Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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TL;DR: In this paper, a finite-difference approach was proposed to obtain a unique set of equations for dielectric optical waveguides with stepped refractive index profiles, where the boundary conditions were formulated and included in the finite difference scheme.
Abstract: An important class of dielectric optical waveguides has stepped refractive index profiles. For these waveguides we present a new finite-difference approach free of spurious modes. The coupled difference equations are formulated in terms of the transverse magnetic field components H/sub x/ and H/sub y/. We show how the boundary conditions can be formulated and included in the finite difference scheme to obtain a unique set of equations. For a step-index fiber a comparison of the numerical results with the analytical solution shows that the relative error in the propagation constant is as low as 4.4/spl times/10/sup /spl minus/7/ for an index difference of 7.3%. For a rib waveguide, we compare our results with previously published data based on other methods. Field plots of the dominant and the weak transverse field components of the magnetic field for the fundamental mode of a buried rib waveguide are also given. >
155 citations
TL;DR: In this article, an extension to 1D relativistic hydrodynamics of the piecewise parabolic method (PPM) of Colella and Woodward using an exact Riemann solver is presented.
155 citations
TL;DR: In this article, the authors present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes, which consists of a combination of well-known numerical procedures such as Sturm sequences, the bisection method, Newton's and Brents methods, Richardson extrapolation, and inverse iteration.
Abstract: The method of normal modes is frequently used to solve acoustic propagation problems in stratified oceans. The propagation numbers for the modes are the eigenvalues of the boundary value problem to determine the depth dependent normal modes. Errors in the numerical determination of these eigenvalues appear as phase shifts in the range dependence of the acoustic field. Such errors can severely degrade the accuracy of the normal mode representation, particularly at long ranges. In this paper we present a fast finite difference method to accurately determine these propagation numbers and the corresponding normal modes. It consists of a combination of well‐known numerical procedures such as Sturm sequences, the bisection method, Newton’s and Brent’s methods, Richardson extrapolation, and inverse iteration. We also introduce a modified Richardson extrapolation procedure that substantially increases the speed and accuracy of the computation.
154 citations
TL;DR: In this article, the numerical solution of the one-dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, is reported. And the performance of the proposed algorithm, considering a test problem, is investigated.
Abstract: Certain problems arising in engineering are modeled by nonstandard parabolic initial-boundary value problems in one space variable, which involve an integral term over the spatial domain of a function of the desired solution. Hence, in the past few years interest has substantially increased in the solutions of these problems. As a result numerous research papers have also been devoted to the subject. Although considerable amount of work has been done in the past, there is still a lack of a completely satisfactory computational scheme. Also, there are some cases that have not been studied numerically yet. In the current article several approaches for the numerical solution of the one-dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, are reported. Finite difference methods have been proposed for the numerical solution of the new nonclassic boundary value problem. To investigate the performance of the proposed algorithm, we consider solving a test problem. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
154 citations
TL;DR: In this article, surface impedance boundary conditions (SIBC) are introduced into the FDTD method to reduce the solution space and produce significant computational savings, and an efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented.
Abstract: Surface impedance concepts are introduced into the finite-difference time-domain (FDTD) method. Lossy conductors are replaced by surface impedance boundary conditions (SIBC), reducing the solution space and producing significant computational savings. Specifically, a SIBC is developed to replace a lossy dielectric half-space. An efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented. Finally, three problems are studied to illustrate the accuracy of the FDTD-SIBC formulation: a plane wave incident on a lossy dielectric half-space, a line current over a lossy dielectric half-space, and wave propagation in a parallel-plate waveguide with lossy walls. >
154 citations