to curved space.

Xie, Zheng; Ma, Bin; Shen, Qinghua

2009-01-01

130

A three-dimensional S{sub N} high-order diamond differencing discretization with a consistent acceleration scheme  

Energy Technology Data Exchange (ETDEWEB)

The extension of the diamond differencing scheme to high-order spatial approximation is described in the context of a regular, three-dimensional (3D) discrete ordinates method. This spatial discretization keeps the advantages of the well-known linear diamond differencing (DD) scheme in terms of rigorousness and simplicity of derivation, while extending it to high-order solutions. Along with the implementation of high-order diamond differencing comes the search for a consistent acceleration method for the S{sub N} source iteration. The proposed method relies on a Diffusion Synthetic Acceleration (DSA) scheme, combined with a Krylov Subspace Algorithm, GMRES. This two-level acceleration scheme has been proven efficient in case of realistic problems at any order. Numerical results are provided on 2D/3D legacy benchmarks and establish good properties of our solver.

Martin, Nicolas [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, Station ' Centre-Ville' , Montreal, Que., H3C 3A7 (Canada); Hebert, Alain, E-mail: alain.hebert@polymtl.c [Institut de Genie Nucleaire, Ecole Polytechnique de Montreal, P.O. Box 6079, Station ' Centre-Ville' , Montreal, Que., H3C 3A7 (Canada)

2009-11-15

131

Scheme for measuring experimentally the velocity of pilot waves and the discreteness of time  

International Nuclear Information System (INIS)

We consider the following two questions. Suppose that a quantum system suffers a change of the boundary condition or the potential at a given space location. Then (1)when will the wavefunction shows a response to this change at another location? And (2)how does the wavefunction changes?The answer to question (1) could reveal how a quantum system gets information on the boundary condition or the potential. Here we show that if the response takes place immediately, then it can allow superluminal signal transfer. Else if the response propagates in space with a finite velocity, then it could give a simple explanation why our world shows classicality on the macroscopic scale. Furthermore, determining the exact value of this velocity can either clarify the doubts on static experiments for testing Bell's inequality, or support the pilot-wave interpretation of quantum mechanics. We propose a feasible experimental scheme for measuring this velocity, which can be implemented with state-of-art technology, e.g., single-electron biprism interferometry.Question (2) is studied with a square-well potential model, and we find a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions. To solve the paradox, we predict that when a change of the potential occurs at a given space location, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore it gives a simple proof that time is discrete, with Planck time being the smallest unit. Combining with the answer to question (1), systems with a larger size and a slower velocity could have a larger unit of time, making it possible to test the discreteness of time experimentally. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.

2010-12-22

132

Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods  

Energy Technology Data Exchange (ETDEWEB)

Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

Kim, S. [Purdue Univ., West Lafayette, IN (United States)

1994-12-31

133

Finite difference approximations for a fractional diffusion/anti-diffusion equation  

CERN Document Server

A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann analysis: stability criteria are found and checked numerically. Moreover, we investigate the consistency and convergence of these schemes.

Azerad, Pascal

2011-01-01

134

A parallel finite-difference method for computational aerodynamics  

Science.gov (United States)

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

Swisshelm, Julie M.

1989-01-01

135

A parallel finite-difference method for computational aerodynamics  

International Nuclear Information System (INIS)

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed. 14 refs

1989-04-03

136

Discrete cosine transform and hash functions toward implementing a (robust-fragile) watermarking scheme  

Science.gov (United States)

This paper proposes a blind multi-watermarking scheme based on designing two back-to-back encoders. The first encoder is implemented to embed a robust watermark into remote sensing imagery by applying a Discrete Cosine Transform (DCT) approach. Such watermark is used in many applications to protect the copyright of the image. However, the second encoder embeds a fragile watermark using `SHA-1' hash function. The purpose behind embedding a fragile watermark is to prove the authenticity of the image (i.e. tamper-proof). Thus, the proposed technique was developed as a result of new challenges with piracy of remote sensing imagery ownership. This led researchers to look for different means to secure the ownership of satellite imagery and prevent the illegal use of these resources. Therefore, Emirates Institution for Advanced Science and Technology (EIAST) proposed utilizing existing data security concept by embedding a digital signature, "watermark", into DubaiSat-1 satellite imagery. In this study, DubaiSat-1 images with 2.5 meter resolution are used as a cover and a colored EIAST logo is used as a watermark. In order to evaluate the robustness of the proposed technique, a couple of attacks are applied such as JPEG compression, rotation and synchronization attacks. Furthermore, tampering attacks are applied to prove image authenticity.

Al-Mansoori, Saeed; Kunhu, Alavi

2013-10-01

137

Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrodinger operator  

CERN Multimedia

With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations. We construct, in particular, the Darboux transformations for the general self adjoint schemes with five and seven neighbouring points. We also introduce a distinguished discretization of the two-dimensional stationary Schrodinger equation, described by a 5-point difference scheme involving two potentials, which admits a Darboux transformation.

Nieszporski, M; Doliwa, A

2003-01-01

138

A Finite Difference Ghost-Cell Multigrid Approach for Poisson Equation with Mixed Boundary Conditions in Arbitrary Domain  

CERN Document Server

In this paper we present a multigrid approach to solve the Poisson equation in arbitrary domain (identified by a level set function) and mixed boundary conditions. The discretization is based on finite difference scheme and ghost-cell method. This multigrid strategy can be applied also to more general problems where a non-eliminated boundary condition approach is used. Arbitrary domain make the definition of the restriction operator for boundary conditions hard to find. A suitable restriction operator is provided in this work, together with a proper treatment of the boundary smoothing, in order to avoid degradation of the convergence factor of the multigrid due to boundary effects. Several numerical tests confirm the good convergence property of the new method.

Coco, Armando

2011-01-01

139

Implementation of a high-order compact finite-difference lattice Boltzmann method in generalized curvilinear coordinates  

Science.gov (United States)

In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar–Gross–Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the implementation of the high-order compact finite-difference Lattice Boltzmann method (CFDLBM) in the generalized curvilinear coordinates is robust, efficient and accurate for solving steady and unsteady incompressible flows over practical geometries.

Hejranfar, Kazem; Ezzatneshan, Eslam

2014-06-01

140

Management-retrieval code system for sub-library of discrete level schemes and gamma radiation branching ratios  

International Nuclear Information System (INIS)

The sub-library of discrete level schemes and gamma radiation branching ratios (DLS) is translated from the evaluated nuclear structure data file (ENSDF). The data are further checked and corrected. In consideration of the demands for different kinds of research fields most of the evaluated experimental levels and their gamma rays in the ENSDF are kept in DLS data file. the management-retrieval code can provide two retrieving ways. One is a retrieval for a single nucleus (SN), and the other is one for a neutron reaction (NR). The latter contains four kinds of retrieving types corresponding four types of different fast neutron calculation codes. The code can cut off and select the required level and gamma rays from whole discrete level scheme according to user's demands

1997-09-01

 
 
 
 
141

Digital Waveguides versus Finite Difference Structures: Equivalence and Mixed Modeling  

Directory of Open Access Journals (Sweden)

Full Text Available Digital waveguides and finite difference time domain schemes have been used in physical modeling of spatially distributed systems. Both of them are known to provide exact modeling of ideal one-dimensional (1D band-limited wave propagation, and both of them can be composed to approximate two-dimensional (2D and three-dimensional (3D mesh structures. Their equal capabilities in physical modeling have been shown for special cases and have been assumed to cover generalized cases as well. The ability to form mixed models by joining substructures of both classes through converter elements has been proposed recently. In this paper, we formulate a general digital signal processing (DSP-oriented framework where the functional equivalence of these two approaches is systematically elaborated and the conditions of building mixed models are studied. An example of mixed modeling of a 2D waveguide is presented.

Karjalainen Matti

2004-01-01

142

The Rate of Convergence of Finite-Difference Approximations for Parabolic Bellman Equations with Lipschitz Coefficients in Cylindrical Domains  

International Nuclear Information System (INIS)

We consider degenerate parabolic and elliptic fully nonlinear Bellman equations with Lipschitz coefficients in domains. Error bounds of order h1/2 in the sup norm for certain types of finite-difference schemes are obtained

2007-06-01

143

Calculating photonic Green's functions using a non-orthogonal finite difference time domain method  

CERN Multimedia

In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain (FDTD) method, originally proposed by Yee, also known as the Order-N method, which has recently become a popular way of calculating photonic band structures. We give a new, transparent derivation of the Order-N method which, in turn, enables us to give a simple yet rigorous derivation of the criterion for numerical stability as well as statements of charge and energy conservation which are exact even on the discrete lattice. We implement this using a general, non-orthogonal co-ordinate system without incurring the computational overheads normally associated with non-orthogonal FDTD. We present results for local densities of states calculated using this method for a number of systems. Firstly, we consider a simple one dimensional dielectric multilayer, identifying the suppres...

Ward, A J

1998-01-01

144

Finite Difference Method of the Study on Radioactivities DispersionModeling in Environment of Ground  

International Nuclear Information System (INIS)

It has been resulted the mathematics equation as model of constructingthe computer algorithm deriving from the transport equation having been theform of radionuclides dispersion in the environment of ground as a result ofdiffusion and advection process. The derivation of mathematics equation usedthe finite difference method into three schemes, the explicit scheme,implicit scheme and Crank-Nicholson scheme. The computer algorithm then wouldbe used as the basic of making the software in case of making a monitoringsystem of automatic radionuclides dispersion on the area around the nuclearfacilities. By having the three schemes, so it would be, in choosing thesoftware system, able to choose the more approximate with the fact. (author)

2000-07-25

145

Iterative solutions of finite difference diffusion equations  

International Nuclear Information System (INIS)

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

1981-01-01

146

An anti-diffusive scheme for viability problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper is concerned with numerical approximation of viability kernels. We use a characterization of the viability kernel by the value function of an optimal control problem. Since this value function is discontinuous, usual discretization schemes (such as finite differences) provide poor approximation quality because of numerical diffusion. We investigate the use of the ultra-bee scheme for its anti-diffusive property in the transport of discontinuous functions. Numerical experiments, com...

Bokanowski, Olivier; Martin, Sophie; Munos, Remi; Zidani, Hasnaa

2004-01-01

147

A New Conservative Difference Scheme for the General Rosenau-RLW Equation  

Directory of Open Access Journals (Sweden)

Full Text Available A new conservative finite difference scheme is presented for an initial-boundary value problem of the general Rosenau-RLW equation. Existence of its difference solutions are proved by Brouwer fixed point theorem. It is proved by the discrete energy method that the scheme is uniquely solvable, unconditionally stable, and second-order convergent. Numerical examples show the efficiency of the scheme.

Zhang Tian-De

2010-01-01

148

Generalized Alternating-Direction Implicit Finite-Difference Time-Domain Method in Curvilinear Coordinate System  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, a novel approach is introduced towards an efficient Finite-Difference Time-Domain (FDTD) algorithm by incorporating the Alternating Direction Implicit (ADI) technique to the Nonorthogonal FDTD (NFDTD) method. This scheme can be regarded as an extension of the conventional ADI-FDTD scheme into a generalized curvilinear coordinate system. The improvement on accuracy and the numerical efficiency of the ADI-NFDTD over the conventional nonorthogonal and the ADI-FDTD algorithms is ca...

Wei Song; Yang Hao

2010-01-01

149

Finite difference numerical methods for boundary control problems governed by hyperbolic partial differential equations  

Science.gov (United States)

This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.

Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.

1983-01-01

150

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.  

Science.gov (United States)

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique. PMID:24527060

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

151

Discrete level schemes and their gamma radiation branching ratios (CENPL-DLS). Pt. 1  

International Nuclear Information System (INIS)

The DLS data file, which is a sub-library (version 1) of Chinese Evaluated Nuclear Parameter Library (CENPL), consists of data and information of discrete levels and gamma radiations. The data and information of this data file are translated from the Evaluated Nuclear Structure Data File (ENSDF). The transforming code from ENSDF to DLS was written. In the DLS data file, there are the data on discrete levels with determinate energy and their gamma radiations. At present, this file contains the data of 79456 levels and 100411 gammas for 1908 nuclides

1994-12-01

152

Skew-symmetric convection form and secondary conservative finite difference methods for moving grids  

Science.gov (United States)

The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-symmetric form have not been extended to those for moving grids. In this study, the skew-symmetric form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniform flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.

Morinishi, Yohei; Koga, Kazuki

2014-01-01

153

Using finite difference method to simulate casting thermal stress  

Directory of Open Access Journals (Sweden)

Full Text Available Thermal stress simulation can provide a scientific reference to eliminate defects such as crack, residual stress centralization and deformation etc., caused by thermal stress during casting solidification. To study the thermal stress distribution during casting process, a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method (FDM, namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete. A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process. Two practical verifications were carried out, and the results from simulation basically coincided with practical cases. The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress, and to predict the occurrence of hot tearing. Because heat transfer and stress analysis are all based on FDM, they can use the same FD model, which can avoid the matching process between different models, and hence reduce temperature-load transferring errors. This approach makes the simulation of fluid flow, heat transfer and stress analysis unify into one single model.

Liao Dunming

2011-05-01

154

Piecewise linear transformation in diffusive flux discretization  

CERN Document Server

To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along material discontinuities using only cell concentration values. This is often resolved by introducing auxiliary node, edge, or face concentration values that are explicitly interpolated from the surrounding cell concentrations. We propose to discretize the diffusive flux after applying a local piecewise linear coordinate transformation that effectively removes the discontinuities. The resulting scheme does not need any auxiliary concentrations and is therefore remarkably simpler, while being second-order accurate under the assumption that the structure of the domain is locally layered.

Vidovi?, D; Puši?, M; Pokorni, B

2014-01-01

155

Linear rational finite differences from derivatives of barycentric rational interpolants  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Derivatives of polynomial interpolants lead in a natural way to approximations of derivatives of the interpolated function, e.g., through finite differences. We extend a study of the approximation of derivatives of linear barycentric rational interpolants and present improved finite difference formulas arising from these interpolants. The formulas contain the classical finite differences as a special case and are more stable for calculating one-sided derivatives as well as derivatives close t...

Klein, Georges; Berrut, Jean-paul

2012-01-01

156

An assessment of semi-discrete central schemes for hyperbolic conservation laws  

International Nuclear Information System (INIS)

High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume schemes, implemented within a well-designed framework, are extremely efficient with (potentially) very low memory storage. Finally, we have found by computational experiment that second and third-order strong-stability preserving (SSP) time integration methods with the number of stages greater than the order provide a useful enhanced stability region. However, we observe that non-SSP and non-optimal SSP schemes with SSP factors less than one can still be very useful if used with time-steps below the standard CFL limit. The 'well-designed' integration schemes that we have examined appear to perform well in all instances where the time step is maintained below the standard physical CFL limit

2003-01-01

157

Discrete level schemes and their gamma radiation branching ratios (CENPL-DLS): Pt.2  

International Nuclear Information System (INIS)

The DLS data files contains the data and information of nuclear discrete levels and gamma rays. At present, it has 79461 levels and 93177 gamma rays for 1908 nuclides. The DLS sub-library has been set up at the CNDC, and widely used for nuclear model calculation and other field. the DLS management retrieval code DLS is introduced and an example is given for "5"6Fe. (1 tab.)

1996-06-01

158

An analytical discrete ordinates solution for two-dimensional problems based on nodal schemes  

International Nuclear Information System (INIS)

In this work, the ADO method is used to solve the integrated one dimensional equations generated by the application of a nodal scheme on the two dimensional transport problem in cartesian geometry. Particularly, relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed auxiliary equations. The ADO approach, along with a level symmetric quadrature scheme, lead to an important reduction in the order of the associated eigenvalue systems. Numerical results are presented for a two dimensional problem in order to compare with available results in the literature. (author)

2009-10-02

159

Improving sub-grid scale accuracy of boundary features in regional finite-difference models  

Science.gov (United States)

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Panday, Sorab; Langevin, Christian D.

2012-01-01

160

Improvement of the finite difference lattice Boltzmann method for low mach number flows  

International Nuclear Information System (INIS)

This paper presents a numerical method to compute flow-acoustic resonance at low Mach number within a reasonable computing time. Light water reactors have experienced flow-acoustic resonance which is attributed to unsteady compressible flows at low Mach number. This phenomenon is undesirable because the induced sound causes loud noise and vibrations of the mechanical structures. However, a numerical simulation of this flow-acoustic resonance at low Mach number requires a large computing time and a highly accurate method in order to simultaneously compute flows and acoustic waves. The finite difference lattice Boltzmann method which is a powerful tool for obtaining computational fluid dynamics has high accuracy for simultaneous calculation of flows and acoustic waves. It becomes an efficient method to compute low Mach number flow if the computing time is shortened. In this paper, the finite difference lattice Boltzmann method was sped up. Three improvements were proposed: development of a new particle model, modification of the governing equation, and employment of an efficient time marching scheme. The computing time of the proposed finite difference lattice Boltzmann model was compared with the conventional finite difference lattice Boltzmann model for the calculation of the cubic cavity flow. The results showed that the computing time of the proposed model is 30% of the time needed by the conventional finite difference lattice Boltzmann model. The flow-acoustic resonance at low Mach number at the side branch was calculated using the proposed model. The numerical results showed quantitative agreement with the experimental data. (author)

2009-10-02

 
 
 
 
161

Convergence Property of Response Matrix Method for Various Finite-Difference Formulations Used in the Nonlinear Acceleration Method  

International Nuclear Information System (INIS)

Convergence properties were investigated for the response matrix method with various finite-difference formulations that can be utilized in the nonlinear acceleration method. The nonlinear acceleration method is commonly used for the diffusion calculation with the advanced nodal method or the transport calculation with the method of characteristics. Efficiency of the nonlinear acceleration method depends on convergences on two different levels, i.e., those of the finite-difference calculation and the correction factor. This paper focuses on the former topic, i.e., the convergence property of finite-difference calculations using the response matrix method. Though various finite-difference formulations can be used in the nonlinear acceleration method, systematic analysis of the convergence property for the finite-difference calculation has not been carried out so far. The spectral radius of iteration matrixes was estimated for the various finite-difference calculations assuming the response matrix method with the red-black sweep. From the calculation results, numerical stability of the various finite-difference formulations was clarified, and a favorable form of the finite-difference formulation for the nonlinear iteration was recommended. The result of this paper will be useful for implementation of the nonlinear acceleration scheme with the response matrix method

2005-03-01

162

Discrete Mechanics and Optimal Control: an Analysis  

CERN Document Server

The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper is to directly discretize the variational description of the system's motion. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. We show that the DMOC approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The numerical performance of DMOC and its relationsh...

Ober-Bloebaum, S; Marsden, J E

2008-01-01

163

An assessment of semi-discrete central schemes for hyperbolic conservation laws.  

Energy Technology Data Exchange (ETDEWEB)

High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and introduce minimal dispersive and diffusive effects. High-resolution methods promise to provide greatly enhanced solution methods for Sandia's mainstream shock hydrodynamics and compressible flow applications, and they admit the possibility of a generalized framework for treating multi-physics problems such as the coupled hydrodynamics, electro-magnetics and radiative transport found in Z pinch physics. In this work, we describe initial efforts to develop a generalized 'black-box' conservation law framework based on modern high-resolution methods and implemented in an object-oriented software framework. The framework is based on the solution of systems of general non-linear hyperbolic conservation laws using Godunov-type central schemes. In our initial efforts, we have focused on central or central-upwind schemes that can be implemented with only a knowledge of the physical flux function and the minimal/maximal eigenvalues of the Jacobian of the flux functions, i.e., they do not rely on extensive Riemann decompositions. Initial experimentation with high-resolution central schemes suggests that contact discontinuities with the concomitant linearly degenerate eigenvalues of the flux Jacobian do not pose algorithmic difficulties. However, central schemes can produce significant smearing of contact discontinuities and excessive dissipation for rotational flows. Comparisons between 'black-box' central schemes and the piecewise parabolic method (PPM), which relies heavily on a Riemann decomposition, shows that roughly equivalent accuracy can be achieved for the same computational cost with both methods. However, PPM clearly outperforms the central schemes in terms of accuracy at a given grid resolution and the cost of additional complexity in the numerical flux functions. Overall we have observed that the finite volume schemes, implemented within a well-designed framework, are extremely efficient with (potentially) very low memory storage. Finally, we have found by computational experiment that second and third-order strong-stability preserving (SSP) time integration methods with the number of stages greater than the order provide a useful enhanced stability region. However, we observe that non-SSP and non-optimal SSP schemes with SSP factors less than one can still be very useful if used with time-steps below the standard CFL limit. The 'well-designed' integration schemes that we have examined appear to perform well in all instances where the time step is maintained below the standard physical CFL limit.

Christon, Mark Allen; Robinson, Allen Conrad; Ketcheson, David Isaac

2003-09-01

164

A Scheme to Share Information via Employing Discrete Algorithm to Quantum States  

International Nuclear Information System (INIS)

We propose a protocol for information sharing between two legitimate parties (Bob and Alice) via public-key cryptography. In particular, we specialize the protocol by employing discrete algorithm under mod that maps integers to quantum states via photon rotations. Based on this algorithm, we find that the protocol is secure under various classes of attacks. Specially, owe to the algorithm, the security of the classical privacy contained in the quantum public-key and the corresponding cipher text is guaranteed. And the protocol is robust against the impersonation attack and the active wiretapping attack by designing particular checking processing, thus the protocol is valid. (general)

2011-02-15

165

Equivalent constants to be used in finite difference diffusion calculations  

International Nuclear Information System (INIS)

Nowadays, we use very accurate transport codes for the fine treatment, in space and energy, of the very heterogeneous reactor lattices. However, such a procedure is prohibitively expensive for the core calculations and we only use it for the calculation of small subregions of the reactor (assemblies). The whole core calculation is generally performed using few groups diffusion codes on a rather simplified geometry. This calculation scheme implies the previous determination of broad-groups constants for homogenized regions. One of the most common methods to do this is called the flux weighted method. It is clear however that (for many well known reasons) using such group constants generally leads to unacceptable discrepancies in the reaction rates and consequently in the multiplication factors, in particular when absorbing or strong moderating regions are present. Despite those difficulties, if we want to perform diffusion calculations, we must introduce effective constants that reproduce transport reaction rates. The diffusion calculation with these constants will be equivalent, in a certain sense, to a reference. To achieve this goal, a code (EQUIPAGE) was written. Using an iterative procedure, matching reaction rates, this code is able to generate for each of the broad-groups a set of equivalent constants to be used in a finite difference diffusion calculation

1980-05-01

166

A nine-point finite difference operator for reduction of the Grid Orientation Effect  

Energy Technology Data Exchange (ETDEWEB)

The Grid Orientation Effect is a long-standing problem plaguing reservoir simulators that employ finite difference schemes for solution. The nine-point finite difference scheme is a well known way of reducing this effect. The schemes available in the literature are applicable only to point distributed grid systems. However, most simulators used in practice employ block centered grid systems. In this report we present a derivation of a new nine-point scheme for the block centered grid systems. The derivation is based on physical consideration and hence is free from any problems such as asymmetry or negativity of interblock transmissibilities that arise in some published schemes. The scheme is applicable to non-uniform rectangular grids and to reservoirs with inhomogeneous permeability distributions; both isotropic and anisotropic cases are treated. The expressions resulting from the new scheme reduce to those published in the literature when a square uniform grid and homogeneous isotropic permeability are considered. The reduction in the Grid Orientation Effect due to the new scheme is illustrated by a study of the steam-flood process in a five-spot pattern.

Shah, R.C.

1983-11-01

167

On the Rate of Convergence of the Finite-Difference Approximations for Parabolic Bellman Equations with Constant Coefficients  

International Nuclear Information System (INIS)

The error bounds of order h?1/2 for two types of finite-difference approximation schemes of parabolic Bellman equations with constant coefficients are obtained, where h is x-mesh size and ? is t-mesh size. The key methods employed are the maximum principles for the Bellman equation and the approximation schemes

2008-12-01

168

Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation  

Science.gov (United States)

A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

Jameson, A.

1976-01-01

169

Robust Watermarking Scheme for Multispectral Images Using Discrete Wavelet Transform and Tucker Decomposition  

Directory of Open Access Journals (Sweden)

Full Text Available Watermarking represents a potentially effective tool for the protection and verification of ownership rights in remote sensing images. Multispectral images (MSIs are the main type of images acquired by remote sensing radiometers. In this paper, a robust multispectral image watermarking technique based on the discrete wavelet transform (DWT and the tucker decomposition (TD is proposed. The core idea behind our proposed technique is to apply TD on the DWT coefficients of spectral bands of multispectral images. We use DWT to effectively separate multispectral images into different sub-images and TD to efficiently compact the energy of sub-images. Then watermark is embedded in the elements of the last frontal slices of the core tensor with the smallest absolute value. The core tensor has a good stability and represents the multispectral image properties. The experimental results on LANDSAT images show the proposed approach is robust against various types of attacks such as lossy compression, cropping, addition of noise etc.

Hai Fang

2013-11-01

170

An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources  

CERN Document Server

We present a new lossy compressor for discrete sources. For coding a source sequence $x^n$, the encoder starts by assigning a certain cost to each reconstruction sequence. It then finds the reconstruction that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of a sequence is given by a linear combination of its empirical probabilities of some order $k+1$ and its distortion relative to the source sequence. The linear structure of the cost in the empirical count matrix allows the encoder to employ a Viterbi-like algorithm for obtaining the minimizing reconstruction sequence simply. We identify a choice of coefficients for the linear combination in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance of any Markov source in the limit of large $n$, provided $k$ is increased as $o(\\log n)$.

Jalali, Shirin; Weissman, Tsachy

2009-01-01

171

A H-infinity Fault Detection and Diagnosis Scheme for Discrete Nonlinear System Using Output Probability Density Estimation  

International Nuclear Information System (INIS)

In this paper, a H-infinity fault detection and diagnosis (FDD) scheme for a class of discrete nonlinear system fault using output probability density estimation is presented. Unlike classical FDD problems, the measured output of the system is viewed as a stochastic process and its square root probability density function (PDF) is modeled with B-spline functions, which leads to a deterministic space-time dynamic model including nonlinearities, uncertainties. A weighting mean value is given as an integral function of the square root PDF along space direction, which leads a function only about time and can be used to construct residual signal. Thus, the classical nonlinear filter approach can be used to detect and diagnose the fault in system. A feasible detection criterion is obtained at first, and a new H-infinity adaptive fault diagnosis algorithm is further investigated to estimate the fault. Simulation example is given to demonstrate the effectiveness of the proposed approaches.

2009-03-05

172

A finite difference method for nonlinear parabolic-elliptic systems of second order partial differential equations  

Directory of Open Access Journals (Sweden)

Full Text Available This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations and the other of the elliptic type (equations with a parameter in a cube in $R^{1+n}$. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.

Marian Malec

2007-01-01

173

Investigation of finite difference recession computation techniques applied to a nonlinear recession problem  

International Nuclear Information System (INIS)

This report presents comparisons of results of five implicit and explicit finite difference recession computation techniques with results from a more accurate ''benchmark'' solution applied to a simple one-dimensional nonlinear ablation problem. In the comparison problem a semi-infinite solid is subjected to a constant heat flux at its surface and the rate of recession is controlled by the solid material's latent heat of fusion. All thermal properties are assumed constant. The five finite difference methods include three front node dropping schemes, a back node dropping scheme, and a method in which the ablation problem is embedded in an inverse heat conduction problem and no nodes are dropped. Constancy of thermal properties and the semiinfinite and one-dimensional nature of the problem at hand are not necessary assumptions in applying the methods studied to more general problems. The best of the methods studied will be incorporated into APL's Standard Heat Transfer Program

1978-01-01

174

A Skin Tone Based Stenographic Scheme using Double Density Discrete Wavelet Transforms.  

Directory of Open Access Journals (Sweden)

Full Text Available Steganography is the art of concealing the existence of data in another transmission medium i.e. image, audio, video files to achieve secret communication. It does not replace cryptography but rather boosts the security using its obscurity features. In the proposed method Biometric feature (Skin tone region is used to implement Steganography[1]. In our proposed method Instead of embedding secret data anywhere in image, it will be embedded in only skin tone region. This skin region provides excellent secure location for data hiding. So, firstly skin detection is performed using, HSV (Hue, Saturation, Value color space in cover images. Thereafter, a region from skin detected area is selected, which is known as the cropped region. In this cropped region secret message is embedded using DD-DWT (Double Density Discrete Wavelet Transform. DD-DWT overcomes the intertwined shortcomings of DWT (like poor directional selectivity, Shift invariance, oscillations and aliasing[2].optimal pixel adjustment process (OPA is used to enhance the image quality of the stego-image. Hence the image obtained after embedding secret message (i.e. Stego image is far more secure and has an acceptable range of PSNR. The proposed method is much better than the previous works both in terms of PSNR and robustness against various attacks (like Gaussian Noise, salt and pepper Noise, Speckle Noise, rotation, JPEG Compression, Cropping, and Contrast Adjustment etc.

Varsha Gupta

2013-07-01

175

Explicit and implicit finite-difference methods for the diffusion equation in two dimensions  

Energy Technology Data Exchange (ETDEWEB)

In this paper we focus our attention on rotationally symmetric problems, where cylinder coordinates are suitable. For Cartesian grid arrangements finite-difference schemes for the diffusion equation in two spatial dimensions are introduced. The temporal evolution is determined by implicit and explicit techniques. In addition to exactly solvable diffusion model problems we present numerical results of simulation experiments of a diamond disc window. (orig.)

Schneider, R.

2003-08-01

176

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations  

Science.gov (United States)

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Dey, C.; Dey, S. K.

1983-01-01

177

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier--Stokes equations  

CERN Document Server

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.

Einkemmer, Lukas

2013-01-01

178

Hidden sl$_{2}$-algebra of finite-difference equations  

CERN Document Server

The connection between polynomial solutions of finite-difference equations and finite-dimensional representations of the sl_2-algebra is established. (Talk presented at the Wigner Symposium, Guadalajara, Mexico, August 1995; to be published in Proceedings)

Smirnov, Yu F; Smirnov, Yuri; Turbiner, Alexander

1995-01-01

179

FINITE DIFFERENCE SIMULATION OF LOW CARBON STEEL MANUAL ARC WELDING  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This study discusses the evaluation and simulation of angular distortion in welding joints, and the ways of controlling and treating them, while welding plates of (low carbon steel) type (A-283-Gr-C) through using shielded metal arc welding. The value of this distortion is measured experimentally and the results are compared with the suggested finite difference method computer program. Time dependent temperature distributions are obtained using finite difference method. This distribution is u...

Al-sa Ady, Moneer H.; Abdulsattar, Mudar A.; Al-khafagy, Laith S.

2011-01-01

180

The representation of absorbers in finite difference diffusion codes  

International Nuclear Information System (INIS)

In this paper we present a new method of representing absorbers in finite difference codes utilising the analytical flux solution in the vicinity of the absorbers. Taking an idealised reactor model, numerical comparisons are made between the finite difference eigenvalues and fluxes and results obtained from a purely analytical treatment of control rods in a reactor (the Codd-Rennie method), and agreement is found to be encouraging. The method has been coded for the IBM7090. (author)

1963-01-01

 
 
 
 
181

Analysis of the finite difference time domain technique to solve the Schroedinger equation for quantum devices  

International Nuclear Information System (INIS)

An extension of the finite difference time domain is applied to solve the Schroedinger equation. A systematic analysis of stability and convergence of this technique is carried out in this article. The numerical scheme used to solve the Schroedinger equation differs from the scheme found in electromagnetics. Also, the unit cell employed to model quantum devices is different from the Yee cell used by the electrical engineering community. A bound for the time step is derived to ensure stability. Several numerical experiments in quantum structures demonstrate the accuracy of a second order, comparable to the analysis of electromagnetic devices with the Yee cell

2004-06-15

182

Optimized discrete wavelet transforms in the cubed sphere with the lifting scheme—implications for global finite-frequency tomography  

Science.gov (United States)

Wavelets are extremely powerful to compress the information contained in finite-frequency sensitivity kernels and tomographic models. This interesting property opens the perspective of reducing the size of global tomographic inverse problems by one to two orders of magnitude. However, introducing wavelets into global tomographic problems raises the problem of computing fast wavelet transforms in spherical geometry. Using a Cartesian cubed sphere mapping, which grids the surface of the sphere with six blocks or 'chunks', we define a new algorithm to implement fast wavelet transforms with the lifting scheme. This algorithm is simple and flexible, and can handle any family of discrete orthogonal or bi-orthogonal wavelets. Since wavelet coefficients are local in space and scale, aliasing effects resulting from a parametrization with global functions such as spherical harmonics are avoided. The sparsity of tomographic models expanded in wavelet bases implies that it is possible to exploit the power of compressed sensing to retrieve Earth's internal structures optimally. This approach involves minimizing a combination of a ?2 norm for data residuals and a ?1 norm for model wavelet coefficients, which can be achieved through relatively minor modifications of the algorithms that are currently used to solve the tomographic inverse problem.

Chevrot, Sébastien; Martin, Roland; Komatitsch, Dimitri

2012-12-01

183

Error estimates for finite difference approximations of American put option price  

CERN Document Server

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space discretisation parameter is proved by reformulating the corresponding optimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellman equation. Furthermore, the error arising from restricting the discrete problem to a finite grid by reducing the original problem to a bounded domain is estimated.

Šiška, David

2011-01-01

184

A fast Cauchy-Riemann solver. [differential equation solution for boundary conditions by finite difference approximation  

Science.gov (United States)

The inhomogeneous Cauchy-Riemann equations in a rectangle are discretized by a finite difference approximation. Several different boundary conditions are treated explicitly, leading to algorithms which have overall second-order accuracy. All boundary conditions with either u or v prescribed along a side of the rectangle can be treated by similar methods. The algorithms presented here have nearly minimal time and storage requirements and seem suitable for development into a general-purpose direct Cauchy-Riemann solver for arbitrary boundary conditions.

Ghil, M.; Balgovind, R.

1979-01-01

185

A holistic finite difference approach models linear dynamics consistently  

CERN Multimedia

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of finite difference models under nonlinear and other perturbations on grids with finite spacing. For example, the advection-diffusion equation is found to be stably modelled for all advection speeds and all grid spacing. The theorems establish an extremely good form for the artificial internal boundary conditions that need to be introduced to apply centre manifold theory. When numerically solving nonlinear partial differential equations, this approach can be used to derive systematically finite difference models which automatically have excellent characteristics. Their good performance for finite grid spacing implies that fewer grid points may be used and consequently there will be less difficulties with stiff rapidly decaying modes in continuum problems.

Roberts, A J

2000-01-01

186

Consistency Analysis of Finite Difference Approximations to PDE Systems  

CERN Multimedia

n the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals in the independent variables. The notion of strong consistency which we introduced earlier for linear systems is extended to nonlinear ones. For orthogonal and uniform grids we describe an algorithmic procedure for verification of strong consistency based on computation of difference standard bases. The concepts and algorithmic methods of the present paper are illustrated by two finite difference approximations to the two-dimensional Navier-Stokes equations. One of these approximations is strongly consistent and another is not.

Gerdt, Vladimir P

2011-01-01

187

Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation  

International Nuclear Information System (INIS)

Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a low order method.

2012-01-01

188

Serpentine: Finite Difference Methods for Wave Propagation in Second Order Formulation  

Energy Technology Data Exchange (ETDEWEB)

Wave propagation phenomena are important in many DOE applications such as nuclear explosion monitoring, geophysical exploration, estimating ground motion hazards and damage due to earthquakes, non-destructive testing, underground facilities detection, and acoustic noise propagation. There are also future applications that would benefit from simulating wave propagation, such as geothermal energy applications and monitoring sites for carbon storage via seismic reflection techniques. In acoustics and seismology, it is of great interest to increase the frequency bandwidth in simulations. In seismic exploration, greater frequency resolution enables shorter wave lengths to be included in the simulations, allowing for better resolution in the seismic imaging. In nuclear explosion monitoring, higher frequency seismic waves are essential for accurate discrimination between explosions and earthquakes. When simulating earthquake induced motion of large structures, such as nuclear power plants or dams, increased frequency resolution is essential for realistic damage predictions. Another example is simulations of micro-seismic activity near geothermal energy plants. Here, hydro-fracturing induces many small earthquakes and the time scale of each event is proportional to the square root of the moment magnitude. As a result, the motion is dominated by higher frequencies for smaller seismic events. The above wave propagation problems are all governed by systems of hyperbolic partial differential equations in second order differential form, i.e., they contain second order partial derivatives of the dependent variables. Our general research theme in this project has been to develop numerical methods that directly discretize the wave equations in second order differential form. The obvious advantage of working with hyperbolic systems in second order differential form, as opposed to rewriting them as first order hyperbolic systems, is that the number of differential equations in the second order system is significantly smaller. Another issue with re-writing a second order system into first order form is that compatibility conditions often must be imposed on the first order form. These (Saint-Venant) conditions ensure that the solution of the first order system also satisfies the original second order system. However, such conditions can be difficult to enforce on the discretized equations, without introducing additional modeling errors. This project has previously developed robust and memory efficient algorithms for wave propagation including effects of curved boundaries, heterogeneous isotropic, and viscoelastic materials. Partially supported by internal funding from Lawrence Livermore National Laboratory, many of these methods have been implemented in the open source software WPP, which is geared towards 3-D seismic wave propagation applications. This code has shown excellent scaling on up to 32,768 processors and has enabled seismic wave calculations with up to 26 Billion grid points. TheWPP calculations have resulted in several publications in the field of computational seismology, e.g.. All of our current methods are second order accurate in both space and time. The benefits of higher order accurate schemes for wave propagation have been known for a long time, but have mostly been developed for first order hyperbolic systems. For second order hyperbolic systems, it has not been known how to make finite difference schemes stable with free surface boundary conditions, heterogeneous material properties, and curvilinear coordinates. The importance of higher order accurate methods is not necessarily to make the numerical solution more accurate, but to reduce the computational cost for obtaining a solution within an acceptable error tolerance. This is because the accuracy in the solution can always be improved by reducing the grid size h. However, in practice, the available computational resources might not be large enough to solve the problem with a low order method.

Petersson, N A; Sjogreen, B

2012-03-26

189

The Discrete Geometric Conservation Law and the Nonlinear Stability of ALE Schemes for the Solution of Flow Problems on Moving Grids  

Science.gov (United States)

Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.

Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline

2001-12-01

190

Variational integrators on fractional Lagrangian systems in the framework of discrete embedddings  

CERN Document Server

In this paper, we introduce the notion of discrete embedding which is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. We first define the Gauss finite differences embedding. In this setting, we study variational integrator on classical Lagrangian systems. Finally, we extend these constructions to the fractional case. In particular, we define the Gauss Gr\\"unwald-Letnikov embedding and the corresponding variational integrator on fractional Lagrangian systems.

Bourdin, Loïc; Greff, Isabelle; Inizan, Pierre

2011-01-01

191

Examination on Fast Algorithms of Compact Finite Difference Calculation for Finite Difference Time Domain Acoustic Wave Simulation  

Science.gov (United States)

In this study we examined a fast and efficient calculation method for compact finite-differences (FDs). The proposed method employs a recursive filter (RF) method. This method is based on z-transformation and its RF algorithm. Analysis of sound propagation using compact FDs with the RF method was implemented. Using the RF algorithm, we can implement compact finite difference time domain (FD-TD) analysis as a simpler code than a conventional technique using LU factorization, i.e., the Tomas method. The results obtained in this study clarified that the RF method reduces calculation time required for compact FDs.

Yoda, Takeshi; Okubo, Kan; Tagawa, Norio; Tsuchiya, Takao

2011-07-01

192

Finite difference time domain modelling of particle accelerators  

International Nuclear Information System (INIS)

Finite Difference Time Domain (FDTD) modelling has been successfully applied to a wide variety of electromagnetic scattering and interaction problems for many years. Here the method is extended to incorporate the modelling of wake fields in particle accelerators. Algorithmic comparisons are made to existing wake field codes, such as MAFIA T3. 9 refs., 7 figs

1989-03-20

193

Solving the track wall equation by the finite difference method  

Energy Technology Data Exchange (ETDEWEB)

The two-dimensional equation of a track wall was rewritten in a form suitable for the finite difference method and numerically solved using the MATHEMATICA software. The results obtained were compared with the ones obtained using other computer software for calculation of the track parameters and profile, as well as, with experimental data, and good agreement was found.

Nikezic, D. [University of Kragujevac, Faculty of Science, R. Domanovic 12, 34000 Kragujevac (Serbia); Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)], E-mail: nikezic@kg.ac.yu; Stevanovic, N.; Kostic, D.; Savovic, S. [University of Kragujevac, Faculty of Science, R. Domanovic 12, 34000 Kragujevac (Serbia); Tse, K.C.C.; Yu, K.N. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)

2008-08-15

194

Solving the track wall equation by the finite difference method  

International Nuclear Information System (INIS)

The two-dimensional equation of a track wall was rewritten in a form suitable for the finite difference method and numerically solved using the MATHEMATICA software. The results obtained were compared with the ones obtained using other computer software for calculation of the track parameters and profile, as well as, with experimental data, and good agreement was found

2008-08-01

195

A FINITE DIFFERENCE SOLUTION OF NUCLEAR REACTOR KINETICS EQUATIONS  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference first order integration formula for a set of ordinary differential equations has been developed. It has been shown that this formula gives better estimation of an error in the meaning of an Euclidean norm than those already known. The proposed method has been illustrated by examples. A special attention has been paid to nuclear reactor kinetics equations.

Micha? Podowski

1972-01-01

196

On the spectrum of relativistic Schrödinger equation in finite differences  

CERN Multimedia

We develop a method for constructing asymptotic solutions of finite-difference equations and implement it to a relativistic Schroedinger equation which describes motion of a selfgravitating spherically symmetric dust shell. Exact mass spectrum of black hole formed due to the collapse of the shell is determined from the analysis of asymptotic solutions of the equation.

Berezin, V A; Neronov, Andrii Yu

1999-01-01

197

Continuous dependence and differentiation of solutions of finite difference equations  

Directory of Open Access Journals (Sweden)

Full Text Available Conditions are given for the continuity and differentiability of solutions of initial value problems and boundary value problems for the nth order finite difference equation, u(m+n=f(m,u(m,u(m+1,…,u(m+n−1,m∈ℤ.

Linda Lee

1991-01-01

198

Derivation of the finite difference equations for a heterogeneous reactor  

International Nuclear Information System (INIS)

General procedure for obtaining specified finite-difference equations of a heterogeneous reactor is described for the particular case of a two-dimensional reactor with a square lattice of blocks general problems on obtaining equations in geometrically regular heterogeneous lattice of cylindrical rods are discussed. The solution in a reactor cell is presented in a form of a linear combination of experimental functions satisfying inside the cell the kinetic equation and some boundary conditions. On the basis of considering an expression for an error in a certain succession of functionals investigated the equations of communication of experimental functions amplitudes in neighbouring cells are obtained. It is shown on an example of a square lattice as to how by means of an analytic exlusion of ''superfluous'' amplitudes from equations, the finite difference equations are obtained which describe the neutron flux macro-passage over the reactor and have the appearance of a finite-difference approximation of a diffusion equation. The whole study is carried out on the basis of a kinetic equation with a continuous energy dependence. Final finite difference equations are registered in a group approximation

1980-01-01

199

HEATING-7, Multidimensional Finite-Difference Heat Conduction Analysis  

International Nuclear Information System (INIS)

1 - Description of program or function: HEATING 7.2i and 7.3 are the most recent developments in a series of heat-transfer codes and obsolete all previous versions distributed by RSICC as SCA-1/HEATING5 and PSR-199/HEATING 6. Note that Unix and PC versions of HEATING7 are available in the CCC-545/SCALE 4.4 package. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat- generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a run-time memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. In June 1997 HEATING 7.3 was added to the HEATING 7.2i packages, and the Unix and PC versions of both 7.2i and 7.3 were merged into one package. HEATING 7.3 is being released as a beta-test version; therefore, it does not entirely replace HEATING 7.2i. There is no published documentation for HEATING 7.3; but a listing of input specifications, which reflects changes for 7.3, is included in the PSR-199 documentation. For 3-D problems, surface fluxes may be plotted with H7TECPLOT which requires the proprietary software TECPLOT. HEATING 7.3 runs under Windows95 and WindowsNT on PC's. No future modifications are planned for HEATING7. See README.1ST for more information. 2 - Method of solution: Three steady-state solution techniques are available: point-successive over-relaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion.) The solution of the system of equations arising from the implicit techniques is accomplished by point-successive over-relaxation iteration and includes procedures to estimate the optimum acceleration parameter. 3 - Restrictions on the complexity of the problem: All surfaces in a model must be parallel to one of the coordinate axes which makes modeling complex geometries difficult. Transient change of phase problems can only be solved with one of the explicit techniques - an implicit change-of-phase capability has not been implemented

2000-01-01

200

The Effect of Nodalization on the Accuracy of the Finite Difference Solution of the Transient Conduction Equation.  

Energy Technology Data Exchange (ETDEWEB)

One of the important phenomena that thermal-hydraulic codes such as RELAP5 must accurately calculate is heat transfer between a fluid and solid. Currently all thermal-hydraulic safety codes use the finite-difference technique to solve the transient conduction equation. This paper will examine the effect of different nodalization strategies on the accuracy of the finite-difference solution of a transient conduction problem with one convective boundary condition and no internal heat generation. The paper concludes with recommendations for choosing an appropriate nodalization scheme for modeling conduction in a wall without internal heat generation.

Aumiller, D.L.

2000-07-01

 
 
 
 
201

On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 1: semi-implicit scheme  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We discuss a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis. We describe a semi-implicit time discretization that extends the range of numerical stability relative to an explicit scheme. We also introduce and discuss the effects of an artificial collisional operator, which is necessary to take care of the velocity space filamentation problem, unavoidable in collisionless plasmas. The...

Camporeale, Enrico; Delzanno, Gian Luca; Bergen, Benjamin K.; Moulton, J. David

2013-01-01

202

Finite difference analysis for Navier-Stokes and energy equations of Couette-Poiseuille flow  

International Nuclear Information System (INIS)

Numerical results for the problem of combined convective heat transfer in a vertical annular gap between two concentric Isothermal cylinders, are presented. Emphasis was given to the effects of the inlet temperature, flow direction and the inner cylinder rotation on hydrodynamic and heat transfer characteristics. The boundary layer simplifications of the Navier-Stokes equations and the energy equation were solved by means of an extension of the linearized finite difference scheme used previously by Coney and El-Shaarawi (1975). The results were obtained for Re of 100, 200 and 250, 04 and -2x1044. 14 refs.; 11 figs

1988-01-01

203

Numerical simulation of shock wake propagation using the finite difference lattice Boltzmann method  

International Nuclear Information System (INIS)

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the Finite Difference Lattice Boltzmann Method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions

2002-10-01

204

Numerical simulation of shock wake propagation using the finite difference lattice Boltzmann method  

Energy Technology Data Exchange (ETDEWEB)

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the Finite Difference Lattice Boltzmann Method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions.

Kang, Ho Keun; Ro, Ki Deok [Gyeongnam National Univ., Tongyeong (Korea, Republic of); Tsutahara, Michihisa [Kobe Univ., Kobe (Japan); Lee, Young Ho [Korea Maritime Univ., Busan (Korea, Republic of)

2002-10-01

205

Finite-difference modeling with variable grid-size and adaptive time-step in porous media  

Science.gov (United States)

Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.

Liu, Xinxin; Yin, Xingyao; Wu, Guochen

2014-04-01

206

Earthquake Rupture dynamics in complex geometries using coupled high-order finite difference methods and finite volume methods  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a 2-D multi-block method for earthquake rupture dynamics in complex geometries using summation-byparts (SBP) high-order finite differences on structured grids coupled to nite volume methods on unstructured meshes. The node-centered nite volume method is used on unstructured triangular meshes to resolve earthquake ruptures propagating along non-planar faults with complex geometrical features. The unstructured meshes discretize the fault geometry only in the vicinity of the faults an...

O´reilly, Ossian; Dunham, Eric M.; Kozdon, Jeremy E.; Nordstro?m, Jan

2012-01-01

207

Time-dependent optimal heater control using finite difference method  

Energy Technology Data Exchange (ETDEWEB)

Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying temperature of forming window.

Li, Zhen Zhe; Heo, Kwang Su; Choi, Jun Hoo; Seol, Seoung Yun [Chonnam National Univ., Gwangju (Korea, Republic of)

2008-07-01

208

Finite-difference modeling experiments for seismic interferometry :  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In passive seismic interferometry, new reflection data can be retrieved by crosscorrelating recorded noise data. The quality of the retrieved reflection data is, among others, dependent on the duration and number of passive sources present during the recording time, the source distribution, and the source strength. To investigate these relations we set up several numerical modeling studies. To carry out the modeling in a feasible time, we design a finite-difference algorithm for the simulatio...

Thorbecke, J. W.; Draganov, D.

2011-01-01

209

Stochastic finite differences for elliptic diffusion equations in stratified domains  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We describe Monte Carlo algorithms to solve elliptic partial differen- tial equations with piecewise constant diffusion coefficients and general boundary conditions including Robin and transmission conditions as well as a damping term. The treatment of the boundary conditions is done via stochastic finite differences techniques which possess an higher order than the usual methods. The simulation of Brownian paths inside the domain relies on variations around the walk on spheres method with or...

2013-01-01

210

Introduction to finite-difference methods for numerical fluid dynamics  

Energy Technology Data Exchange (ETDEWEB)

This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.

Scannapieco, E.; Harlow, F.H.

1995-09-01

211

Esquema de discretização Flux-Spline aplicado à secagem, em meio poroso capilar Flux-Spline discretization scheme applied to drying in capillary porous media  

Directory of Open Access Journals (Sweden)

Full Text Available Este trabalho foi desenvolvido com o objetivo de se apresentar a aplicação de um esquema de discretização mais eficiente para volumes finitos, denominado Flux-Spline utilizando-se, para tal, de dois casos de transporte difusivo de umidade e calor, através de um meio poroso capilar. Os resultados da solução numérica do sistema de equações formado pelas equações de Luikov mostram desempenho adequado do esquema para este tipo de problema, quando comparado ao tradicional esquema de diferença central e ao método da transformada integral.This study was conducted with the objective to present a more efficient discretization scheme to finite volumes method called Flux-Spline, utilising for the purpose two cases of pure diffusion in capillary porous media. The results of numerical simulation of the equations system formed by Luikov equations showed a good performance of the scheme in comparison to the Central Difference Scheme and Generalised Integral Transform Technique method.

Paulo C. Oliveira

2003-04-01

212

Seismic imaging using finite-differences and parallel computers  

Energy Technology Data Exchange (ETDEWEB)

A key to reducing the risks and costs of associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Prestack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar wave equation using finite differences. As part of an ongoing ACTI project funded by the US Department of Energy, a finite difference, 3-D prestack, depth migration code has been developed. The goal of this work is to demonstrate that massively parallel computers can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite difference, prestack, depth migration practical for oil and gas exploration. Several problems had to be addressed to get an efficient code for the Intel Paragon. These include efficient I/O, efficient parallel tridiagonal solves, and high single-node performance. Furthermore, to provide portable code the author has been restricted to the use of high-level programming languages (C and Fortran) and interprocessor communications using MPI. He has been using the SUNMOS operating system, which has affected many of his programming decisions. He will present images created from two verification datasets (the Marmousi Model and the SEG/EAEG 3D Salt Model). Also, he will show recent images from real datasets, and point out locations of improved imaging. Finally, he will discuss areas of current research which will hopefully improve the image quality and reduce computational costs.

Ober, C.C. [Sandia National Labs., Albuquerque, NM (United States)

1997-12-31

213

High order well-balanced schemes  

Energy Technology Data Exchange (ETDEWEB)

In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They discuss two classes of schemes, one based on high-order accurate, non-oscillatory finite difference operators which are well-balanced for a general class of equilibria, and the other one based on well-balanced quadratures, which can - in principle - be applied to all equilibria. Applications include equilibria at rest, where the flow velocity vanishes, and also the more challenging moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria.

Noelle, Sebastian [Institut fur Physikalische Chemie der RWTH; Xing, Yulong [ORNL; Shu, Chi-wang [Brown University

2010-01-01

214

Finite difference evolution equations and quantum dynamical semigroups  

International Nuclear Information System (INIS)

We consider the recently proposed [Bonifacio, Lett. Nuovo Cimento, 37, 481 (1983)] coarse grained description of time evolution for the density operator rho(t) through a finite difference equation with steps tau, and we prove that there exists a generator of the quantum dynamical semigroup type yielding an equation giving a continuous evolution coinciding at all time steps with the one induced by the coarse grained description. The map rho(0)?rho(t) derived in this way takes the standard form originally proposed by Lindblad [Comm. Math. Phys., 48, 119 (1976)], even when the map itself (and, therefore, the corresponding generator) is not bounded. (author)

1983-01-01

215

Investigation of Wave Propagation in Different Dielectric Media by Using Finite Difference Time Domain (FDTD Method  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, the wave propagation in free space and different dielectric material by using Finite Difference Time Domain (FDTD method has been studied. Among various numerical methods Finite Difference Time Domain method is being used to study the time evolution behavior of electromagnetic field by solving the Maxwell’sequation in time domain. In this paper, FDTD method has been employed to study the wave propagation in free space and different dielectric materials. The wave equations are discretized in time and space as required by this FDTD method and leaf-frog algorithm is used to find the solution. We observed wave propagation for one and two dimensional cases. We also observed wave propagation through lossy medium for one dimensional case. For two dimensional cases the patterns of wave incident on rectangular dielectric slab, square metal, RCC pillar were observed. In order to visualize the wave propagation, the evaluation of the excitation at various locations of problem space is monitored. The numerical results agree with the propagation characteristics as expected.

Md. Kamal Hossain

2010-10-01

216

On destabilizing implicit factors in discrete advection-diffusion equations  

Energy Technology Data Exchange (ETDEWEB)

In the present paper, we find necessary and sufficient stability conditions for a simple one-time step finite difference discretization of an N-dimensional advection-diffusion equation. Furthermore, it is shown that when the implicit factors differ in each direction, a strange behavior occurs: By increasing one implicit factor in only one direction, a stable scheme can become unstable. It is thus suggested to use a single implicit direction (for efficient computing), or the same implicit factor in each direction. 7 refs., 3 figs.

Beckers, J.M. (Univ. of Liege (Belgium))

1994-04-01

217

HEXG - a centre mesh finite difference code to solve multigroup diffusion equations in two dimensional hexagonal geometry  

International Nuclear Information System (INIS)

For analysing the hexagonal reactor by multigroup diffusion theory a two dimensional finite difference code HEXG has been written. Mesh-centred finite difference scheme with hexagonal meshes gives rise to seven point coupling. One can consider 30deg, 60deg, 90deg, 120deg symmetry in addition to a full core treatment. HEXG can be used for analysis of a single fuel assembly with reflective boundary conditions on all sides. One can also perform a detailed core analysis with single fuel pin representation wherein the external boundary condition is either xero flux or vacuum boundary. The solution method is point successive over relaxation (PSOR) with a generalised coarse mesh rebalancing (CMR) acceleration scheme for the inner loop of iterations. HEXG is used for determining the eigenvalue or K-effective, flux, adjoint flux and power distributions in hexagonal lattice/core configurations. (author). 14 refs., 5 tabs., 8 figs

1989-01-01

218

A two-dimensional finite difference solution for the transient thermal behavior of tubular solar collector  

Science.gov (United States)

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.

1976-01-01

219

A Variational Finite Difference Method for Time-Dependent Stokes Flow on Irregular Domains  

CERN Document Server

We restate time-dependent Stokes flow for incompressible Newtonian fluids as a variational problem relating velocity, pressure, and deviatoric stress variables, which leads to a simple weighted finite difference discretization on staggered Cartesian grids. The method easily handles irregular domains involving both free surfaces and moving solid boundaries by exploiting natural boundary conditions, while supporting spatially varying viscosity and density. Due to its basis in extremizing a well-posed quadratic functional, the resulting linear system is sparse and symmetric indefinite. It can also be converted to an equivalent sparse, symmetric positive-definite system by applying a simple and inexpensive algebraic manipulation, allowing the use of a wide range of efficient linear solvers. We demonstrate that the method achieves first order convergence in velocity on a range of test cases. In addition, we apply our method as part of a simple Navier-Stokes solver to illustrate that it can reproduce the characteri...

Batty, Christopher

2010-01-01

220

Finite Difference Elastic Wave Field Simulation On GPU  

Science.gov (United States)

Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.

Hu, Y.; Zhang, W.

2011-12-01

 
 
 
 
221

Finite-Difference Frequency-Domain Method in Nanophotonics  

DEFF Research Database (Denmark)

Optics and photonics are exciting, rapidly developing fields building their success largely on use of more and more elaborate artificially made, nanostructured materials. To further advance our understanding of light-matter interactions in these complicated artificial media, numerical modeling is often indispensable. This thesis presents the development of rigorous finite-difference method, a very general tool to solve Maxwellâ??s equations in arbitrary geometries in three dimensions, with an emphasis on the frequency-domain formulation. Enhanced performance of the perfectly matched layers is obtained through free space squeezing technique, and nonuniform orthogonal grids are built to greatly improve the accuracy of simulations of highly heterogeneous nanostructures. Examples of the use of the finite-difference frequency-domain method in this thesis range from simulating localized modes in a three-dimensional photonic-crystal membrane-based cavity, a quasi-one-dimensional nanobeam cavity and arrays of side-coupled nanobeam cavities, to modeling light propagation through metal films with single or periodically arranged multiple subwavelength slits.

Ivinskaya, Aliaksandra

2011-01-01

222

Finite-difference analysis of shells impacting rigid barriers  

International Nuclear Information System (INIS)

The present investigation represents an initial attempt to develop an efficient numerical procedure for predicting the deformations and impact force time-histories of shells which impact upon a rigid target. The general large-deflection equations of motion of the shell are expressed in finite-difference form in space and integrated in time through application of the central-difference temporal operator. The effect of material nonlinearities is treated by a mechanical-sublayer material model which handles the strain-hardening, Bauschinger, and strain-rate effects. The general adequacy of this shell treatment has been validated by comparing predictions with the results of various experiments in which structures have been subjected to well-defined transient forcing functions (typically high-explosive impulse loading). The 'new' ingredient addressed in the present study involves an accounting for impact interaction and response of both the target structure and the attacking body. The impact capability of the code consists of two basic components: (a) an inspection technique which determines the occurrence and location of a collision between the shell and the target. (b) an impact force application technique which determines impact pressure based on shell penetration and penetration stiffness of the shell through the equilibrium equations to influence the response of the shell. By this procedure, the local collision analysis is combined simply in an efficient manner with the spatial and temporal finite-different solution procedure to predict the resulting transient nonlinear response of impacting shells

1977-08-19

223

High-Field Wave Packets in Semiconductor Quantum Wells: A Real-Space Finite-Difference Time-Domain Formalism  

Digital Repository Infrastructure Vision for European Research (DRIVER)

An untraditional space-time method for describing the dynamics of high-field electron-hole wave packets in semiconductor quantum wells is presented. A finite-difference time-domain technique is found to be computationally efficient and can incorporate Coulomb, static, terahertz, and magnetic fields to all orders, and thus can be applied to study many areas of high-field semiconductor physics. Several electro-optical and electro-magneto-optical excitation schemes are studied, some well know...

Hughes, S.

2004-01-01

224

Finite-difference solution of the space-angle-lethargy-dependent slowing-down transport equation  

International Nuclear Information System (INIS)

A procedure has been developed for solving the slowing-down transport equation for a cylindrically symmetric reactor system. The anisotropy of the resonance neutron flux is treated by the spherical harmonics formalism, which reduces the space-angle-Iethargy-dependent transport equation to a matrix integro-differential equation in space and lethargy. Replacing further the lethargy transfer integral by a finite-difference form, a set of matrix ordinary differential equations is obtained, with lethargy-and space dependent coefficients. If the lethargy pivotal points are chosen dense enough so that the difference correction term can be ignored, this set assumes a lower block triangular form and can be solved directly by forward block substitution. As in each step of the finite-difference procedure a boundary value problem has to be solved for a non-homogeneous system of ordinary differential equations with space-dependent coefficients, application of any standard numerical procedure, for example, the finite-difference method or the method of adjoint equations, is too cumbersome and would make the whole procedure practically inapplicable. A simple and efficient approximation is proposed here, allowing analytical solution for the space dependence of the spherical-harmonics flux moments, and hence the derivation of the recurrence relations between the flux moments at successive lethargy pivotal points. According to the procedure indicated above a computer code has been developed for the CDC -3600 computer, which uses the KEDAK nuclear data file. The space and lethargy distribution of the resonance neutrons can be computed in such a detailed fashion as the neutron cross-sections are known for the reactor materials considered. The computing time is relatively short so that the code can be efficiently used, either autonomously, or as part of some complex modular scheme. Typical results will be presented and discussed in order to prove and illustrate the applicability of the method proposed. (author)

1972-01-17

225

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows  

Science.gov (United States)

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark

1998-01-01

226

Direct method of solving finite difference nonlinear equations for multicomponent diffusion in a gas centrifuge  

International Nuclear Information System (INIS)

This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)

1996-09-22

227

A coarse-mesh nodal method-diffusive-mesh finite difference method  

Energy Technology Data Exchange (ETDEWEB)

Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.

Joo, H.; Nichols, W.R.

1994-05-01

228

A coarse-mesh nodal method-diffusive-mesh finite difference method  

International Nuclear Information System (INIS)

Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper

1994-06-11

229

Implicit Schemes for Numeric Integration. Part 1: Long Baratropic and Gravity Wave Equations Esquemas Implicitos de Integracao Numerica Parte 1: Equacoes de Ondas Longas, Baratropicas de Gravidade.  

Science.gov (United States)

Implicit finite-difference schemes used in Numerical Weather Prediction because the time saved in the calculations may be used in improving the accuracy of the space finite-difference schemes. The computational properties of an implicit scheme were studie...

M. A. M. Lemes Y. Yamazaki

1981-01-01

230

Stability analysis for acoustic wave propagation in tilted TI media by finite differences  

Science.gov (United States)

Several papers in recent years have reported instabilities in P-wave modelling, based on an acoustic approximation, for inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media). In particular, instabilities tend to occur if the axis of symmetry varies rapidly in combination with strong contrasts of medium parameters, which is typically the case at the foot of a steeply dipping salt flank. In a recent paper, we have proposed and demonstrated a P-wave modelling approach for TTI media, based on rotated stress and strain tensors, in which the wave equations reduce to a coupled set of two second-order partial differential equations for two scalar stress components: a normal component along the variable axis of symmetry and a lateral component of stress in the plane perpendicular to that axis. Spatially constant density is assumed in this approach. A numerical discretization scheme was proposed which uses discrete second-derivative operators for the non-mixed second-order derivatives in the wave equations, and combined first-derivative operators for the mixed second-order derivatives. This paper provides a complete and rigorous stability analysis, assuming a uniformly sampled grid. Although the spatial discretization operator for the TTI acoustic wave equation is not self-adjoint, this operator still defines a complete basis of eigenfunctions of the solution space, provided that the solution space is somewhat restricted at locations where the medium is elliptically anisotropic. First, a stability analysis is given for a discretization scheme, which is purely based on first-derivative operators. It is shown that the coefficients of the central difference operators should satisfy certain conditions. In view of numerical artefacts, such a discretization scheme is not attractive, and the non-mixed second-order derivatives of the wave equation are discretized directly by second-derivative operators. It is shown that this modification preserves stability, provided that the central difference operators of the second-order derivatives dominate over the twice applied operators of the first-order derivatives. In practice, it turns out that this is almost the case. Stability of the desired discretization scheme is enforced by slightly weighting down the mixed second-order derivatives in the wave equation. This has a minor, practically negligible, effect on the kinematics of wave propagation. Finally, it is shown that non-reflecting boundary conditions, enforced by applying a taper at the boundaries of the grid, do not harm the stability of the discretization scheme.

Bakker, Peter M.; Duveneck, Eric

2011-05-01

231

Visualization of elastic wavefields computed with a finite difference code  

Energy Technology Data Exchange (ETDEWEB)

The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.

Larsen, S. [Lawrence Livermore National Lab., CA (United States); Harris, D.

1994-11-15

232

Effects of sources on time-domain finite difference models.  

Science.gov (United States)

Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed. PMID:24993210

Botts, Jonathan; Savioja, Lauri

2014-07-01

233

A finite difference model for cMUT devices.  

Science.gov (United States)

A finite difference method was implemented to simulate capacitive micromachined ultrasonic transducers (cMUTs) and compared to models described in the literature such as finite element methods. Similar results were obtained. It was found that one master curve described the clamped capacitance. We introduced normalized capacitance versus normalized bias voltage and metallization rate, independent of layer thickness, gap height, and size membrane, leading to the determination of a coupling factor master curve. We present here calculations and measurements of electrical impedance for cMUTs. An electromechanical equivalent circuit was used to perform simulations. Our experimental measurements confirmed the theoretical results in terms of resonance, anti-resonance frequencies, clamped capacitance, and electromechanical coupling factor. Due to inhomogeneity of the tested element array and strong parasitic capacitance between cells, the maximum coupling coefficient value achieved was 0.27. Good agreement with theory was obtained for all findings. PMID:16463486

Certon, Dominique; Teston, Franck; Patat, Frédéric

2005-12-01

234

Obtaining Potential Field Solution with Spherical Harmonics and Finite Differences  

CERN Document Server

Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current and divergence free magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: i) Remeshing the magnetogram onto a grid with uniform resolution in latitude, and limiting the highest order of the spherical harmonics to the anti-alias limit; ii) Using an iterative finite difference algorithm t...

Toth, Gabor; Huang, Zhenguang; 10.1088/0004-637X/732/2/102

2011-01-01

235

Finite-difference solution of the compressible stability eigenvalue problem  

Science.gov (United States)

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Malik, M. R.

1982-01-01

236

Computational electrodynamics the finite-difference time-domain method  

CERN Document Server

This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.

Taflove, Allen

2005-01-01

237

Cm solutions of systems of finite difference equations  

Directory of Open Access Journals (Sweden)

Full Text Available Let ℝ be the real number axis. Suppose that G, H are Cm maps from ℝ2n+3 to ℝ. In this note, we discuss the system of finite difference equations G(x,f(x,f(x+1,…,f(x+n,g(x,g(x+1,…,g(x+n+0 and H(x,g(x,g(x+1,…,g(x+n,f(x,f(x+1,…,f(x+n=0 for all x∈ℝ, and give some relatively weak conditions for the above system of equations to have unique Cm solutions (m≥0.

Jianmin Ma

2003-06-01

238

A Non-Blind Watermarking Scheme for Gray Scale Images in Discrete Wavelet Transform Domain using Two Subbands  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Digital watermarking is the process to hide digital pattern directly into a digital content. Digital watermarking techniques are used to address digital rights management, protect information and conceal secrets. An invisible non-blind watermarking approach for gray scale images is proposed in this paper. The host image is decomposed into 3-levels using Discrete Wavelet Transform. Based on the parent-child relationship between the wavelet coefficients the Set Partitioning in...

Shahid, Abdur; Badsha, Shahriar; Kabeer, Md Rethwan; Ahsan, Junaid; Mahmud, Mufti

2012-01-01

239

Acoustic, finite-difference, time-domain technique development  

International Nuclear Information System (INIS)

A close analog exists between the behavior of sound waves in an ideal gas and the radiated waves of electromagnetics. This analog has been exploited to obtain an acoustic, finite-difference, time-domain (AFDTD) technique capable of treating small signal vibrations in elastic media, such as air, water, and metal, with the important feature of bending motion included in the behavior of the metal. This bending motion is particularly important when the metal is formed into sheets or plates. Bending motion does not have an analog in electromagnetics, but can be readily appended to the acoustic treatment since it appears as a single additional term in the force equation for plate motion, which is otherwise analogous to the electromagnetic wave equation. The AFDTD technique has been implemented in a code architecture that duplicates the electromagnetic, finite-difference, time-domain technique code. The main difference in the implementation is the form of the first-order coupled differential equations obtained from the wave equation. The gradient of pressure and divergence of velocity appear in these equations in the place of curls of the electric and magnetic fields. Other small changes exist as well, but the codes are essentially interchangeable. The pre- and post-processing for model construction and response-data evaluation of the electromagnetic code, in the form of the TSAR code at Lawrence Livermore National Laboratory, can be used for the acoustic version. A variety of applications is possible, pending validation of the bending phenomenon. The applications include acoustic-radiation-pattern predictions for a submerged object; mine detection analysis; structural noise analysis for cars; acoustic barrier analysis; and symphonic hall/auditorium predictions and speaker enclosure modeling

1994-05-01

240

One-dimensional coupled Burgers’ equation and its numerical solution by an implicit logarithmic finite-difference method  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.

Vineet K. Srivastava

2014-03-01

 
 
 
 
241

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration  

CERN Document Server

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetization tensor terms using a sparse grid integration scheme. This method improves the accuracy of comput...

Chernyshenko, Dmitri

2014-01-01

242

A full Eulerian finite difference approach for solving fluid-structure coupling problems  

CERN Document Server

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.

Sugiyama, Kazuyasu; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro

2010-01-01

243

GPU Accelerated 2-D Staggered-grid Finite Difference Seismic Modelling  

Directory of Open Access Journals (Sweden)

Full Text Available The staggered-grid finite difference (FD method demands significantly computational capability and is inefficient for seismic wave modelling in 2-D viscoelastic media on a single PC. To improve computation speedup, a graphic processing units (GPUs accelerated method was proposed, for modern GPUs have now become ubiquitous in desktop computers and offer an excellent cost-to-performance-ratio parallelism. The geophysical model is decomposed into subdomains for PML absorbing conditions. The vertex and fragment processing are fully used to solve FD schemes in parallel and the latest updated frames are swapped in Framebuffer Object (FBO attachments as inputs for the next simulation step. The seismic simulation program running on modern PCs provides significant speedup over a CPU implementation, which makes it possible to simulate realtime complex seismic propagation in high resolution of 2048*2048 gridsizes on low-cost PCs.

Suping Peng

2011-08-01

244

High-order finite difference solution for 3D nonlinear wave-structure interaction  

DEFF Research Database (Denmark)

This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular cylinder are presented and compared to the fully nonlinear potential code XWAVE as well as to experiments.

Ducrozet, Guillaume; Bingham, Harry B.

2010-01-01

245

Hybrid Lattice Boltzmann/Finite Difference simulations of viscoelastic multicomponent flows in confined geometries  

CERN Document Server

We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical resu...

Gupta, A; Scagliarini, A

2014-01-01

246

Computationally efficient finite-difference modal method for the solution of Maxwell's equations.  

Science.gov (United States)

In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method. PMID:24323014

Semenikhin, Igor; Zanuccoli, Mauro

2013-12-01

247

Lie-algebraic discretization of differential equations  

CERN Multimedia

A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl_2-algebra based approach, (quasi)-exactly-solvable finite-difference equations are described. It is shown that the operators having the Hahn, Charlier and Meixner polynomials as the eigenfunctions are reproduced in present approach. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

Smirnov, Yu F; Smirnov, Yuri; Turbiner, Alexander

1995-01-01

248

Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties  

Directory of Open Access Journals (Sweden)

Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code. However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.

Georgios S. Stamatakos

2009-10-01

249

FLUOMEG: a planar finite difference mesh generator for fluid flow problems with parallel boundaries  

International Nuclear Information System (INIS)

A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables

1980-01-01

250

Depropagation and propagation simulation of the acoustic waves by using finite differences operators; Simulacao da propagacao e depropagacao de ondas acusticas usando operadores de diferencas finitas  

Energy Technology Data Exchange (ETDEWEB)

The numerical simulation of shot gathers over a (2D) velocity field, which corresponds to a model of Atlantic continental shelf, at the continental break area, using a typical model of the Brazilian Atlantic coast, suggested by PETROBRAS. The finite difference technique (FD) is used to solve the second derivatives in time and space of the acoustic wave equation, using fourth order operators to solve the spatial derivatives and second order operators to solve the time derivative. It is applied an explicitly scheme to calculate the pressure field values at a future instant. The use of rectangular mesh helps to generate data less noisy, since we can control better the numerical dispersion. The source functions (wavelets), as the first and the second derivatives of the gaussian function, are proper to generate synthetic seismograms with the FD method, because they allow an easy discretization. On the forward modeling, which is the simulation of wave fields, allows to control the stability limit of the method, wherever be the given velocity field, just employing compatible small values of the sample rate. The algorithm developed here, which uses only the FD technique, is able to perform the forward modeling, saving the image times, which can be used latter to perform the retropropagation of the wave field and thus migrate the source-gathers the reverse time extrapolation is able to test the used velocity model, and detect determine errors up to 5% on the used velocity model. (author)

Botelho, Marco A.B.; Santos, Roberto H.M. dos; Silva, Marcelo S. [Universidade Federal da Bahia (UFBA), Salvador, BA (Brazil). Centro de Pesquisa em Geofisica e Geologia

2004-07-01

251

Implementations of the optimal multigrid algorithm for the cell-centered finite difference on equilateral triangular grids  

Energy Technology Data Exchange (ETDEWEB)

A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.

Ewing, R.E.; Saevareid, O.; Shen, J. [Texas A& M Univ., College Station, TX (United States)

1994-12-31

252

Schemes of transmission of classical information via quantum channels with many senders: discrete and continuous variables cases  

CERN Document Server

Superadditivity effects in the classical capacity of discrete multi-access channels (MACs) and continuous variable (CV) Gaussian MACs are analysed. New examples of the manifestation of superadditivity in the discrete case are provided including, in particular, a channel which is fully symmetric with respect to all senders. Furthermore, we consider a class of channels for which {\\it input entanglement across more than two copies of the channels is necessary} to saturate the asymptotic rate of transmission from one of the senders to the receiver. The 5-input entanglement of Shor error correction codewords surpass the capacity attainable by using arbitrary two-input entanglement for these channels. In the CV case, we consider the properties of the two channels (a beam-splitter channel and a "non-demolition" XP gate channel) analyzed in [Czekaj {\\it et al.}, Phys. Rev. A {\\bf 82}, 020302 (R) (2010)] in greater detail and also consider the sensitivity of capacity superadditivity effects to thermal noise. We observ...

Czekaj, L; Chhajlany, R W; Horodecki, P

2011-01-01

253

An improved scheme for pressure-velocity coupling in control-volume based finite-element discretization  

International Nuclear Information System (INIS)

A method based on the so-called predictor-corrector upwind scheme and pressure-velocity coupling using Physical Advection Correction (PAC) terms has been developed. The preference of this method over previous challenges is that this method has a very simple geometrical interpolation process and is easier to implement for three-dimensional applications. The basic elements of the flow calculation are discussed and numerical results are presented to demonstrate the method. (author)

2003-05-28

254

A 3D Mimetic Finite Difference Method for Rupture Dynamics  

Science.gov (United States)

We are developing a method for solving earthquake rupture dynamics problems on structured curvilinear meshes. The advantage of a curvilinear mesh over a rectangular mesh is that it can accommodate free-surface topography as well as non-planar fault geometry. The advantages of using a structured mesh over an unstructured mesh (as used in many finite element methods) is simplicity and computational efficiency. Structured meshes also make a number of computational tasks easier, such as parallelization, or coupling with other codes that use similar structured meshes. To build the discretized equations of motion on a structured, yet non Cartesian mesh, we use a mimetic method, so named because it takes special care to mimic the important conservation properties of the original equations of motion. We begin by writing the equations of motion in terms of gradient and divergence operators. We then derive a discrete grad (or div) operator by differentiating an interpolation function of the discrete variable. Next, that grad (or div) operator is plugged into a discrete analog of Gauss' Identity and manipulated to find the adjoint div (or grad) operator. We use a computer algebra system to handle the manipulations, which is practically essential for the 3D case because of the extreme lengths of the expressions to be coded. The code is currently implemented as a "rapid prototype" in MATLAB and undergoing validation prior to conversion to a high performance language. We compare results for simple types of rupture that have analytical solutions.

Ely, G.; Minster, J.; Day, S.

2004-12-01

255

Finite difference approximation of hedging quantities in the Heston model  

Science.gov (United States)

This note concerns the hedging quantities Delta and Gamma in the Heston model for European-style financial options. A modification of the discretization technique from In 't Hout & Foulon (2010) is proposed, which enables a fast and accurate approximation of these important quantities. Numerical experiments are given that illustrate the performance.

in't Hout, Karel

2012-09-01

256

Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation  

CERN Multimedia

In this paper, a fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. We prove that our scheme is unconditional stable and $L^2$ error estimate for the linear case with the convergence rate $O(h^{k+1}+(\\Delta t)^2+(\\Delta t)^\\frac{\\alpha}{2}h^{k+1/2})$. Numerical examples are presented to show the efficiency and accuracy of our scheme.

Wei, Leilei

2012-01-01

257

Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling  

Science.gov (United States)

Seismic wave modeling is a cornerstone of geophysical data acquisition, processing, and interpretation, for which finite-difference methods are often applied. In this paper, we extend the velocity-pressure formulation of the acoustic wave equation to marine seismic modeling using the staggered-grid finite-difference method. The scheme is developed using a fourth-order spatial and a second-order temporal operator. Then, we define a stability coefficient (SC) and calculate its maximum value under the stability condition. Based on the dispersion relationship, we conduct a detailed dispersion analysis for submarine sediments in terms of the phase and group velocity over a range of angles, stability coefficients, and orders. We also compare the numerical solution with the exact solution for a P-wave line source in a homogeneous submarine model. Additionally, the numerical results determined by a Marmousi2 model with a rugged seafloor indicate that this method is sufficient for modeling complex submarine structures.

Qian, Jin; Wu, Shiguo; Cui, Ruofei

2013-01-01

258

Kelvin wave propagation along straight boundaries in C-grid finite-difference models  

Science.gov (United States)

Discrete solutions for the propagation of coastally-trapped Kelvin waves are studied, using a second-order finite-difference staggered grid formulation that is widely used in geophysical fluid dynamics (the Arakawa C-grid). The fundamental problem of linear, inviscid wave propagation along a straight coastline is examined, in a fluid of constant depth with uniform background rotation, using the shallow-water equations which model either barotropic (surface) or baroclinic (internal) Kelvin waves. When the coast is aligned with the grid, it is shown analytically that the Kelvin wave speed and horizontal structure are recovered to second-order in grid spacing h. When the coast is aligned at 45° to the grid, with the coastline approximated as a staircase following the grid, it is shown analytically that the wave speed is only recovered to first-order in h, and that the horizontal structure of the wave is infected by a thin computational boundary layer at the coastline. It is shown numerically that such first-order convergence in h is attained for all other orientations of the grid and coastline, even when the two are almost aligned so that only occasional steps are present in the numerical coastline. Such first-order convergence, despite the second-order finite differences used in the ocean interior, could degrade the accuracy of numerical simulations of dynamical phenomena in which Kelvin waves play an important role. The degradation is shown to be particularly severe for a simple example of near-resonantly forced Kelvin waves in a channel, when the energy of the forced response can be incorrect by a factor of 2 or more, even with 25 grid points per wavelength.

Griffiths, Stephen D.

2013-12-01

259

A finite difference model for free surface gravity drainage  

Energy Technology Data Exchange (ETDEWEB)

The unconfined gravity flow of liquid with a free surface into a well is a classical well test problem which has not been well understood by either hydrologists or petroleum engineers. Paradigms have led many authors to treat an incompressible flow as compressible flow to justify the delayed yield behavior of a time-drawdown test. A finite-difference model has been developed to simulate the free surface gravity flow of an unconfined single phase, infinitely large reservoir into a well. The model was verified with experimental results in sandbox models in the literature and with classical methods applied to observation wells in the Groundwater literature. The simulator response was also compared with analytical Theis (1935) and Ramey et al. (1989) approaches for wellbore pressure at late producing times. The seepage face in the sandface and the delayed yield behavior were reproduced by the model considering a small liquid compressibility and incompressible porous medium. The potential buildup (recovery) simulated by the model evidenced a different- phenomenon from the drawdown, contrary to statements found in the Groundwater literature. Graphs of buildup potential vs time, buildup seepage face length vs time, and free surface head and sand bottom head radial profiles evidenced that the liquid refills the desaturating cone as a flat moving surface. The late time pseudo radial behavior was only approached after exaggerated long times.

Couri, F.R.; Ramey, H.J. Jr.

1993-09-01

260

A Robust and Non-Blind Watermarking Scheme for Gray Scale Images Based on the Discrete Wavelet Transform Domain  

Science.gov (United States)

In this paper, a new adaptive watermarking algorithm is proposed for still image based on the wavelet transform. The two major applications for watermarking are protecting copyrights and authenticating photographs. Our robust watermarking [3] [22] is used for copyright protection owners. The main reason for protecting copyrights is to prevent image piracy when the provider distributes the image on the Internet. Embed watermark in low frequency band is most resistant to JPEG compression, blurring, adding Gaussian noise, rescaling, rotation, cropping and sharpening but embedding in high frequency is most resistant to histogram equalization, intensity adjustment and gamma correction. In this paper, we extend the idea to embed the same watermark in two bands (LL and HH bands or LH and HL bands) at the second level of Discrete Wavelet Transform (DWT) decomposition. Our generalization includes all the four bands (LL, HL, LH, and HH) by modifying coefficients of the all four bands in order to compromise between acceptable imperceptibility level and attacks' resistance.

Bakhouche, A.; Doghmane, N.

2008-06-01

 
 
 
 
261

AN INTERPOLATING CURVE SUBDIVISION SCHEME BASED ON DISCRETE FIRST DERIVATIVE / UN ESQUEMA DE SUBDIVISIÓN INTERPOLANTE BASADO EN LA PRIMERA DERIVADA DISCRETA  

Scientific Electronic Library Online (English)

Full Text Available SciELO Colombia | Language: English Abstract in spanish En este artículo se desarrolla un nuevo esquema de cuatro puntos para la subdivisión interpolante de curvas basado en la primera derivada discreta (DFDS), el cual, reduce la formación de oscilaciones indeseables que pueden surgir en la curva límite cuando los puntos de control no obedecen a una para [...] metrización uniforme. Se empleó un conjunto de 3000 curvas cuyos puntos de control fueron generados aleatoriamente. Curvas suaves fueron obtenidas tras siete pasos de subdivisión empleando los esquemas DFDS, Cuatro-puntos (4P), Nuevo de cuatro-puntos (N4P), Cuatro-puntos ajustado (T4P) y el Esquema interpolante geométricamente controlado (GC4P). Sobre cada curva suave se evaluó la propiedad de tortuosidad. Un análisis de las distribuciones de frecuencia obtenidas para esta propiedad, empleando la prueba de Kruskal-Wallis, revela que el esquema DFDS posee los menores valores de tortuosidad en un rango más estrecho. Abstract in english This paper develops a new scheme of four points for interpolating curve subdivision based on the discrete first derivative (DFDS), which reduces the apparition of undesirable oscillations that can be formed on the limit curve when the control points do not follow a uniform parameterization. We used [...] a set of 3000 curves whose control points were randomly generated. Smooth curves were obtained after seven steps of subdivision using five schemes DFDS, Four-Point (4P), New four-point (N4P), Tight four-point (T4P) and the geometrically controlled scheme (GC4P). The tortuosity property was evaluated on every smooth curve. An analysis for the frequency distributions of this property using the Kruskal-Wallis test reveals that DFDS scheme has the lowest values in a close range.

ALBEIRO, ESPINOSA BEDOYA; GERMÁN, SÁNCHEZ TORRES; JOHN WILLIAN, BRANCH BEDOYA.

262

On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 1: semi-implicit scheme  

CERN Document Server

We discuss a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis. We describe a semi-implicit time discretization that extends the range of numerical stability relative to an explicit scheme. We also introduce and discuss the effects of an artificial collisional operator, which is necessary to take care of the velocity space filamentation problem unavoidable in collisionless plasmas. The computational efficiency and the cost-effectiveness of this method are compared to a Particle-in-Cell (PIC) method in the case of a two-dimensional phase space. The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability, and plasma echo. The Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to the PIC.

Camporeale, Enrico; Bergen, Benjamin K; Moulton, J David

2013-01-01

263

Simulation of heat pipe rapid transient performance using a multi-nodal implicit finite difference scheme  

International Nuclear Information System (INIS)

Heat pipes are being considered as a part of the thermal management system of many space crafts due to the fact that heat pipes are capable of passively transporting large amounts of thermal energy over considerable distances with essentially no temperature drop. Mathematical modeling of heat pipe performance has been developed for both transient and steady state modes: however, existing transient heat pipe models are of limited accuracy during vary rapid transients. The modeling of the response of the vapor region in the event of rapid transients (including frozen start-ups) has not been investigated fully. The purpose of this study is to model the performance of a screened wick heat pipe in rapid transient modes and to determine the limiting conditions under which the heat pipe will operate

1986-01-13

264

Cartesian Coordinate, Oblique Boundary, Finite Differences and Interpolation  

CERN Document Server

A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact difference stencils involving only nearest neighbors. Implementation for general "Robin" boundary conditions and for boundaries between media of different dielectric constant for arbitrary-shaped regions is described in detail. The scheme also provides for the interpolation of field (potential gradient) which, despite first-order peak errors immediately adjacent to the boundaries, has overall second order accuracy, and thus provides with good accuracy what is required in particle-in-cell codes: the force. Numerical tests on the implementation confirm the scalings and the accuracy.

Hutchinson, Ian H

2011-01-01

265

Vertical Discretization of Hydrostatic Primitive Equations with Finite Element Method  

Science.gov (United States)

A vertical finite element (VFE) discretization of hydrostatic primitive equations is developed for the dynamical core of a numerical weather prediction (NWP) system at KIAPS, which is horizontally discretized by a spectral element on a cubed-sphere grid. The governing equations are discretized on a hybrid pressure-based vertical coordinate [1]. Compared with a vertical finite difference (VFD) discretization, which is only first order accurate for non-uniform grids, the VFE has many advantages such that it gives more accurate results, all variables are defined in the same full level, the level of vertical noise might be reduced [2], and it is easily coupled with existing physics packages, developed for a Lorentz staggering grid system. Due to these reasons, we adopted the VFE scheme presented by Untch [2] for the vertical discretization. Instead of using semi-Lagrangian and semi-implicit schemes of ECMWF, we use the Eulerian equations and second-order Runge-Kutta scheme as the first step in implementing the VFE for the dynamical core of the KIAPS's NWP model. Since the Eulerian hydrostatic equations are used in this study, both integral and derivative operators are required to implement the VFE using the Galerkin method with b-splines as basis functions. To compare the accuracy of the VFE with the VFD, the two-dimensional test case of mountain waves is used where physical configuration and initial conditions are the same as that of Durran [3]. In this case, the horizontal and vertical velocities obtained by the analytical solution, VFD, VFE-linear and VFE-cubic are compared to understand their numerical features and the vertical flux of horizontal momentum is also presented as the measurement of solution accuracy since it is sensitive to errors in a solution [3]. It is shown that the VFE with a cubic b-spline function is more accurate than the VFD and VFE with a linear b-spline function as the vertical flux is closer to unity, which will be presented in the conference. Reference Simmons, A. J., Burridge, D. M., 1981: An energy and angular momentum conserving vertical finite difference scheme and hybrid vertical coordinates. Mon. Wea. Rev., 109, 758-766. Untch, A., Hortal, M., 2004: A finite-element schemes for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model. Q. J. R. Meteorol. Soc., 130, 1505-1530. Durran, D. R., Klemp, J. B., 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111, 2341-2361.

Yi, Tae-Hyeong; Park, Ja-Rin

2014-05-01

266

3D Finite Difference Modelling of Basaltic Region  

Science.gov (United States)

The main purpose of the work was to generate realistic data to be applied for testing of processing and migration tools for basaltic regions. The project is based on the three - dimensional finite difference code (FD), TIGER, made by Sintef. The FD code was optimized (parallelized) by the author, to run on parallel computers. The parallel code enables us to model large-scale realistic geological models and to apply traditional seismic and micro seismic sources. The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously. The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium. In the FD code, the elastic wave field computation is implemented by a higher order FD solution to the elastic wave equation and the wave fields are computed on a staggered grid, shifted half a node in one or two directions. The geological model is a gridded basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to the depth of 3.5 km. The 2frac {1}{2}D model has been constructed using the compound modeling software from Norsk Hydro. The vertical parameter distribution is obtained from observations in two wells. At The depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The author would like to thank Norsk Hydro, Statoil, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with the new IBM, p690 Regatta system.

Engell-Sørensen, L.

2003-04-01

267

Finite-difference time-domain simulations of metamaterials  

Science.gov (United States)

Metamaterials are periodic structures created by many identical scattering objects which are stationary and small compared to the wavelength of electromagnetic wave applied to it so that when combined with different elements, these materials have the potential to be coupled to the applied electromagnetic wave without modifying the structure. Due to their unusual properties that are not readily available in nature, metamaterials have been drawing significant attentions in many research areas, including theoretical, experimental as well as numerical investigations. As one of the major computational electromagnetic modeling methods, finite-difference time-domain (FDTD) technique tackles problems by providing a full wave solution. FDTD, which is able to show transient evolution of interactions between electromagnetic wave and physical objects, not only has the advantage in dispersive and nonlinear material simulations, but also has the ability to model circuit elements including semiconductor devices. All these features make FDTD a competitive candidate in numerical methods of metamaterial simulations. This dissertation presents the implementation of FDTD technique to deal with three dimensional (3D) problems characterized with metamaterial structures. We endeavor to make the FDTD engine multi-functional and fast, as depicted in the following three efforts: (1) We incorporated FDTD engine with the stable and highly efficient model for materials with dispersion, nonlinearity and gain properties. (2) We coupled FDTD engine with SPICE, the general-purpose and powerful analog electronic circuit simulator. This makes FDTD ready to simulate complex semiconductor devices and provides a variety of possibilities for novel metamaterials. (3) We investigated the cutting-edge area of Graphics Processing Units (GPU) computing module to speed up the FDTD engine, and implemented subgridding system to target more efficient modeling for metamaterial applications with embedded fine structures. The contribution of this work is toward the development of a powerful FDTD engine for modern metamaterial analysis. Our implementation could be used to improve the analysis of a number of electromagnetic problems.

Hao, Zhengwei

268

Accelerated conjugate gradient algorithm with finite difference Hessian/vector product approximation for unconstrained optimization  

Science.gov (United States)

In this paper we propose a fundamentally different conjugate gradient method, in which the well-known parameter [beta]k is computed by an approximation of the Hessian/vector product through finite differences. For search direction computation, the method uses a forward difference approximation to the Hessian/vector product in combination with a careful choice of the finite difference interval. For the step length computation we suggest an acceleration scheme able to improve the efficiency of the algorithm. Under common assumptions, the method is proved to be globally convergent. It is shown that for uniformly convex functions the convergence of the accelerated algorithm is still linear, but the reduction in function values is significantly improved. Numerical comparisons with conjugate gradient algorithms including CONMIN by Shanno and Phua [D.F. Shanno, K.H. Phua, Algorithm 500, minimization of unconstrained multivariate functions, ACM Trans. Math. Softw. 2 (1976) 87-94], SCALCG by Andrei [N. Andrei, Scaled conjugate gradient algorithms for unconstrained optimization, Comput. Optim. Appl. 38 (2007) 401-416; N. Andrei, Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Optim. Methods Softw. 22 (2007) 561-571; N. Andrei, A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Appl. Math. Lett. 20 (2007) 645-650], and new conjugacy condition and related new conjugate gradient by Li, Tang and Wei [G. Li, C. Tang, Z. Wei, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math. 202 (2007) 523-539] or truncated Newton TN by Nash [S.G. Nash, Preconditioning of truncated-Newton methods, SIAM J. on Scientific and Statistical Computing 6 (1985) 599-616] using a set of 750 unconstrained optimization test problems show that the suggested algorithm outperforms these conjugate gradient algorithms as well as TN.

Andrei, Neculai

2009-08-01

269

A convergent finite difference method for a nonlinear variational wave equation  

CERN Document Server

We establish rigorously convergence of a semi-discrete upwind scheme for the nonlinear variational wave equation $u_{tt} - c(u)(c(u) u_x)_x = 0$ with $u|_{t=0}=u_0$ and $u_t|_{t=0}=v_0$. Introducing Riemann invariants $R=u_t+c u_x$ and $S=u_t-c u_x$, the variational wave equation is equivalent to $R_t-c R_x=\\tilde c (R^2-S^2)$ and $S_t+c S_x=-\\tilde c (R^2-S^2)$ with $\\tilde c=c'/(4c)$. An upwind scheme is defined for this system. We assume that the the speed $c$ is positive, increasing and both $c$ and its derivative are bounded away from zero and that $R|_{t=0}, S|_{t=0}\\in L^1\\cap L^3$ are nonpositive. The numerical scheme is illustrated on several examples.

Holden, H; Risebro, N H

2007-01-01

270

Finite-difference numerical simulations of underground explosion cavity decoupling  

Science.gov (United States)

Earth models containing a significant portion of ideal fluid (e.g., air and/or water) are of increasing interest in seismic wave propagation simulations. Examples include a marine model with a thick water layer, and a land model with air overlying a rugged topographic surface. The atmospheric infrasound community is currently interested in coupled seismic-acoustic propagation of low-frequency signals over long ranges (~tens to ~hundreds of kilometers). Also, accurate and efficient numerical treatment of models containing underground air-filled voids (caves, caverns, tunnels, subterranean man-made facilities) is essential. In support of the Source Physics Experiment (SPE) conducted at the Nevada National Security Site (NNSS), we are developing a numerical algorithm for simulating coupled seismic and acoustic wave propagation in mixed solid/fluid media. Solution methodology involves explicit, time-domain, finite-differencing of the elastodynamic velocity-stress partial differential system on a three-dimensional staggered spatial grid. Conditional logic is used to avoid shear stress updating within the fluid zones; this approach leads to computational efficiency gains for models containing a significant proportion of ideal fluid. Numerical stability and accuracy are maintained at air/rock interfaces (where the contrast in mass density is on the order of 1 to 2000) via a finite-difference operator "order switching" formalism. The fourth-order spatial FD operator used throughout the bulk of the earth model is reduced to second-order in the immediate vicinity of a high-contrast interface. Current modeling efforts are oriented toward quantifying the amount of atmospheric infrasound energy generated by various underground seismic sources (explosions and earthquakes). Source depth and orientation, and surface topography play obvious roles. The cavity decoupling problem, where an explosion is detonated within an air-filled void, is of special interest. A point explosion source located at the center of a spherical cavity generates only diverging compressional waves. However, we find that shear waves are generated by an off-center source, or by a non-spherical cavity (e.g. a tunnel). Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Aldridge, D. F.; Preston, L. A.; Jensen, R. P.

2012-12-01

271

Fast finite difference Poisson solvers on heterogeneous architectures  

Science.gov (United States)

In this paper we propose and evaluate a set of new strategies for the solution of three dimensional separable elliptic problems on CPU-GPU platforms. The numerical solution of the system of linear equations arising when discretizing those operators often represents the most time consuming part of larger simulation codes tackling a variety of physical situations. Incompressible fluid flows, electromagnetic problems, heat transfer and solid mechanic simulations are just a few examples of application areas that require efficient solution strategies for this class of problems. GPU computing has emerged as an attractive alternative to conventional CPUs for many scientific applications. High speedups over CPU implementations have been reported and this trend is expected to continue in the future with improved programming support and tighter CPU-GPU integration. These speedups by no means imply that CPU performance is no longer critical. The conventional CPU-control-GPU-compute pattern used in many applications wastes much of CPU's computational power. Our proposed parallel implementation of a classical cyclic reduction algorithm to tackle the large linear systems arising from the discretized form of the elliptic problem at hand, schedules computing on both the GPU and the CPUs in a cooperative way. The experimental result demonstrates the effectiveness of this approach.

Valero-Lara, Pedro; Pinelli, Alfredo; Prieto-Matias, Manuel

2014-04-01

272

Finite difference simulations of seismic wave propagation for understanding earthquake physics and predicting ground motions: Advances and challenges  

International Nuclear Information System (INIS)

Seismic waves radiated from an earthquake propagate in the Earth and the ground shaking is felt and recorded at (or near) the ground surface. Understanding the wave propagation with respect to the Earth's structure and the earthquake mechanisms is one of the main objectives of seismology, and predicting the strong ground shaking for moderate and large earthquakes is essential for quantitative seismic hazard assessment. The finite difference scheme for solving the wave propagation problem in elastic (sometimes anelastic) media has been more widely used since the 1970s than any other numerical methods, because of its simple formulation and implementation, and its easy scalability to large computations. This paper briefly overviews the advances in finite difference simulations, focusing particularly on earthquake mechanics and the resultant wave radiation in the near field. As the finite difference formulation is simple (interpolation is smooth), an easy coupling with other approaches is one of its advantages. A coupling with a boundary integral equation method (BIEM) allows us to simulate complex earthquake source processes

2013-08-12

273

Analysis of an Il’in Scheme for a System of Singularly Perturbed Convection-Diffusion Equations  

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Full Text Available In this paper, a numerical solution for a system of singularly perturbed convection-diffusion equations is studied. The system is discretized by the Il’in scheme on a uniform mesh. It is proved that the numerical scheme has first order accuracy, which is uniform with respect to the perturbation parameters. We show that the condition number of the discrete linear system obtained from applying the Il’in scheme for a system of singularly perturbed convection-diffusion equations is O(N and the relevant coefficient matrix is well conditioned in comparison with the matrices obtained from applying upwind finite difference schemes on this problem. Numerical results confirm the theory of the method.

Mohammad Ghorbanzadeh

2011-07-01

274

Analysis of the monotonicity conditions in the mimetic finite difference method for elliptic problems  

Science.gov (United States)

The maximum principle is one of the most important properties of solutions of partial differential equations. Its numerical analog, the discrete maximum principle (DMP), is one of the most difficult properties to achieve in numerical methods, especially when the computational mesh is distorted to adapt and conform to the physical domain or the problem coefficients are highly heterogeneous and anisotropic. Violation of the DMP may lead to numerical instabilities such as oscillations and to unphysical solutions such as heat flow from a cold material to a hot one. In this work, we investigate sufficient conditions to ensure the monotonicity of the mimetic finite difference (MFD) method on two- and three-dimensional meshes. These conditions result in a set of general inequalities for the elements of the mass matrix of every mesh element. Efficient solutions are devised for meshes consisting of simplexes, parallelograms and parallelepipeds, and orthogonal locally refined elements as those used in the AMR methodology. On simplicial meshes, it turns out that the MFD method coincides with the mixed-hybrid finite element methods based on the low-order Raviart-Thomas vector space. Thus, in this case we recover the well-established conventional angle conditions of such approximations. Instead, in the other cases a suitable design of the MFD method allows us to formulate a monotone discretization for which the existence of a DMP can be theoretically proved. Moreover, on meshes of parallelograms we establish a connection with a similar monotonicity condition proposed for the Multi-Point Flux Approximation (MPFA) methods. Numerical experiments confirm the effectiveness of the considered monotonicity conditions.

Lipnikov, K.; Manzini, G.; Svyatskiy, D.

2011-04-01

275

Tradable Schemes  

CERN Document Server

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very elegant way, due to the fact that in our tradable based formulation there appear no drift terms in the PDE. We construct a mixed scheme based on this idea and apply it to price various types of arithmetic Asian options, as well as plain vanilla options (both european and american style) on stocks paying known cash dividends. We find prices which are accurate to $\\sim 0.1%$ in about 10ms on a Pentium 233MHz computer and to $\\sim 0.001%$ in a second. The scheme can also be used for market conform pricing, by fitting it to observed option prices.

Hoogland, Jiri Kamiel; Hoogland, Jiri; Neumann, Dimitri

2000-01-01

276

A staggered-grid finite-difference method with perfectly matched layers for poroelastic wave equations.  

Science.gov (United States)

A particle velocity-strain, finite-difference (FD) method with a perfectly matched layer (PML) absorbing boundary condition is developed for the simulation of elastic wave propagation in multidimensional heterogeneous poroelastic media. Instead of the widely used second-order differential equations, a first-order hyperbolic leap-frog system is obtained from Biot's equations. To achieve a high accuracy, the first-order hyperbolic system is discretized on a staggered grid both in time and space. The perfectly matched layer is used at the computational edge to absorb the outgoing waves. The performance of the PML is investigated by calculating the reflection from the boundary. The numerical method is validated by analytical solutions. This FD algorithm is used to study the interaction of elastic waves with a buried land mine. Three cases are simulated for a mine-like object buried in "sand," in purely dry "sand" and in "mud." The results show that the wave responses are significantly different in these cases. The target can be detected by using acoustic measurements after processing. PMID:11425097

Zeng, Y Q; Liu, Q H

2001-06-01

277

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

Directory of Open Access Journals (Sweden)

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.

Tsugio Fukuchi

2014-06-01

278

Mimetic finite difference method for the stokes problem on polygonal meshes  

Energy Technology Data Exchange (ETDEWEB)

Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.

Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA

2009-01-01

279

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation  

Science.gov (United States)

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Litaker, Eric T.

1994-12-01

280

Treatment of late time instabilities in finite difference EMP scattering codes  

Energy Technology Data Exchange (ETDEWEB)

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to the late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances.

Simpson, L.T.; Arman, S.; Holland, R.

1982-12-01

 
 
 
 
281

Treatment of late time instabilities in finite difference EMP scattering codes  

International Nuclear Information System (INIS)

Time-domain solutions to the finite-differenced Maxwell's equations give rise to several well-known nonphysical propagation anomalies. In particular, when a radiative electric-field look back scheme is employed to terminate the calculation, a high-frequency, growing, numerical instability is introduced. This paper describes the constraints made on the mesh to minimize this instability, and a technique of applying an absorbing sheet to damp out this instability without altering the early time solution. Also described are techniques to extend the data record in the presence of high-frequency noise through application of a low-pass digital filter and the fitting of a damped sinusoid to the late-time tail of the data record. An application of these techniques is illustrated with numerical models of the FB-111 aircraft and the B-52 aircraft in the in-flight refueling configuration using the THREDE finite difference computer code. Comparisons are made with experimental scale model measurements with agreement typically on the order of 3 to 6 dB near the fundamental resonances

1982-01-01

282

Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs  

Science.gov (United States)

This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.

Bollig, Evan F.; Flyer, Natasha; Erlebacher, Gordon

2012-08-01

283

Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs  

International Nuclear Information System (INIS)

This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.

2012-08-30

284

Finite-difference method for the calculation of low-energy positron diffraction  

Energy Technology Data Exchange (ETDEWEB)

A scheme of calculation avoiding the muffin-tin approximation is presented for low-energy positron diffraction. The finite-difference method is used to solve the Schr{umlt o}dinger equation. All the steps of the calculation are described. The first one is the elaboration of a grid of points in the various areas, where the wave function must be known. The potential is then calculated including the electronic reorganization, due to interatomic bondings or dangling bonds. The wave function is obtained by solving a large system of linear equations. The tensor approach to compare experimental and theoretical spectra is also described. The main improvement with respect to conventional calculation resides in the possibility of evaluating the charge exchanges, orbital per orbital, inside atoms, and between atoms. An application to the GaAs(110) surface leads to a good agreement between experiment and theory with geometrical parameters close to those found in standard studies. An oscillatory behavior of the total atomic charge in the topmost layers is revealed. A cartography in three dimensions of the electronic density in the first atomic layers is provided. {copyright} {ital 1996 The American Physical Society.}

Joly, Y. [Laboratoire de Cristallographie, Centre National de la Recherche Scientifique, Boite Postale 166, F-38042 Grenoble Cedex 9 (France)

1996-05-01

285

Finite-difference method for the calculation of low-energy positron diffraction  

International Nuclear Information System (INIS)

A scheme of calculation avoiding the muffin-tin approximation is presented for low-energy positron diffraction. The finite-difference method is used to solve the Schroedinger equation. All the steps of the calculation are described. The first one is the elaboration of a grid of points in the various areas, where the wave function must be known. The potential is then calculated including the electronic reorganization, due to interatomic bondings or dangling bonds. The wave function is obtained by solving a large system of linear equations. The tensor approach to compare experimental and theoretical spectra is also described. The main improvement with respect to conventional calculation resides in the possibility of evaluating the charge exchanges, orbital per orbital, inside atoms, and between atoms. An application to the GaAs(110) surface leads to a good agreement between experiment and theory with geometrical parameters close to those found in standard studies. An oscillatory behavior of the total atomic charge in the topmost layers is revealed. A cartography in three dimensions of the electronic density in the first atomic layers is provided. copyright 1996 The American Physical Society

1996-05-01

286

Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver  

CERN Multimedia

In multiscale, multi-physics applications, there is an increasing need for coupling numerical solvers that are each applied to a different part of the problem. Here we consider the case of coupling a Lattice Boltzmann fluid model and a Finite Difference Navier-Stokes solver. The coupling is implemented so that the entire computational domain can be divided in two regions, with the FD solver running on one of them and the LB one on the other. We show how the various physical quantities of the two approaches should be related to ensure a smooth transition at the interface between the regions. We demonstrate the feasibility of the method on the Poiseuille flow, where the LB and FD schemes are used on adjacent sub-domains. The same idea can be also developed to couple LB models with Finite Volumes, or Finite Elements calculations. The motivation for developing such a type of coupling is that, depending on the geometry of the flow, one technique can be more efficient, less memory consuming, or physically more appr...

Latt, J; Chopard, B; Albuquerque, Paul; Chopard, Bastien; Latt, Jonas

2005-01-01

287

The computation of pressure waves in shock tubes by a finite difference procedure  

International Nuclear Information System (INIS)

A finite difference solution of one-dimensional unsteady isentropic compressible flow equations is presented. The computer program has been tested by solving some cases of the Riemann shock tube problem. Predictions are in good agreement with those presented by other authors. Some inaccuracies may be attributed to the wave smearing consequent of the finite-difference treatment. (author)

1988-01-01

288

ACOUSTIC SIGNAL BASED TRAFFIC FLOW EVALUATION METHOD USING THE CALCULUS OF FINITE DIFFERENCES ???????? ??????????? ????????????? ????????????? ?????? ?? ????????????? ????????? ? ?????????????? ???????? ?????????? ???????? ?????????  

Directory of Open Access Journals (Sweden)

Full Text Available In this article, acoustic signal based traffic flow evaluation method using the calculus of finite differences is considered. The analytical survey for traffic flow evaluations using acoustic signals is performed. The calculus of finite differences application in traffic flow evaluation is investigated. As the result of this work, the considered method of efficiency is evaluated

Posmitnyy Y. V.

2012-12-01

289

On Forecasting Macro-Economic Indicators with the Help of Finite-Difference Equations and Econometric Methods  

Directory of Open Access Journals (Sweden)

Full Text Available The article considers data on the gross domestic product, consumer expenditures, gross investments and volume of foreign trade for the national economy. It is assumed that time is a discrete variable with one year iteration. The article uses finite-difference equations. It considers models with a high degree of the regulatory function of the state with respect to the consumer market. The econometric component is based on the hypothesis that each of the above said macro-economic indicators for this year depends on the gross domestic product for the previous time periods. Such an assumption gives a possibility to engage the least-squares method for building up linear models of the pair regression. The article obtains the time series model, which allows building point and interval forecasts for the gross domestic product for the next year based on the values of the gross domestic product for the current and previous years. The article draws a conclusion that such forecasts could be considered justified at least in the short-term prospect. From the mathematical point of view the built model is a heterogeneous finite-difference equation of the second order with constant ratios. The article describes specific features of such equations. It illustrates graphically the analytical view of solutions of the finite-difference equation. This gives grounds to differentiate national economies as sustainable growth economies, one-sided, weak or being in the stage of successful re-formation. The article conducts comparison of the listed types with specific economies of modern states.

Polshkov Yulian M.

2013-11-01

290

Helmholtz's inverse problem of the discrete calculus of variations  

CERN Multimedia

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide the class of all possible Lagrangian formulations.

Bourdin, Loïc

2012-01-01

291

Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods  

Science.gov (United States)

A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.

DeBonis, James R.

2013-01-01

292

A two-dimensional finite-difference solution for the transient thermal behavior of a tubular solar collector  

Science.gov (United States)

A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique were analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.

Lansing, F. L.

1980-01-01

293

Voronoi-cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids  

International Nuclear Information System (INIS)

We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schroedinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.

2011-03-01

294

Similarity and generalized finite-difference solutions of parabolic partial differential equations.  

Science.gov (United States)

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Clausing, A. M.

1971-01-01

295

The Dirihlet problem for the fractional Poisson’s equation with Caputo derivatives: A finite difference approximation and a numerical solution  

Directory of Open Access Journals (Sweden)

Full Text Available A finite difference approximation for the Caputo fractional derivative of the 4-?, 1 < ? ? 2 order has been developed. A difference schemes for solving the Dirihlet’s problem of the Poisson’s equation with fractional derivatives has been applied and solved. Both the stability of difference problem in its right-side part and the convergence have been proved. A numerical example was developed by applying both the Liebman and the Monte-Carlo methods.

Beibalaev V.D.

2012-01-01

296

Uniformly convergent scheme for Convection-Diffusion problem  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper a study of uniformly convergent method proposed by Il’in –Allen-South well scheme was made. A condition was contemplated for uniform convergence in the specified domain. This developed scheme is uniformly convergent for any choice of the diffusion parameter. The search provides a first- order uniformly convergent method with discrete maximum norm. It was observed that the error increases as step size h gets smaller for mid range values of perturbation parameter. Then an analysis carried out by [16] was employed to check the validity of solution with respect to physical aspect and it was in agreement with the analytical solution. The uniformly convergent method gives better results than the finite difference methods. The computed and plotted solutions of this method are in good – agreement with the exact solution.

K. Sharath Babu

2012-03-01

297

A higher-order spatial FDTD scheme with CFS PML for 3D numerical simulation of wave propagation in cold plasma  

CERN Multimedia

A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are used to discretize Maxwell's curl equations and a uniaxial perfectly matched layer with the complex frequency-shifted equations is introduced to terminate the computational domain. A numerical dispersion study of second- and higher-order techniques is elaborated and their stability criteria are extracted for each scheme. Comparisons with analytical solutions verify the accuracy of the proposed methods and the low dispersion error of the higher-order schemes.

Prokopidis, Konstantinos P

2013-01-01

298

Three-dimensional Finite Difference-Time Domain Solution of Dirac Equation  

CERN Multimedia

The Dirac equation is solved using three-dimensional Finite Difference-Time Domain (FDTD) method. $Zitterbewegung$ and the dynamics of a well-localized electron are used as examples of FDTD application to the case of free electrons.

Simicevic, Neven

2008-01-01

299

Modeling Exposure to Electromagnetic Fields with Realistic Anatomical Models: The Brooks Finite Difference Time Domain (FDTD).  

Science.gov (United States)

Air Force Research Laboratory/Human Effectiveness Directorate Radio Frequency Radiation Branch (AFRL/RHDR) and Naval Health Research Center (NHRC) have long used Finite Difference Time Domain (FDTD) software to study radiofrequency radiation (RF) bioeffec...

J. Payne J. Ziriax L. Harris S. Adams

2008-01-01

300

Vibration analysis of rotating turbomachinery blades by an improved finite difference method  

Science.gov (United States)

The problem of calculating the natural frequencies and mode shapes of rotating blades is solved by an improved finite difference procedure based on second-order central differences. Lead-lag, flapping and coupled bending-torsional vibration cases of untwisted blades are considered. Results obtained by using the present improved theory have been observed to be close lower bound solutions. The convergence has been found to be rapid in comparison with the classical first-order finite difference method. While the computational space and time required by the present approach is observed to be almost the same as that required by the first-order theory for a given mesh size, accuracies of practical interest can be obtained by using the improved finite difference procedure with a relatively smaller matrix size, in contrast to the classical finite difference procedure which requires either a larger matrix or an extrapolation procedure for improvement in accuracy.

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

 
 
 
 
301

Stochastic finite difference lattice Boltzmann method for steady incompressible viscous flows  

International Nuclear Information System (INIS)

With the advent of state-of-the-art computers and their rapid availability, the time is ripe for the development of efficient uncertainty quantification (UQ) methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data. The spectral stochastic finite element method (SSFEM) which is one of the widely used UQ methods, regards uncertainty as generating a new dimension and the solution as dependent on this dimension. A convergent expansion along the new dimension is then sought in terms of the polynomial chaos system, and the coefficients in this representation are determined through a Galerkin approach. This approach provides an accurate representation even when only a small number of terms are used in the spectral expansion; consequently, saving in computational resource can be realized compared to the Monte Carlo (MC) scheme. Recent development of a finite difference lattice Boltzmann method (FDLBM) that provides a convenient algorithm for setting the boundary condition allows the flow of Newtonian and non-Newtonian fluids, with and without external body forces to be simulated with ease. Also, the inherent compressibility effect in the conventional lattice Boltzmann method, which might produce significant errors in some incompressible flow simulations, is eliminated. As such, the FDLBM together with an efficient UQ method can be used to treat incompressible flows with built in uncertainty, such as blood flow in stenosed arteries. The objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the FDLBM with a SSFEM. Validation against MC solutions of channel/Couette, driven cavity, and sudden expansion flows are carried out.

2010-08-20

302

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing  

Science.gov (United States)

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Garrett, L. B.; Smith, G. L.; Perkins, J. N.

1972-01-01

303

A Spatially-Analytical Scheme for Surface Temperatures and Conductive Heat Fluxes in Urban Canopy Models  

Science.gov (United States)

In the urban environment, surface temperatures and conductive heat fluxes through solid media (roofs, walls, roads and vegetated surfaces) are of paramount importance for the comfort of residents (indoors) and for microclimatic conditions (outdoors). Fully discrete numerical methods are currently used to model heat transfer in these solid media in parametrisations of built surfaces commonly used in weather prediction models. These discrete methods usually use finite difference schemes in both space and time. We propose a spatially-analytical scheme where the temperature field and conductive heat fluxes are solved analytically in space. Spurious numerical oscillations due to temperature discontinuities at the sublayer interfaces can be avoided since the method does not involve spatial discretisation. The proposed method is compared to the fully discrete method for a test case of one-dimensional heat conduction with sinusoidal forcing. Subsequently, the analytical scheme is incorporated into the offline version of the current urban canopy model (UCM) used in the Weather Research and Forecasting model and the new UCM is validated against field measurements using a wireless sensor network and other supporting measurements over a suburban area under real-world conditions. Results of the comparison clearly show the advantage of the proposed scheme over the fully discrete model, particularly for more complicated cases.

Wang, Zhi-Hua; Bou-Zeid, Elie; Smith, James A.

2011-02-01

304

DEVELOPMENT OF FINITE DIFFERENCE METHOD APPLIED TO CONSOLIDATION ANALYSIS OF EMBANKMENTS  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This study presents the development of the finite difference method applied to consolidation analysis of embankments. To analyse the consolidation of the embankment as real as possible, the finite difference method in two dimensional directions was performed. Existing soils under embankments have varying stresses due to stress history and geological background. Therefore, Skempton’s parameter “A” which is a function of vertical stresses was taken into account in this study. Two case stu...

Vipman Tandjiria

1999-01-01

305

Modelling of Wave Propagation in Wire Media Using Spatially Dispersive Finite-Difference Time-Domain Method: Numerical Aspects  

CERN Document Server

The finite-difference time-domain (FDTD) method is applied for modelling of wire media as artificial dielectrics. Both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation (ADE) method. According to the authors' knowledge, this is the first time when the spatial dispersion effect is considered in the FDTD modelling. The stability of developed spatially dispersive FDTD formulations is analysed through the use of von Neumann method combined with the Routh-Hurwitz criterion. The results show that the conventional stability Courant limit is preserved using standard discretisation scheme for wire media modelling. Flat sub-wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive FDTD formulation. Results of the simulations demonstrate excellent sub-wavelength imaging capability of the wire medium slabs. The size of the simulation domain is significantly reduced using the modified perfectly matched ...

Zhao, Y; Hao, Y; Zhao, Yan; Belov, Pavel; Hao, Yang

2006-01-01

306

a Comparative Study of Time-Stepping Techniques for the Incompressible Navier-Stokes Equations: from Fully Implicit Non-Linear Schemes to Semi-Implicit Projection Methods  

Science.gov (United States)

We present a numerical comparison of some time-stepping schemes for the discretization and solution of the non-stationary incompressible Navier- Stokes equations. The spatial discretization is by non-conforming quadrilateral finite elements which satisfy the LBB condition. The major focus is on the differences in accuracy and efficiency between the backward Euler, Crank-Nicolson and fractional-step schemes used in discretizing the momentum equations. Further, the differences between fully coupled solvers and operator-splitting techniques (projection methods) and the influence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemes and non-conforming finite elements allows the comparison of schemes which are representative for many methods used in practice. On Cartesian grids this approach encompasses some well-known staggered grid finite difference discretizations too. The results which are obtained for several typical flow problems are thought to be representative and should be helpful for a fair rating of solution schemes, particularly in long-time simulations

Turek, Stefan

1996-05-01

307

A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics  

Directory of Open Access Journals (Sweden)

Full Text Available The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand, and predict the dynamics of obesity populations. The construction of the proposed discrete scheme is developed such that it is dynamically consistent with the original differential equations model. Since the total population in this mathematical model is assumed constant, the proposed scheme has been constructed to satisfy the associated conservation law and positivity condition. Numerical comparisons between the competitive nonstandard scheme developed here and Euler's method show the effectiveness of the proposed nonstandard numerical scheme. Numerical examples show that the nonstandard difference scheme methodology is a good option to solve numerically different mathematical models where essential properties of the populations need to be satisfied in order to simulate the real world.

Gilberto González-Parra

2008-12-01

308

Dependency of finite difference solutions on grid structures and turbulence models for cascade flows; Yokuretsu nagare no sabunkai ni oyobosu koshi kozo to ranryu model no eikyo no kento  

Energy Technology Data Exchange (ETDEWEB)

For cascade with a high turning and a large camber, it is difficult to impose grid orthogonality as well as point-to-point periodicity simultaneously on a single structured grid. In this study, the effects of periodic and non-periodic grids on finite difference solutions are investigated for two-dimensional transonic flows about rotor blades. The spatial derivatives of the Reynolds-averaged Navier-Stokes equations are discretized with central difference approximations and matrix dissipation models. The resulting system of equations is integrated in time with an explicit 2-stage Rational Runge-Kutta scheme. For turbulence closure, Baldwin-Lomax model, Baldwin-Barth model, and Spalart-Allmaras model are compared. The non-periodic grids have favorable resolutions for the shock system and the wake. The shock-induced production of the eddy-viscosity is remarkable in the Baldwin-Barth model. The Spalart-Allmaras model works well, even on the periodic grids, in comparison with the other models. 9 refs., 15 figs.

Omote, H.; Morinishi, K.; Satofuka, N. [Kyoto Inst. of Technology, Kyoto (Japan)

1998-09-25

309

On the validity of the modified equation approach to the stability analysis of finite-difference methods  

Science.gov (United States)

The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

Chang, Sin-Chung

1987-01-01

310

Discrete wave mechanics: An introduction  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Discrete wave mechanics is formulated for particles in one-dimensional systems by use of a simple finite difference equation. The solutions involve wave vectors (instead of wave functions) as well as a newly defined “wave vector energy.” In the limit, as c ? ?, the treatment reduces to that of Schrödinger's wave mechanics. Specific calculations are made for completely free particles as well as for particles confined to a one-dimensional box. The results exhibit a striking compatibili...

Wall, Frederick T.

1986-01-01

311

On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 2: fully-implicit scheme  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently ...

Camporeale, E.; Delzanno, G. L.; Bergen, B. K.; Moulton, J. D.

2013-01-01

312

Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation  

CERN Multimedia

We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulating internal boundaries which are later removed. The Kuramoto-Sivashinsky equation is used as an example to show how holistic finite differences may be applied to fourth order, nonlinear, spatio-temporal dynamical systems. This novel centre manifold approach is holistic in the sense that it treats the dynamical equations as a whole, not just as the sum of separate terms.

MacKenzie, T

2000-01-01

313

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics  

CERN Document Server

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p

Gedney, Stephen

2011-01-01

314

Radon diffusion in an anhydrous andesitic melt: a finite difference solution  

International Nuclear Information System (INIS)

Radon-222 diffusion in an anhydrous andesitic melt was investigated. The melts were glass discs formed artificially from melted volcanic materials. Solutions of the relevant diffusion equations were done by the explicit finite difference method. Results were compared to analytical solutions reported in the literature and good agreement was found. We have shown that the explicit finite difference method is effective and accurate for solving equations that describe 222Rn diffusion in andesitic melts, which is especially important when arbitrary initial and boundary conditions are required.

2011-02-01

315

Radon diffusion in an anhydrous andesitic melt: a finite difference solution  

Energy Technology Data Exchange (ETDEWEB)

Radon-222 diffusion in an anhydrous andesitic melt was investigated. The melts were glass discs formed artificially from melted volcanic materials. Solutions of the relevant diffusion equations were done by the explicit finite difference method. Results were compared to analytical solutions reported in the literature and good agreement was found. We have shown that the explicit finite difference method is effective and accurate for solving equations that describe {sup 222}Rn diffusion in andesitic melts, which is especially important when arbitrary initial and boundary conditions are required.

Savovic, Svetislav, E-mail: savovic@kg.ac.r [Faculty of Science, R. Domanovica 12, 34000 Kragujevac (Serbia); Djordjevich, Alexandar; Tse, Peter W. [City University of Hong Kong, 83 Tat Chee Avenue, Kowloon (Hong Kong); Krstic, Dragana [Faculty of Science, R. Domanovica 12, 34000 Kragujevac (Serbia)

2011-02-15

316

A Second Order Finite Difference Approximation for the Fractional Diffusion Equation  

Directory of Open Access Journals (Sweden)

Full Text Available We consider an approximation of one-dimensional fractional diffusion equation. We claim and show that the finite difference approximation obtained from the Grünwald-Letnikov formulation, often claimed to be of first order accuracy, is in fact a second order approximation of the fractional derivative at a point away from the grid points. We use this fact to device a second order accurate finite difference approximation for the fractional diffusion equation. The proposed method is also shown to be unconditionally stable. By this approach, we treat three cases of difference approximations in a unified setting. The results obtained are justified by numerical examples.

H. M. Nasir

2013-07-01

317

Finite-difference frequency-domain study of subwavelength lensing in left-handed materials  

CERN Document Server

We show that the finite-difference frequency-domain method is well-suited to study subwavelength lensing effects in left-handed materials (LHM's) and related problems. The method is efficient and works in the frequency domain, eliminating the need for specifying dispersion models for the permeability and permittivity as required by the popular finite-difference time-domain method. We show that "superlensing" in a LHM slab with refractive index n = -1 can be approached by introducing an arbitrarily small loss term. We also study a thin silver slab, which can exhibit subwavelength imaging in the electrostatic limit.

Wang, X; Schatz, G C; Gray, Stephen K.; Schatz, George C.

2006-01-01

318

Modelagem Sísmica via métodos das diferenças finitas: caso da bacia do Amazonas / Seismic Modeling by finites difference method: case of Amazon basin  

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: Portuguese Abstract in portuguese Este trabalho tem por objetivo apresentar os resultados da modelagem sísmica em meios com fortes descontinuidades de propriedades físicas, com ênfase na existência de difrações e múltiplas reflexões, tendo a Bacia do Amazonas como referência à modelagem. As condições de estabilidade e de fronteiras [...] utilizadas no cálculo do campo de ondas sísmicas foram analisadas numericamente pelo método das diferenças finitas, visando melhor compreensão e controle da interpretação de dados sísmicos. A geologia da Bacia do Amazonas é constituída por rochas sedimentares depositadas desde o Ordoviciano até o Recente que atingem espessuras da ordem de 5 km. Os corpos de diabásio, presentes entre os sedimentos paleozóicos, estão dispostos na forma de soleiras, alcançam espessuras de centenas de metros e perfazem um volume total de aproximadamente 90000 Km³. A ocorrência de tais estruturas é responsável pela existência de reflexões múltiplas durante a propagação da onda sísmica o que impossibilita melhor interpretação dos horizontes refletores que se encontram abaixo destas soleiras. Para representar situações geológicas desse tipo foram usados um modelo (sintético) acústico de velocidades e um código computacional elaborado via método das diferenças finitas com aproximação de quarta ordem no espaço e no tempo da equação da onda. A aplicação dos métodos de diferenças finitas para o estudo de propagação de ondas sísmicas melhorou a compreensão sobre a propagação em meios onde existem heterogeneidades significativas, tendo como resultado boa resolução na interpretação dos eventos de reflexão sísmica em áreas de interesse. Como resultado dos experimentos numéricos realizados em meio de geologia complexa, foi observada a influência significativa das reflexões múltiplas devido à camada de alta velocidade, isto provocou maior perda de energia e dificultou a interpretação dos alvos. Por esta razão recomenda-se a integração de dados de superfície com os de poço, com o objetivo de obter melhor imagem dos alvos abaixo das soleiras de diabásio. Abstract in english This paper discusses the seismic modeling in medium with strong discontinuities in its physical properties. The approach takes in consideration the existences diffractions and multiple reflections in the analyzed medium, which, at that case, is the Amazon Basin. The stability and boundary conditions [...] of modeling were analyzed by the method of the finite differences. Sedimentary rocks deposited since the Ordovician to the present, reaching depth up to 5 Km. The bodies of diabasic between the paleozoic sediments are layers reaching thickness of hundred meters, which add to 90.000 km3, form the geology of the Amazon Basin. The occurrence of these structures is responsible for multiple reflections during the propagation of the seismic waves, which become impossible a better imaging of horizons located bellow the layers. The representation this geological situation was performed an (synthetic) acoustic velocity model. The numerical discretization scheme is based in a fourth order approximation of the acoustic wave equation in space and time The understanding of the wave propagation heterogeneous medium has improved for the application of the finite difference method. The method achieves a good resolution in the interpretation of seismic reflection events. The numerical results discusses in this paper have allowed to observed the influence of the multiple reflection in a high velocity layer. It increase a loss of energy and difficult the interpretation of the target. For this reason the integration of surface data with the well data is recommended, with the objective to get one better image of the targets below of the diabasic layer.

Lindemberg Lima, Fernandes; João Carlos Ribeiro, Cruz; Claudio José Cavalcante, Blanco; Ana Rosa Baganha, Barp.

319

Comparison of finite differences and finite elements in the case of large fast power reactor  

International Nuclear Information System (INIS)

A large number of test calculations in two-dimension hexagonal geometry for different configurations of SUPER-PHENIX 1 type Fast Reactor have been performed to compare finite differences theory versus finite elements theory performances. At present, no definitive advantages were found for the application of the finite elements method to two dimensional hexagonal design calculations

1981-04-24

320

A finite-difference calculation of point defect migration into a dislocation loop  

International Nuclear Information System (INIS)

A finite-difference calculation was carried out of the point defect flux from a surrounding spherical reservoir to a dislocation loop. Computations were done using material parameters pertinent to zirconium. The results were used to comment on the accuracy and range of applicability of some results in the literature. (auth)

1979-01-01

 
 
 
 
321

FPGA Implementation of the Two-Dimensional Finite-Difference Time- Domain (FDTD) Algorithm.  

Science.gov (United States)

Three-Dimensional Finite-Difference Time-Domain (3D FDTD) is a powerful method for modelling the electromagnetic field. The 3D FDTD buried object detection forward model is emerging as a useful application in mine detection and other subsurface sensing ar...

W. Chen M. Leeser C. Rappaport P. Kosmas

2004-01-01

322

Finite Difference-Time Domain solution of Dirac equation and the Klein Paradox  

CERN Multimedia

The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein paradox: potential step barriers and linear potentials. No Klein paradox is observed.

Simicevic, Neven

2009-01-01

323

Eulerian Finite-Difference Calculations of Explosions in Partially Water-Filled Overstrong Cylindrical Containment Vessels.  

Science.gov (United States)

Calculations, using the two-dimensional Eulerian finite-difference code CSQ, were performed for the problem of a small spherical high-explosive charge detonated in a closed heavy-walled cylindrical container partially filled with water. Data from correspo...

S. L. Thompson W. Herrmann

1977-01-01

324

Dispersion properties of nonradiating configurations: Finite-difference time-domain modeling  

Science.gov (United States)

A finite-difference time-domain (FDTD) numerical analysis is used to demonstrate that a toroidal solenoid, coaxial with an electric dipole, is a remarkable nonradiating configuration. It can be used to measure the dielectric permittivity of any ambient matter. It becomes a directional radiator at an interface between two dielectric media, depositing energy in the material with the highest polarizability.

Boardman, A. D.; Marinov, K.; Zheludev, N.; Fedotov, V. A.

2005-09-01

325

FINITE-DIFFERENCE ELECTROMAGNETIC DEPOSITION/THERMOREGULATORY MODEL: COMPARISON BETWEEN THEORY AND MEASUREMENTS (JOURNAL VERSION)  

Science.gov (United States)

The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...

326

Streamline-coordinate finite-difference method for hot metal deformations  

Energy Technology Data Exchange (ETDEWEB)

The hot metal deformation in the rolling process is a typical example of near-steady, quasi two-dimensional non-Newtonian flows. An isotropic work-hardening model characterized by a dislocation energy-density is presented and analyzed the streamline-coordinate finite-difference method. 21 refs., 4 figs., 3 tabs.

Chung, S.G. (Western Michigan Univ., Kalamazoo, MI (United States)); Kuwahara, K. (The Institute of Space and Astronautical Science, Sagamihara (Japan)); Richmond, O. (Alcoa Labs., Alcoa Center, PA (United States))

1993-09-01

327

The comparison of homotopy perturbation method with finite difference method for determination of maximum beam deflection  

Science.gov (United States)

This paper deals with the determination of maximum beam deflection using homotopy perturbation method (HPM) and finite difference method (FDM). By providing some examples, we compare the results with exact solutions and conclude that HPM is more accurate, more stable and effective and can therefore be found widely applicable in structrue engineering.

Saravi, Masoud; Hermann, Martin; Khah, Hadi Ebrahimi

2013-02-01

328

Implicit Finite-Difference (IFD) Acoustic Model in a Shallow Water Environment.  

Science.gov (United States)

In this thesis an implicit finite-difference (IFD) computer model was developed by Jaeger to solve the parabolic equation. The model preserves continuity of pressure and the normal component of particle velocity at the ocean bottom where there is an inter...

M. E. Kosnik

1984-01-01

329

The Wigner function of the relativistic finite-difference oscillator in an external field  

Energy Technology Data Exchange (ETDEWEB)

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner quasi-distribution function for the stationary states as well as for the states of thermodynamical equilibrium are obtained and their correct limits are shown.

Nagiyev, S M; Guliyeva, G H; Jafarov, E I [Institute of Physics, Azerbaijan National Academy of Sciences, Javid av. 33, AZ1143 Baku (Azerbaijan)], E-mail: ejafarov@physics.ab.az

2009-10-30

330

Finite difference simulations of particle velocity records from small scale explosive tests  

International Nuclear Information System (INIS)

Spherically symmetric finite difference calculations are presented which successfully simulate the particle velocity measurements from small-scale explosive experiments performed at SRI International both in spheres of 2C4 rock-matching grout and high porosity, low density LD2C4 grout, and in cylinders of saturated tuffs from the Nevada Test Site

1983-08-02

331

A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on Shifted Grünwald Estimate  

Directory of Open Access Journals (Sweden)

Full Text Available In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.

Abdollah BORHANIFAR

2013-01-01

332

A Fractional Finite Difference Method for Solving the Fractional Poisson Equation Based on Shifted Grünwald Estimate  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this study fractional Poisson equation is scrutinized through finite difference using shifted Grünwald estimate. A novel method is proposed numerically. The existence and uniqueness of solution for the fractional Poisson equation are proved. Exact and numerical solution are constructed and compared. Then numerical result shows the efficiency of the proposed method.

Borhanifar, Abdollah; Valizadeh, Sohrab

2013-01-01

333

Numerical stability of the Saul'yev finite difference algorithms for electrochemical kinetic simulations: Matrix stability analysis for an example problem involving mixed boundary conditions  

DEFF Research Database (Denmark)

The stepwise numerical stability of the Saul'yev finite difference discretization of an example diffusional initial boundary value problem from electrochemical kinetics has been investigated using the matrix method of stability analysis. Special attention has been paid to the effect of the discretization of the mixed, linear boundary condition on stability, assuming the two-point, forward-difference approximation for the gradient at the left boundary (electrode). Criteria regulating the error growth in time have been identified. In particular it has been shown that, in contrast to the claims of unconditional stability of the Saul'yev algorithms, reported in the literature, the left-right variant of the Saul'yev algorithm becomes unstable for large values of the dimensionless diffusion parameter λ = δt/h2, under mixed boundary conditions. This limitation is not, however, severe for most practical applications.

Bieniasz, Leslaw K.; Ã?sterby, Ole

1995-01-01

334

Comparison between a finite difference model (PUMA) and a finite element model (DELFIN) for simulation of the reactor of the atomic power plant of Atucha I  

International Nuclear Information System (INIS)

The reactor code PUMA, developed in CNEA, simulates nuclear reactors discretizing space in finite difference elements. Core representation is performed by means a cylindrical mesh, but the reactor channels are arranged in an hexagonal lattice. That is why a mapping using volume intersections must be used. This spatial treatment is the reason of an overestimation of the control rod reactivity values, which must be adjusted modifying the incremental cross sections. Also, a not very good treatment of the continuity conditions between core and reflector leads to an overestimation of channel power of the peripherical fuel elements between 5 to 8 per cent. Another code, DELFIN, developed also in CNEA, treats the spatial discretization using heterogeneous finite elements, allowing a correct treatment of the continuity of fluxes and current among elements and a more realistic representation of the hexagonal lattice of the reactor. A comparison between results obtained using both methods in done in this paper. (author). 4 refs., 3 figs

1996-11-18

335

A Mathematical Description of the IDSA for Supernova Neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann's Equation  

CERN Document Server

In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the \\emph{Isotropic Diffusion Source Approximation} (IDSA). Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized.

Berninger, Heiko; Gander, Martin; Liebendörfer, Mathias; Michaud, Jérôme; Vasset, Nicolas

2012-01-01

336

A Fully Discrete Finite Element Scheme for the Derrida-Lebowitz-Speer-Spohn Equation / Un esquema de elementos finitos completamente discreto para la ecuación de Derrida-Lebowitz-Speer- Spohn  

Scientific Electronic Library Online (English)

Full Text Available SciELO Colombia | Language: English Abstract in spanish La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS) es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos. En este artículo, se presenta una discretización por elementos [...] finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta. Abstract in english The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a finite element discretization for a exponential form [...] ulation of a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of the discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.

Jorge Mauricio, Ruiz Vera; Ignacio, Mantilla Prada.

2013-06-01

337

Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory  

Energy Technology Data Exchange (ETDEWEB)

The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

1997-10-01

338

Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry  

International Nuclear Information System (INIS)

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two steps for the analytical reconstruction of the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates (SN) transport model in slab geometry. The first step of the algorithm is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the grid set up on the spatial domain. The second step is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the SN model. Numerical results are given so we can illustrate the accuracy of the two reconstruction techniques, as described in this paper.

2010-11-01

339

On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 2: fully-implicit scheme  

CERN Multimedia

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC. This paper concludes the study presented in Camporeale et al. (2013) where the same method has been described for a semi-implicit time discretization, and was compared against an explicit PIC.

Camporeale, E; Bergen, B K; Moulton, J D

2013-01-01

340

Three-Dimensional Sound Field Analysis Using Compact Explicit-Finite Difference Time Domain Method with Graphics Processing Unit Cluster System  

Science.gov (United States)

In this study, the compact explicit-finite difference time domain (CE-FDTD) method is applied to the three-dimensional sound field analysis to reduce computer resources. There are various derivative schemes in the CE-FDTD method. They are first examined theoretically to evaluate the numerical accuracy. As a theoretical result, it is found that the interpolated wide band (IWB) scheme has the widest bandwidth in which the cut-off frequency is in agreement with the Nyquist frequency. The calculation performance is theoretically estimated, then experimentally evaluated with the graphics processing unit cluster system. As a result, it is found that the memory usage of the IWB scheme is less than one-third of that of the standard leapfrog (SLF) scheme to achieve the same cut-off frequency. It is also found that the calculation time of the IWB scheme with the shared memory is about 19% compared with that of the SLF scheme with the graphics processing unit (GPU) cluster system. The impulse response is calculated for a large room with a volume capacity of about 4500 m3 in which the sampling rate was 40 kHz. It is confirmed that the three-dimensional sound field with the natural reverberation can be calculated by the IWB scheme.

Ishii, Takuto; Tsuchiya, Takao; Okubo, Kan

2013-07-01

 
 
 
 
341

Discretization on a general staggered grid  

Energy Technology Data Exchange (ETDEWEB)

A discretization scheme on a general staggered grid is described. This discretization is used in conjunction with an arbitrary Lagrangean-Eulerian method that allows use of a fixed Eulerian grid, a Lagrangean grid, or an adaptive grid. 11 refs.

Sulsky, D.L. (New Mexico Univ., Albuquerque, NM (United States). Dept. of Mathematics and Statistics); Brackbill, J.U. (Los Alamos National Lab., NM (United States))

1991-01-01

342

Efficient Energyminimization in Finite-Difference Micromagnetics: Speeding up Hysteresis Computations  

CERN Document Server

We implement an efficient energy-minimization algorithm for finite-difference micromagnetics that proofs especially usefull for the computation of hysteresis loops. Compared to results obtained by time integration of the Landau-Lifshitz-Gilbert equation, a speedup of up to two orders of magnitude is gained. The method is implemented in a finite-difference code running on CPUs as well as GPUs. This setup enables us to compute accurate hysteresis loops of large systems with a reasonable computational efford. As a benchmark we solve the {\\mu}Mag Standard Problem #1 with a high spatial resolution and compare the results to the solution of the Landau-Lifshitz-Gilbert equation in terms of accuracy and computing time.

Abert, Claas; Bruckner, Florian; Satz, Armin; Suess, Dieter

2014-01-01

343

On One-Dimensional Stretching Functions for Finite-Difference Calculations  

Science.gov (United States)

The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.

Vinokur, M.

1980-01-01

344

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions  

CERN Document Server

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodal-based finite elements may converge to the wrong solution due to a version of the Babuska paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.

Zhou, Dong; Shirokoff, David; Chidyagwai, Prince; Rosales, Rodolfo Ruben

2013-01-01

345

Different factorizations of the relativistic finite-difference Schrödinger equation and q-oscillators  

CERN Multimedia

The concept of the one -- dimensional quantum mechanics in the relativistic configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger equation (RSE) arising here is the finite -- difference equation with the step equal to the Compton wave length of the particle. The different generalizations of the Dirac -- Infeld-- Hall factorizarion method for this case are constructed. This method enables us to find out all possible finite-difference generalizations of the most important nonrelativistic integrable case -- the harmonic oscillator. As it was shown in \\cite{kmn},\\cite{mir6} the case of RQM the harmonic oscillator = q -- oscillator. It is also shown that the relativistic and nonrelativistic QM's are different representations of the same theory. The transformation connecting these two representations is found in explicit form. It could be considered as the generalization of the Kontorovich -- Lebedev transformation.

Mir-Kasimov, R M

1994-01-01

346

Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping  

Science.gov (United States)

Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

347

Application of an Acceleration Scheme for an Age-Structured Diffusion Model  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we propose an optimized algorithm, which is faster compared to previously described finite difference acceleration scheme, namely the Modified Super-Time-Stepping (Modified STS) scheme for age- structured population models with diffusion.

Boyadzhiev, Doychin

2010-01-01

348

Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which me...

Berg, Jens

2013-01-01

349

Optical Resonator Analog of a Photonic Topological Insulator: a Finite-Difference Time-Domain Study  

Science.gov (United States)

A periodic lattice of optical ring resonators can act as a photonic topological insulator, with the role of spin played by the direction of propagation of light within each ring. Using finite-difference time-domain (FDTD) simulations, we compute the projected band diagram of the system and its transmission spectrum, and demonstrate the existence of the topological edge states. The FDTD results are in good agreement with the predictions of transfer matrix theory.

Liang, G. Q.; Chong, Y. D.

2014-01-01

350

Finite Difference Time-Domain Modelling of Metamaterials: GPU Implementation of Cylindrical Cloak  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Finite difference time-domain (FDTD) technique can be used to model metamaterials by treating them as dispersive material. Drude or Lorentz model can be incorporated into the standard FDTD algorithm for modelling negative permittivity and permeability. FDTD algorithm is readily parallelisable and can take advantage of GPU acceleration to achieve speed-ups of 5x-50x depending on hardware setup. Metamaterial scattering problems are implemented using dispersive FDTD technique on GPU resulting in...

Attique Dawood

2013-01-01

351

FDTD.org: Finite-Difference Time-Domain Literature Database  

Science.gov (United States)

John Schneider and Kurt Shlager at the School of Electrical Engineering and Computer Science at Washington State University provide the Finite-Difference Time-Domain (FDTD) Database. This database contains most, if not all, published work that deals with the application or extensions to the FDTD method. This is not an annotated database and the literature dates back to the 1960's. This database could be useful for scientists looking "for some pointers into the FDTD literature."

1985-01-01

352

TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems  

International Nuclear Information System (INIS)

Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)

1984-01-01

353

A practical implicit finite-difference method: examples from seismic modelling  

Science.gov (United States)

We derive explicit and new implicit finite-difference formulae for derivatives of arbitrary order with any order of accuracy by the plane wave theory where the finite-difference coefficients are obtained from the Taylor series expansion. The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. Our results demonstrate that the accuracy of a (2N + 2)th-order implicit formula is nearly equivalent to that of a (6N + 2)th-order explicit formula for the first-order derivative, and (2N + 2)th-order implicit formula is nearly equivalent to (4N + 2)th-order explicit formula for the second-order derivative. In general, an implicit method is computationally more expensive than an explicit method, due to the requirement of solving large matrix equations. However, the new implicit method only involves solving tridiagonal matrix equations, which is fairly inexpensive. Furthermore, taking advantage of the fact that many repeated calculations of derivatives are performed by the same difference formula, several parts can be precomputed resulting in a fast algorithm. We further demonstrate that a (2N + 2)th-order implicit formulation requires nearly the same memory and computation as a (2N + 4)th-order explicit formulation but attains the accuracy achieved by a (6N + 2)th-order explicit formulation for the first-order derivative and that of a (4N + 2)th-order explicit method for the second-order derivative when additional cost of visiting arrays is not considered. This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance. Our analysis of efficiency and numerical modelling results for acoustic and elastic wave propagation validates the effectiveness and practicality of the implicit finite-difference method.

Liu, Yang; Sen, Mrinal K.

2009-09-01

354

RODCON: a finite difference heat conduction computer code in cylindrical coordinates  

International Nuclear Information System (INIS)

RODCON, a finite difference computer code, was developed to calculate the internal temperature distribution of the fuel rod simulator (FRS) for the Core Flow Test Loop (CFTL). RODCON solves the implicit, time-dependent forward-differencing heat transfer equation in 2-dimensional (Rtheta) cylindrical coordinates at an axial plane with user specified radial material zones and surface conditions at the FRS periphery. Symmetry of the boundary conditions of coolant bulk temperatures and film coefficients at the FRS periphery is not necessary

1980-09-19

355

Transport and dispersion of pollutants in surface impoundments: a finite difference model  

International Nuclear Information System (INIS)

A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model

1980-01-01

356

Transport and dispersion of pollutants in surface impoundments: a finite difference model  

Energy Technology Data Exchange (ETDEWEB)

A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.

Yeh, G.T.

1980-07-01

357

Calculation of electron transfer reorganization energies using the finite difference Poisson-Boltzmann model.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A description is given of a method to calculate the electron transfer reorganization energy (lambda) in proteins using the linear or nonlinear Poisson-Boltzmann (PB) equation. Finite difference solutions to the linear PB equation are then used to calculate lambda for intramolecular electron transfer reactions in the photosynthetic reaction center from Rhodopseudomonas viridis and the ruthenated heme proteins cytochrome c, myoglobin, and cytochrome b and for intermolecular electron transfer be...

1998-01-01

358

An Improvement for the Locally One-Dimensional Finite-Difference Time-Domain Method  

Directory of Open Access Journals (Sweden)

Full Text Available To reduce the memory usage of computing, the locally one-dimensional reduced finite-difference time-domain method is proposed. It is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with locally one-dimensional finite-difference time-domain (LOD-FDTD method, and the concrete expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the LOD-FDTD method is combined with the reduced finite-difference time-domain (R-FDTD method. In the proposed method, the memory requirement of LOD-R-FDTD is reduced by1/6 (3D case of the memory requirement of LOD-FDTD averagely. The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.

Xiuhai Jin

2011-09-01

359

Modeling and Simulation of Hamburger Cooking Process Using Finite Difference and CFD Methods  

Directory of Open Access Journals (Sweden)

Full Text Available Unsteady-state heat transfer in hamburger cooking process was modeled using one dimensional finite difference (FD and three dimensional computational fluid dynamic (CFD models. A double-sided cooking system was designed to study the effect of pressure and oven temperature on the cooking process. Three different oven temperatures (114, 152, 204°C and three different pressures (20, 332, 570 pa were selected and 9 experiments were performed. Applying pressure to hamburger increases the contact area of hamburger with heating plate and hence the heat transfer rate to the hamburger was increased and caused the weight loss due to water evaporation and decreasing cooking time, while increasing oven temperature led to increasing weight loss and decreasing cooking time. CFD predicted results were in good agreement with the experimental results than the finite difference (FD ones. But considering the long time needed for CFD model to simulate the cooking process (about 1 hour, using the finite difference model would be more economic.

J. Sargolzaei

2011-01-01

360

Finite-difference P wave travel time seismic tomography of the crust and uppermost mantle in the Italian region  

Science.gov (United States)

We present a 3-D P wave velocity model of the crust and shallowest mantle under the Italian region, that includes a revised Moho depth map, obtained by regional seismic travel time tomography. We invert 191,850 Pn and Pg wave arrival times from 6850 earthquakes that occurred within the region from 1988 to 2007, recorded by 264 permanent seismic stations. We adopt a high-resolution linear B-spline model representation, with 0.1° horizontal and 2 km vertical grid spacing, and an accurate finite-difference forward calculation scheme. Our nonlinear iterative inversion process uses the recent European reference 3-D crustal model EPcrust as a priori information. Our resulting model shows two arcs of relatively low velocity in the crust running along both the Alps and the Apennines, underlying the collision belts between plates. Beneath the Western Alps we detect the presence of the Ivrea body, denoted by a strong high P wave velocity anomaly. We also map the Moho discontinuity resulting from the inversion, imaged as the relatively sharp transition between crust and mantle, where P wave velocity steps up to values larger than 8 km/s. This simple condition yields an image quite in agreement with previous studies that use explicit representations for the discontinuity. We find a complex lithospheric structure characterized by shallower Moho close by the Tyrrhenian Sea, intermediate depth along the Adriatic coast, and deepest Moho under the two mountain belts.

Gualtieri, L.; Serretti, P.; Morelli, A.

2014-01-01

 
 
 
 
361

Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method  

Science.gov (United States)

We simulate P-SV wave scattering by 2-D parallel cracks using the finite difference method (FDM). Here, special emphasis is put on simplicity; we apply a standard FDM (second-order velocity-stress scheme with a staggered grid) to media including traction-free, infinitesimally thin cracks, which are expressed in a simple manner. As an accuracy test of the present method, we calculate the displacement discontinuity along an isolated crack caused by harmonic waves using the method, which is compared with the corresponding results based on a reliable boundary integral equation method. The test resultantly indicates that the present method yields sufficient accuracy. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation, if the crack density is sufficiently low. The theory appears valid with a crack density up to at least 0.1 for SV wave incidence, whereas the validity limit appears lower for P wave incidence.

Suzuki, Y.; Shiina, T.; Kawahara, J.; Okamoto, T.; Miyashita, K.

2013-12-01

362

Finite difference approach on magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates  

Directory of Open Access Journals (Sweden)

Full Text Available This paper considers the magnetohydrodynamic flow and heat transfer in a viscous incompressible fluid between two parallel porous plates experiencing a discontinuous change in wall temperature. An explicit finite difference scheme has been employed to solve the coupled non-linear equations governing the flow. The flow phenomenon has been characterized by Hartmann number, suction Reynolds number, channel Reynolds number and Prandtl number. The effects of these parameters on the velocity and temperature distribution have been analyzed and the results are presented with the aid of figures. It is observed that a growing suction parameter R retards the velocity of the flow field both in MHD as well as non-MHD flow. The effect of increasing Hartmann number is to decrease the transverse component of velocity for both suction and injection and in absence of suction and injection, while it decreases the axial component of velocity up to the middle of the channel and beyond this the effect reverses. There is a sharp fluctuation in temperature near the walls and at the middle of the channel which may be attributed to the discontinuous change in wall temperature. For fluids having low Prandtl number such as air, the temperature assumes negative values.

S. S. Das, M. Mohanty, R. K. Padhy, M. Sahu

2012-01-01

363

Finite Difference Analysis of Radiative Free Convection Flow Past an Impulsively Started Vertical Plate with Variable Heat and Mass Flux  

Directory of Open Access Journals (Sweden)

Full Text Available A numerical solution of the unsteady radiative free convection flow of an incompressible viscous fluid past an impulsively started vertical plate with variable heat and mass flux is presented here. This type of problem finds application in many technological and engineering fields such as rocket propulsion systems, spacecraft re-entry aerothermodynamics, cosmical flight aerodynamics, plasma physics, glass production and furnace engineering. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing non-linear, coupled equations are solved using an implicit finite difference scheme. Numerical results for the velocity, temperature, concentration, the local and average skinfriction, the Nusselt and Sherwood number are shown graphically, for different values of Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, radiation parameter, heat flux exponent and the mass flux exponent. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer. The local and average skin-friction increases with the increase in radiation parameter. For increasing values of radiation parameter the local as well as average Nusselt number increases.

V. Ramachandra Prasad

2011-01-01

364

An improvement of the filter diagonalization-based post-processing method applied to finite difference time domain calculations of three-dimensional phononic band structures  

International Nuclear Information System (INIS)

When three-dimensional (3D) phononic band structures are calculated by using the finite difference time domain (FDTD) method with a relatively small number of iterations, the results can be effectively improved by post-processing the FDTD time series (FDTD-TS) based on the filter diagonalization method (FDM), instead of the classical fast Fourier transform. In this paper, we propose a way to further improve the performance of the FDM-based post-processing method by introducing a relatively large number of observing points to record the FDTD-TS. To this end, the existing scheme of FDTD-TS preprocessing is modified. With the new preprocessing scheme, the processing efficiency of a single FDTD-TS can be improved significantly, and thus the entire post-processing method can have sufficiently high efficiency even when a relatively large number of observing points are used. The feasibility of the proposed method for improvement is verified by the numerical results.

2012-10-01

365

A mathematical description of the IDSA for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s equation  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the Isotropic Diffusion Source Approximation (IDSA established in [6]. Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA in [6] for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized. Dans cet article, nous donnons une introduction à l’équation de Boltzmann pour le transport des neutrinos dans les modèles de supernovae à effondrement de cœur ainsi qu’une description détaillée de l’Isotropic Diffusion Source Approximation (IDSA développée dans [6]. De plus, nous présentons le traitement numérique d’un modèle de Boltzmann simplifié basé sur une décomposition en temps de l’opérateur et sur un algorithme de volumes finis ainsi que l’adaptation de la discrétisation de l’IDSA de [6] à notre modèle. Les études de l’erreur de discrétisation faites sur le modèle de Boltzmann simplifié et sur l’IDSA montrent que les erreurs sont d’ordre un dans les deux cas. A l’aide d’un exemple numérique, nous comparons et interprétons en détail les deux modèles. Pour cet exemple, l’erreur de modélisation de l’IDSA par rapport au modèle de Boltzmann simplifié est déterminée numériquement et localisée.

Berninger Heiko

2013-01-01

366

Lattice operators from discrete hydrodynamics  

CERN Document Server

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators, which are expected to apply across a broad range of problems in computational physics.

Ramadugu, Rashmi; Adhikari, Ronojoy; Succi, Sauro; Ansumali, Santosh

2012-01-01

367

Lattice operators from discrete hydrodynamics  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators, which are expected to apply across a broad range of problems in computational...

Ramadugu, Rashmi; Thampi, Sumesh P.; Adhikari, Ronojoy; Succi, Sauro; Ansumali, Santosh

2012-01-01

368

Multiscale viscoacoustic waveform inversion with the second generation wavelet transform and adaptive time-space domain finite-difference method  

Science.gov (United States)

Full waveform inversion (FWI) has the potential to provide preferable subsurface model parameters. The main barrier of its applications to real seismic data is heavy computational amount. Numerical modelling methods are involved in both forward modelling and backpropagation of wavefield residuals, which spend most of computational time in FWI. We develop a time-space domain finite-difference (FD) method and adaptive variable-length spatial operator scheme in numerical simulation of viscoacoustic equation and extend them into the viscoacoustic FWI. Compared with conventional FD methods, different operator lengths are adopted for different velocities and quality factors, which can reduce the amount of computation without reducing accuracy. Inversion algorithms also play a significant role in FWI. In conventional single-scale methods, it is likely to converge to local minimums especially when the initial model is far from the real model. To tackle the problem, we introduce the second generation wavelet transform to implement the multiscale FWI. Compared to other multiscale methods, our method has advantages of ease of implementation and better time-frequency local analysis ability. The L2 norm is widely used in FWI and gives invalid model estimates when the data is contaminated with strong non-uniform noises. We apply the L1-norm and the Huber-norm criteria in the time-domain FWI to improve its antinoise ability. Our strategies have been successfully applied in synthetic experiments to both onshore and offshore reflection seismic data. The results of the viscoacoustic Marmousi example indicate that our new FWI scheme consumes smaller computer resources. In addition, the viscoacoustic Overthrust example shows its better convergence and more reasonable velocity and quality factor structures. All these results demonstrate that our method can improve inversion accuracy and computational efficiency of FWI.

Ren, Zhiming; Liu, Yang; Zhang, Qunshan

2014-05-01

369

A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation Un esquema de elementos finitos completamente discreto para la ecuación de Derrida-Lebowitz-Speer-Spohn  

Directory of Open Access Journals (Sweden)

Full Text Available The Derrida-Lebowitz-Speer-Spohn (DLSS equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.La ecuación de Derrida-Lebowitz-Speer-Spohn (DLSS es una ecuación de evolución no lineal de cuarto orden. Esta aparece en el estudio de las fluctuaciones de interface de sistemas de espín y en la modelación de semicoductores cuánticos.  En este artículo, se presenta una discretización por elementos finitos para una formulación exponencial de la ecuación DLSS abordada como un sistema acoplado de ecuaciones. Usando la información disponible acerca del fenómeno físico, se establecen las condiciones de contorno para el sistema acoplado. Se demuestra la existencia de la solución discreta global en el tiempo via un  argumento de punto fijo. Los resultados numéricos ilustran el carácter cuántico de la ecuación. Finalmente se presenta un test del orden de convergencia de la discretización porpuesta.

Jorge Mauricio Ruiz Vera

2013-03-01

370

PKC Scheme Based on DDLP  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper introduces the concept of public key cryptosystem, whose security is based on double discrete logarithm problem (DDLP) with distinct discrete exponents in the multiplicative group of finite fields. The adversary has to solve distinct discrete logarithm problems simultaneously in order to recover a corresponding plaintext from the received cipertext. Therefore, this scheme is expected to gain a higher level of security. We next show that, the newly developed scheme is efficient w...

Chandrashekhar Meshram; Meshram, Suchitra A.

2012-01-01

371

Application of the multigrid method in a deterministic solution scheme for the three-dimensional radiative transfer equation  

International Nuclear Information System (INIS)

An improved solution scheme is developed for the three-dimensional radiative transfer equation (RTE) in inhomogeneous cloudy atmospheres. This solution scheme is deterministic (explicit) and utilizes spherical harmonics series expansion and the finite-volume method for discretization of the RTE. The first-order upwind finite difference is modified to take into account bidirectional flow of radiance in spherical harmonics space, and an iterative solution method is applied. The multigrid method, which is generally employed to achieve rapid convergence in iterative calculation, is incorporated into the solution scheme. The present study suggests that the restriction and prolongation procedure for the multigrid method must be also modified to account for bidirectional flow, and proposes an efficient bidirectional restriction/prolongation procedure that does not increase the computational effort for coarser grids, resulting in a type of wavelet low-pass filter. Several calculation examples for various atmosphere models indicate that the proposed solution scheme is effective for rapid convergence and suitable for obtaining adequate radiation fields in inhomogeneous cloudy atmospheres, although a comparison with the Monte Carlo method suggests that the radiances obtained by this solution scheme at certain angles tends to be smoother. -- Highlights: • We develop a deterministic solution scheme for the 3-D radiative transfer. • The multigrid method is incorporated into an iterative solution scheme. • The multigrid method needs to be modified for the incorporation. • An ingenious procedure for the restriction and prolongation is proposed. • The scheme results in rapid convergence and obtains adequate radiation fields

2014-01-01

372

A finite difference Hartree-Fock program for atoms and diatomic molecules  

Science.gov (United States)

The newest version of the two-dimensional finite difference Hartree-Fock program for atoms and diatomic molecules is presented. This is an updated and extended version of the program published in this journal in 1996. It can be used to obtain reference, Hartree-Fock limit values of total energies and multipole moments for a wide range of diatomic molecules and their ions in order to calibrate existing and develop new basis sets, calculate (hyper)polarizabilities (?, ?, ?, A, B) of atoms, homonuclear and heteronuclear diatomic molecules and their ions via the finite field method, perform DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method, perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and take account of finite nucleus models. The program is easy to install and compile (tarball+configure+make) and can be used to perform calculations within double- or quadruple-precision arithmetic. Program summaryProgram title: 2dhf Catalogue identifier: ADEB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 2 No. of lines in distributed program, including test data, etc.: 171196 No. of bytes in distributed program, including test data, etc.: 9481802 Distribution format: tar.gz Programming language: Fortran 77, C. Computer: any 32- or 64-bit platform. Operating system: Unix/Linux. RAM: Case dependent, from few MB to many GB Classification: 16.1. Catalogue identifier of previous version: ADEB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 98(1996)346 Does the new version supersede the previous version?: Yes Nature of problem: The program finds virtually exact solutions of the Hartree-Fock and density functional theory type equations for atoms, diatomic molecules and their ions. The lowest energy eigenstates of a given irreducible representation and spin can be obtained. The program can be used to perform one-particle calculations with (smooth) Coulomb and Krammers-Henneberger potentials and also DFT-type calculations using LDA or B88 exchange functionals and LYP or VWN correlations ones or the self-consistent multiplicative constant method. Solution method: Single-particle two-dimensional numerical functions (orbitals) are used to construct an antisymmetric many-electron wave function of the restricted open-shell Hartree-Fock model. The orbitals are obtained by solving the Hartree-Fock equations as coupled two-dimensional second-order (elliptic) partial differential equations (PDEs). The Coulomb and exchange potentials are obtained as solutions of the corresponding Poisson equations. The PDEs are discretized by the eighth-order central difference stencil on a two-dimensional single grid, and the resulting large and sparse system of linear equations is solved by the (multicolour) successive overrelaxation ((MC)SOR) method. The self-consistent-field iterations are interwoven with the (MC)SOR ones and orbital energies and normalization factors are used to monitor the convergence. The accuracy of solutions depends mainly on the grid and the system under consideration, which means that within double precision arithmetic one can obtain orbitals and energies having up to 12 significant figures. If more accurate results are needed, quadruple-precision floating-point arithmetic can be used. Reasons for new version: Additional features, many modifications and corrections, improved convergence rate, overhauled code and documentation. Summary of revisions: see ChangeLog found in tar.gz archive Restrictions: The present version of the program is restricted to 60 orbitals. The maximum grid size is determined at compilation time. Unusual features: The program uses two C routines for allocating and deallocating memory. Several BLAS (Basic Linear Algebra System) routines are emulated by the program. When possible they should be replac

Kobus, Jacek

2013-03-01

373

Exposure Assessment Using the Dual-Grid Finite-Difference Time-Domain Method  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A new way to carry out numerical cellular telephone simulation in the presence of the head is presented. Here, two finite-difference time-domain (FDTD) simulations with different spatial and time resolutions are sequentially combined to perform a dual-grid FDTD (DG-FDTD) simulation. The DG-FDTD approach has the significant advantages to remain stable along the computation and to be easy to implement in a typical FDTD code. When compared with classical FDTD analysis, the DG-FDTD approach exhib...

Pascaud, Romain; Gillard, Raphae?l; Loison, Renaud; Wiart, Joe; Wong, Man-fai?

2008-01-01

374

Finite-difference time domain solution of light scattering by arbitrarily shaped particles and surfaces  

DEFF Research Database (Denmark)

This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms for particle and surface scattering calculations and the uniaxial perfectly matched layer (UPML) absorbing boundary conditions for truncation of the FDTD grid. We show that the FDTD approach has a significant potential for studying the light scattering by cloud, dust, and biological particles. The applications of the FDTD approach for beam scattering by arbitrarily shaped surfaces are also discussed.

Tanev, Stoyan; Sun, Wenbo

2012-01-01

375

A finite difference method for inverse solutions of 3-D turbulent boundary-layer flow  

Science.gov (United States)

A finite difference method has been developed to solve the 3-D turbulent boundary-layer equations by inverse procedures: the longitudinal and transverse displacement thicknesses or the wall shear stress components can be prescribed. The method applies to isoenergetic compressible flows and an algebraic turbulence model as well as a two-transport equation model are considered. Applications made in subsonic and transonic flows show that a separation line can be crossed and that it is possible to extend the calculation in a separated zone and beyond a reattachment line. Results obtained are in reasonable agreement with available experimental data.

Delery, J. M.; Formery, M. J.

1983-01-01

376

Finite difference method for the inverse mode computation of a three dimensional turbulent boundary layer  

Science.gov (United States)

A numerical method is proposed which solves turbulent three-dimensional boundary layer equations by an inverse approach where longitudinal and transverse displacement thicknesses are prescribed. The formulation is restricted to an incompressible boundary layer, developing on a flat plate. The equations are solved by a strongly implicit finite difference method. Applications show that a separation line can be crossed without any numerical difficulty and that it is possible to extend the calculation of the boundary layer in the reversed flow region. The flow structure in the vicinity of the separation line is faithfully represented.

Formery, M.; Delery, J.

1982-02-01

377

Calculating modes of quantum wire systems using a finite difference technique  

Directory of Open Access Journals (Sweden)

Full Text Available  In this paper, the Schrodinger equation for a quantum wire is solved using a finite difference approach. A new aspect in this work is plotting wave function on cross section of rectangular cross-sectional wire in two dimensions, periodically. It is found that the correct eigen energies occur when wave functions have a complete symmetry. If the value of eigen energy has a small increase or decrease in neighborhood of the correct energy the symmetry will be destroyed and aperturbation value at the first of wave function will be observed. In addition, the demand on computer memory varies linearly with the size of the system under investigation.

T Mardani

2013-03-01

378

An Exploration of the Approximation of Derivative Functions via Finite Differences  

CERN Multimedia

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent approximations to various derivative functions, including those used in modeling important physical processes on uniform grids. However, our research reveals that difference approximations on uniform grids cannot be applied blindly on nonuniform grids, nor can difference formulas to form consistent approximations to second derivatives. At best, they may lose accuracy; at worst they are inconsistent. Detailed consistency and error analysis, together with simulated examples, will be given.

Jain, Brian

2010-01-01

379

Interval finite difference method for steady-state temperature field prediction with interval parameters  

Science.gov (United States)

A new numerical technique named interval finite difference method is proposed for the steady-state temperature field prediction with uncertainties in both physical parameters and boundary conditions. Interval variables are used to quantitatively describe the uncertain parameters with limited information. Based on different Taylor and Neumann series, two kinds of parameter perturbation methods are presented to approximately yield the ranges of the uncertain temperature field. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed method for solving steady-state heat conduction problem with uncertain-but-bounded parameters. [Figure not available: see fulltext.

Wang, Chong; Qiu, Zhi-Ping

2014-04-01

380

Explicit finite difference solution of the diffusion equation describing the flow of radon through soil  

Energy Technology Data Exchange (ETDEWEB)

Radon diffusion through soil and into air is investigated. The solution of the relevant diffusion equation is given using the explicit finite difference method. Results from a two-medium model (soil-air) are compared to those from a simplified single-medium model (soil alone). The latter are an underestimate in early stages of the diffusion process. Later on, the two models match closely and either one can be used at equilibrium conditions to calculate radon diffusion, estimate indoor radon concentration and assess health hazards.

Savovic, Svetislav, E-mail: savovic@kg.ac.r [City University of Hong Kong, 83 Tat Chee Avenue, Kowloon (Hong Kong); Faculty of Science, R. Domanovica 12, 34000 Kragujevac (Serbia); Djordjevich, Alexandar; Tse, Peter W. [City University of Hong Kong, 83 Tat Chee Avenue, Kowloon (Hong Kong); Nikezic, Dragoslav [Faculty of Science, R. Domanovica 12, 34000 Kragujevac (Serbia)

2011-01-15

 
 
 
 
381

Finite difference solution of the diffusion equation describing the flow of radon through soil  

International Nuclear Information System (INIS)

Full text: The process of radon diffusion through a soil is investigated. The solution of the relevant diffusion equation is by the explicit finite difference method. We compared numerical results obtained assuming diffusion as one-region problem with numerical results obtained treating diffusion as two-region problem. We have shown that both approaches are efficient and accurate in solving the problem of radon diffusion through soil. The method presented for the calculation of radon diffusion through soil allows estimation of the indoor radon concentration

2008-06-01

382

Explicit finite difference solution of the diffusion equation describing the flow of radon through soil  

International Nuclear Information System (INIS)

Radon diffusion through soil and into air is investigated. The solution of the relevant diffusion equation is given using the explicit finite difference method. Results from a two-medium model (soil-air) are compared to those from a simplified single-medium model (soil alone). The latter are an underestimate in early stages of the diffusion process. Later on, the two models match closely and either one can be used at equilibrium conditions to calculate radon diffusion, estimate indoor radon concentration and assess health hazards.

2011-01-01

383

A note on errors arising in finite difference representations of control rod effects  

International Nuclear Information System (INIS)

Two methods for the representation of moving control rods are defined. These methods have been used in recant analogue and digital computer studies on finite difference models of axial transients. The errors involved in their use are evaluated for a typically severe case of flux distortion by comparison with a one group diffusion theory approach. It is shown that with either method, maximum error in rod penetration does not exceed about 0.06 of an interval for a 16 interval model or 0.17 of an interval for an 8 interval model. However, changes in reactivity are estimated much more accurately by the 'quadratic' method than by the 'linear' method. (author)

1961-01-01

384

Spectral and Finite Difference Solutions of the Hyperbolic Heat Transport Equation for Thermoelectric Thin Films  

Directory of Open Access Journals (Sweden)

Full Text Available This paper presents the numerical comparison in the solution of the hyperbolic transport Equation that models the heat flux in thermoelectric materials at nanometric length scales when the wave propagation of heat dominates the diffusive transport described by Fourier’s law. The widely used standard finite difference method fails in well-reproducing some of the physics presented in such systems at that length scale level. As an alternative, the spectral methods assure a well representation of wave behavior of heat given their spectral convergence.

Aldo Figueroa

2013-10-01

385

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case  

Science.gov (United States)

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food.

Hojbot?, C. I.; To?a, V.; Mercea, P. V.

2013-08-01

386

Modelling migration in multilayer systems by a finite difference method: the spherical symmetry case  

International Nuclear Information System (INIS)

We present a numerical model based on finite differences to solve the problem of chemical impurity migration within a multilayer spherical system. Migration here means diffusion of chemical species in conditions of concentration partitioning at layer interfaces due to different solubilities of the migrant in different layers. We detail here the numerical model and discuss the results of its implementation. To validate the method we compare it with cases where an analytic solution exists. We also present an application of our model to a practical problem in which we compute the migration of caprolactam from the packaging multilayer foil into the food

2013-08-12

387

Electromagnetic Wave Propagation in Body Area Networks Using the Finite-Difference-Time-Domain Method  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A rigorous full-wave solution, via the Finite-Difference-Time-Domain (FDTD) method, is performed in an attempt to obtain realistic communication channel models for on-body wireless transmission in Body-Area-Networks (BANs), which are local data networks using the human body as a propagation medium. The problem of modeling the coupling between body mounted antennas is often not amenable to attack by hybrid techniques owing to the complex nature of the human body. For instance, the time-domain ...

Bringuier, Jonathan N.; Raj Mittra

2012-01-01

388

One-dimensional transient finite difference model of an operational salinity gradient solar pond  

Science.gov (United States)

This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.

Hicks, Michael C.; Golding, Peter

1992-01-01

389

The Theory and Application of Upwind Finite Difference Fractional Steps Procedure for Seawater Intrusion  

Directory of Open Access Journals (Sweden)

Full Text Available Numerical simulation and theoretical analysis of seawater intrusion is the mathematical basis for modern environmental science. Its mathematical model is the nonlinear coupled system of partial differential equations with initial-boundary problems. For a generic case of a three-dimensional bounded region, two kinds of finite difference fractional steps pro- cedures are put forward. Optimal order estimates in norm are derived for the error in the approximation solution. The present method has been successfully used in predicting the consequences of seawater intrusion and protection projects.

Yirang Yuan

2012-10-01

390

Numerical Solution for a FG Cylinder Problem Using Finite-Difference Method  

Directory of Open Access Journals (Sweden)

Full Text Available A refined finite-difference approach is presented to solve the thermoelastic problem of functionally graded cylinders. Material properties of the present cylinder are assumed to be graded in the radial direction according to a power-law distribution in terms of the volume fractions of the metal and ceramic constituents. The governing second-order differential equations are derived from the motion and the heat-conduction equations. Numerical results for dimensionless temperature, radial displacement, mechanical stresses and electromagnetic stress are distributed along the radial directions. The effects of time parameter and the functionally graded coefficient are investigated.

Daoud S. Mashat

2011-01-01

391

Application of finite difference techniques to the thermal analysis of the cooling of a slag casting  

International Nuclear Information System (INIS)

It has been proposed to dispose of low grade radioactive waste by reducing it, through pyrolysis, to an inert slag. In this analysis, finite difference techniques are used to predict the cooling of a cylindrical slag casting which is initially in the molten state at 1425 C. The casting cools primarily by thermal radiation and the variation of physical properties with temperatures was included. Two mold designs were considered, a stainless steel mold and a stainless-steel mold with a silicon carbide lining. 4 refs

1980-01-01

392

Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates  

Directory of Open Access Journals (Sweden)

Full Text Available In this work, the three-dimensional Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly, by extending the method of Hockney. The Poisson equation is approximated by second-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results.

Alemayehu Shiferaw

2013-11-01

393

Numerical simulation of shock propatation by the finite difference lattice boltzmann method  

International Nuclear Information System (INIS)

The shock process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over a shock thickness which is comparable to the mean free path of the gas molecules involved. The fluid phenomenon is simulated by using Finite Difference Lattice Boltzmann Method(FDLBM). In this research, the new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of shortening in calculation time and stabilizing in simulation operation. The numerical results agree also with the theoretical predictions

2001-11-01

394

Numerical simulation of shock propatation by the finite difference lattice boltzmann method  

Energy Technology Data Exchange (ETDEWEB)

The shock process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over a shock thickness which is comparable to the mean free path of the gas molecules involved. The fluid phenomenon is simulated by using Finite Difference Lattice Boltzmann Method(FDLBM). In this research, the new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of shortening in calculation time and stabilizing in simulation operation. The numerical results agree also with the theoretical predictions.

Kang, Ho Keun; Kim, Jeong Hwan; Lee, Young Ho [Korea Maritime Univ., Busan (Korea, Republic of); Tsutahara, Michihisa [Kobe Univ., Kobe (Japan)

2001-07-01

395

Analysis of a metallic nano-rod polarizer using finite-difference-time-domain method  

CERN Multimedia

The polarization behavior of metallic nano-rods has been analyzed by means of the finite-difference-time-domain method. When the average spacing between the nano-rods is less than a half wavelength, the layer reflects the light polarized parallel to the nano-rods, as in a nano-slit. However, when the spacing is larger than a half wavelength, the metallic surface absorbs the light, polarized perpendicular to the rods, leading to a polarization reversal. Multiple layers of nano-rods can make a polarizer with a high extinction ratio and good transmittance.

Ju, Young-Gu

2010-01-01

396

Stochastic Exponential Integrators for a Finite Element Discretization of SPDEs  

CERN Multimedia

We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of the noise and the approximation of the exponential function by a rational fraction, we introduce a new scheme, designed for finite elements, finite volumes or finite differences space discretization, similar to the schemes in \\cite{Jentzen3,Jentzen4} for spectral methods and \\cite{GTambue} for finite element methods. We use the projection operator, the smoothing effect of the positive definite self-adjoint operator and linear functionals of the noise in Fourier space to obtain higher order approximations. We consider noise that is white in time and either in $H^1$ or $H^2$ in space and give convergence proofs in the mean square $L^{2}$ norm for a diffusion reaction equation and in mean square $ H^{1}$ norm in the presence of an advection term. For the exponential integrator...

Lord, Gabriel J

2010-01-01

397

Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods  

International Nuclear Information System (INIS)

The nonlinear dynamic response of doubly curved shallow shells resting on Winkler-Pasternak elastic foundation has been studied for step and sinusoidal loadings. Dynamic analogues of Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by numerical examples. The shear parameter G of the Pasternak foundation and the stiffness parameter K of the Winkler foundation have been found to have a significant influence on the dynamic response of the shell. It is concluded from the present study that the HDQ-FD methodolgy is a simple, efficient, and accurate method for the nonlinear analysis of doubly curved shallow shells resting on two-parameter elastic foundation

2005-06-01

398

A fast referenceless PRFS-based MR thermometry by phase finite difference  

Science.gov (United States)

Proton resonance frequency shift-based MR thermometry is a promising temperature monitoring approach for thermotherapy but its accuracy is vulnerable to inter-scan motion. Model-based referenceless thermometry has been proposed to address this problem but phase unwrapping is usually needed before the model fitting process. In this paper, a referenceless MR thermometry method using phase finite difference that avoids the time consuming phase unwrapping procedure is proposed. Unlike the previously proposed phase gradient technique, the use of finite difference in the new method reduces the fitting error resulting from the ringing artifacts associated with phase discontinuity in the calculation of the phase gradient image. The new method takes into account the values at the perimeter of the region of interest because of their direct relevance to the extrapolated baseline phase of the region of interest (where temperature increase takes place). In simulation study, in vivo and ex vivo experiments, the new method has a root-mean-square temperature error of 0.35 °C, 1.02 °C and 1.73 °C compared to 0.83 °C, 2.81 °C, and 3.76 °C from the phase gradient method, respectively. The method also demonstrated a slightly higher, albeit small, temperature accuracy than the original referenceless MR thermometry method. The proposed method is computationally efficient (?0.1 s per image), making it very suitable for the real time temperature monitoring.

Zou, Chao; Shen, Huan; He, Mengyue; Tie, Changjun; Chung, Yiu-Cho; Liu, Xin

2013-08-01

399

MasQU: Finite Differences on Masked Irregular Stokes Q,U Grids  

CERN Multimedia

The future detection of B-mode polarization in the CMB is one of the most important outstanding tests of inflationary cosmology. One of the necessary steps for extracting polarization information in the CMB is reducing contamination from so-called 'ambiguous modes' on a masked sky. This can be achieved by utilising derivative operators on the real-space Stokes Q and U parameters. The main result of this paper is the presentation of an algorithm and a software package to perform this procedure on the full sky, i.e. with projects such as the Planck Surveyor and future satellites in mind; in particular, the package can perform finite differences on masked, irregular grids and is applied to a semi-regular spherical pixelisation, the HEALPix grid. The formalism reduces to the known finite difference solutions in the case of a regular grid. We quantify full-sky improvements on the possible bounds of the CMB B-mode signal. We find that in the specific case of E and B-mode separation, there exists a 'pole problem' in...

Bowyer, Jude; Novikov, Dmitri I

2011-01-01

400

A finite difference approach to the infinity Laplace equation and tug-of-war games  

CERN Document Server

We present a modified version of the $\\epsilon$-step tug-of-war game recently introduced by Peres, Schramm, Sheffield, and Wilson. This new tug-of-war game is identical to the original except near the boundary of the domain $\\partial \\Omega$, but its associated value functions are more regular. Using the dynamic programming principle, we show that the value functions satisfy a certain finite difference equation. By studying solutions of this difference equation directly, we are able to adapt techniques from viscosity solution theory to prove a number of new results. The finite difference equation has unique maximal and minimal solutions, which are identified as the value functions for the two tug-of-war players. We demonstrate uniqueness, and hence the existence of a value for the game, in the case that the running payoff function is nonnegative. In the limit $\\epsilon \\to 0$, we obtain the convergence of the value functions to a viscosity solution of the normalized infinity Laplace equation. We also obtain s...

Armstrong, Scott N

2009-01-01

 
 
 
 
401

A fast quasi-explicit finite difference method for simulating electrochemical phenomena  

Energy Technology Data Exchange (ETDEWEB)

A fast quasi-explicit finite difference (FQEFD) method is developed for the simulation of cyclic voltammetry of electrochemical systems comprising coupled heterogeneous and homogeneous kinetics. The heart of the present approach is the DuFort-Frankel algorithm. The simplicity of formulation of code usually associated with explicit finite difference (EFD) methods is retained. The FQEFD approach is particularly effective for dealing with stiff problems which involve very large values of one or more homogeneous rate constants. For certain problems the enhancement in computational speed of the FQEFD method relative to the EFD method can be many orders of magnitude. The accuracy of the method is demonstrated by simulations of cyclic voltammetry of a simple electron transfer, A+e{sup {minus}} {l equilibrium} B, and of a simple electron transfer coupled with a following quasi-reversible second-order homogeneous chemical reaction, 2B{l equilibrium} C. Simulation results are compared to known, accepted solutions. Quick-Basic programs were executed on an IBM PS2-70 with an 80387 coprocessor, a level of computational power that is adequate for simulating many problems of interest.

Feldberg, S.W. (Brookhaven National Lab., Upton, NY (United States))

1990-01-01

402

A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory  

International Nuclear Information System (INIS)

A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

1987-01-01

403

A new mixed method with finite difference and finite element method for neutron diffusion calculation  

International Nuclear Information System (INIS)

A new method for obtaining three-dimensional neutron flux distribution in a reactor has been developed by taking into account the fact that the X-Y planar geometry is generally complex but the geometry along Z-axis is simple. In this method, the finite element method is applied to the X-Y plane calculation and the finite difference method to the Z-axis. For solving a three-dimensional neutron diffusion equation, these two methods are iterated successively until a consistency of the leakage coefficients is attained between the two. The present method is embodied as a computer program FEDM for FACOM M200 computer. With this program, a three-dimensional diffusion calculation was performed for comparing some numerical results with those by a conventional standard computer code ADC. The comparison has shown that they agree well with each other. Computing time required for this problem by the FEDM was shorter than that by the ADC for obtaining same accuracy on the eigenvalue. To indicate usefulness of this method, a demonstration calculation for a reactor with a complex geometry was performed, which was a difficult case to calculate with a conventional finite difference code. (author)

1981-01-01

404

Computational Electromagnetism and Implicit Discrete Exterior Calculus  

CERN Document Server

Implicit discrete exterior calculus technique for Maxwell's equations in time domain is discussed, which provide flexibility in numerical computing Maxwell's equations on manifold. The implicit scheme and discrete exterior calculus can be united to find an unconditional stable approach, which is obtained by properly defining a discrete Hodge star operator. The algorithm has been implemented on Java development plateform.

Xie, Zheng; Ma, Yujie

2009-01-01

405

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio  

Science.gov (United States)

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.

1987-01-01

406

Finite-difference modeling and dispersion analysis of high-frequency love waves for near-surface applications  

Science.gov (United States)

Love-wave propagation has been a topic of interest to crustal, earthquake, and engineering seismologists for many years because it is independent of Poisson's ratio and more sensitive to shear (S)-wave velocity changes and layer thickness changes than are Rayleigh waves. It is well known that Love-wave generation requires the existence of a low S-wave velocity layer in a multilayered earth model. In order to study numerically the propagation of Love waves in a layered earth model and dispersion characteristics for near-surface applications, we simulate high-frequency (>5 Hz) Love waves by the staggered-grid finite-difference (FD) method. The air-earth boundary (the shear stress above the free surface) is treated using the stress-imaging technique. We use a two-layer model to demonstrate the accuracy of the staggered-grid modeling scheme. We also simulate four-layer models including a low-velocity layer (LVL) or a high-velocity layer (HVL) to analyze dispersive energy characteristics for near-surface applications. Results demonstrate that: (1) the staggered-grid FD code and stress-imaging technique are suitable for treating the free-surface boundary conditions for Love-wave modeling, (2) Love-wave inversion should be treated with extra care when a LVL exists because of a lack of LVL information in dispersions aggravating uncertainties in the inversion procedure, and (3) energy of high modes in a low-frequency range is very weak, so that it is difficult to estimate the cutoff frequency accurately, and "mode-crossing" occurs between the second higher and third higher modes when a HVL exists. ?? 2010 Birkh??user / Springer Basel AG.

Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.; Liu, J.

2010-01-01

407

The Finite Difference Time Domain Method for Computing Single-Particle Density Matrix  

CERN Multimedia

The finite difference time domain (FDTD) method for numerical computation of the thermal density matrix of a general single-particle quantum system is presented. The Schrodinger equation transformed to imaginary time t is solved numerically by the FDTD method using a set of initial wave functions at t=0 . By choosing this initial set appropriately, the set of wave functions generated by the FDTD method as a function of t is used to construct the thermal density matrix. The theory, a numerical algorithm, and illustrative examples are given in this paper. The numerical results show that the method accurately determines the density matrix and hence the thermodynamic properties of a single-particle system.

Sudiarta, I Wayan

2007-01-01

408

Finite-Difference Time-Domain Study of Guided Modes in Nano-plasmonic Waveguides  

CERN Multimedia

The finite-difference time-domain (FDTD) method is applied for studying plasmonic waveguide formed by silver nanorods at optical frequencies. The dispersion diagram of periodic structures formed by an infinite number of nanorods is calculated by applying Bloch's periodic boundary condition therefore only one unit-cell is modelled in simulations. The frequency dispersion of silver nanorods is characterised by Drude material model and taken into account in FDTD simulations by a simple differential equation method. The dispersion diagram calculated using the FDTD method is verified by comparing the frequency domain embedding method. The change of dispersion diagram caused by the elliptical inclusion and different number of rows of nanorods is analysed. Wave propagation in the waveguides formed by a finite number (nine) of nanorods is studied and the transmission for different waveguides is calculated and compared with the corresponding dispersion diagrams. The simulation results show that row(s) of nanorods can ...

Zhao, Y; Zhao, Yan; Hao, Yang

2006-01-01

409

Finite-Difference and Pseudospectral Time-Domain Methods Applied to Backwards-Wave Metamaterials  

CERN Document Server

Backwards-wave (BW) materials that have simultaneously negative real parts of their electric permittivity and magnetic permeability can support waves where phase and power propagation occur in opposite directions. These materials were predicted to have many unusual electromagnetic properties, among them amplification of the near-field of a point source, which could lead to the perfect reconstruction of the source field in an image [J. Pendry, Phys. Rev. Lett. 85, 3966 (2000)]. Often systems containing BW materials are simulated using the finite-difference time-domain (FDTD) technique. We show that this technique suffers from a numerical artifact due to its staggered grid that makes its use in simulations involving BW materials problematic. The pseudospectral time-domain (PSTD) technique, on the other hand, uses a collocated grid and is free of this artifact. It is also shown that when modeling the dispersive BW material, the linear frequency approximation method introduces error that affects the frequency of ...

Feise, M W; Bevelacqua, P J; Feise, Michael W.; Schneider, John B.; Bevelacqua, Peter J.

2004-01-01

410

Low-dispersion finite difference methods for acoustic waves in a pipe  

Science.gov (United States)

A new algorithm for computing one-dimensional acoustic waves in a pipe is demonstrated by solving the acoustic equations as an initial-boundary-value problem. Conventional dissipation-free second-order finite difference methods suffer severe phase distortion for grids with less that about ten mesh points per wavelength. Using the signal generation by a piston in a duct as an example, transient acoustic computations are presented using a new compact three-point algorithm which allows about 60 percent fewer mesh points per wavelength. Both pulse and harmonic excitation are considered. Coupling of the acoustic signal with the pipe resonant modes is shown to generate a complex transient wave with rich harmonic content.

Davis, Sanford

1991-01-01

411

Two-dimensional electrons in periodic magnetic fields: Finite-differences method study  

Directory of Open Access Journals (Sweden)

Full Text Available Using the finite-differences method, the electronic structures of two-dimensional electrons are investigated under a periodic magnetic field. To achieve accuracy, the exact profile of the magnetic field is employed in the numerical calculations. The results show that the system exhibits rich band structures, and the width of sub-bands becomes narrower as |ky| increases. In particular, many bound states are formed in the potential wells, and they are localized. Localization analysis confirms that extended, localized, and intermediate states coexist in the system, which is very different from the case without the modulated magnetic field. These results may help us to learn more about two-dimensional electrons in a periodic magnetic field.

X. W. Zhang

2013-07-01

412

Full-wave finite-difference time-domain simulation of electromagnetic cloaking structures  

CERN Multimedia

This paper proposes a radial dependent dispersive finite-difference time-domain method for the modelling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are `invisible' to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being `visible'. It is also demonstrated numerically that the simplified cloak based on high-order transformations can indeed improve the cloaking performance.

Zhao, Yan; Hao, Yang

2008-01-01

413

On one-dimensional stretching functions for finite-difference calculations. [computational fluid dynamics  

Science.gov (United States)

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055

Vinokur, M.

1983-01-01

414

Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations  

International Nuclear Information System (INIS)

The performance of perfectly matched layer (PML) absorbing boundary conditions is studied for finite-difference time-domain (FDTD) specific absorption rate (SAR) assessment, using convolutional PML (CPML) implementation of PML. This is done by investigating the variation of SAR values when the amount of free-space layers between the studied object and PML boundary is varied. Plane-wave exposures of spherical and rectangular objects and a realistic human body model are considered for testing the performance. Also, some results for dipole excitation are included. Results show that no additional free-space layers are needed between the numerical phantom and properly implemented CPML absorbing boundary, and that the numerical uncertainties due to CPML can be made negligibly small

2007-12-07