Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure

Mohammadian, A.H.; Shankar, Vijaya; Hall, William J.

doi:10.1016/0010-4655(91)90199-u

Cited by 130 publications

(65 citation statements)

References 32 publications

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“…Therefore, with the growing need for solving geometrically complex electromagnetic problems, the development of flexible time-domain Maxwell equation solvers on advanced grids has received considerable interest in the literature. Guided by the consideration of numerical grids, numerous finite volume time-domain methods [28][29][30] and finite element time-domain methods [31][32][33][34] have been put forward to systematically handle geometrically complex problems in CEM, since the most flexible grid, the unstructured grid, is best adapted to the finite volume and finite element approaches. Many vector elements, such as Nedelec elements [31], Whitney forms [35,36], and curl/div conforming vector elements [37] are constructed to provide a discrete analog to the continuous vector algebra and to enforce only minimal continuity across element boundaries.…”

Section: Introductionmentioning

confidence: 99%

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

199

164

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This paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one (1D) and two spatial dimensions (2D). By making use of fictitious points, systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 in 1D and 2D are achieved. Detailed stability analyses are presented for the present approach to examine the up limit in constructing embedded FDTD methods. As natural generalizations of the high-order FDTD schemes, the proposed derivative matching methods automatically reduce to the standard FDTD schemes when the material interfaces are absent. An interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code. Another feature of the present approach is that it can be robustly implemented with other high accuracy time-domain approaches, such as the multiresolution time-domain (MRTD) method and the local spectral time-domain (LSTD) method, to cope 1 with material interfaces. Numerical experiments on both 1D and 2D problems are carried out to test the convergence, examine the stability, access the efficiency, and explore the limitation of the proposed methods. It is found that operating at their best capacity, the proposed high order schemes are at least a million times more efficient than their fourth order versions in both 1D and 2D. Therefore, it is believed that the proposed hierarchical derivative matching methods are highly accurate, efficient, and robust for CEM.

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Section: Introductionmentioning

confidence: 99%

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Zhao

Wang

2004

Journal of Computational Physics

199

164

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“…As the basis functions N e and N h are not required to be continuous across the interface between two adjacent subdomains, a nonconforming mesh can be used between subdomains. The Riemann solver [17][18][19] is used here to calculate the above numerical fluxes. Take the i-th subdomain as the local subdomain, and assume that it is adjacent to the j-th subdomain.…”

Section: Nonlinear Dg-fetd Formulationmentioning

confidence: 99%

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

Li¹,

Zhu²,

Chen³

2017

PIER M

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Abstract-A nonlinear hybrid FDTD/FETD technique based on the parametric quadratic programming method is developed for Maxwell's equations with nonlinear media. The proposed technique allows nonconforming meshes between nonlinear FETD and linear FDTD subdomains. The coarser structured cells of FDTD are used in regular, large and linear media, whereas smaller unstructured elements of FETD based on the parametric quadratic programming method are used to simulate complicated structures with nonlinear media. This hybrid technique is particularly suitable for structures with small nonlinear regions in an otherwise linear medium. Numerical results demonstrate the validity of the proposed method.

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“…Both packages are routinely used on Windows, OS X, and Linux. [20]. b) shows the Python code used to instruct the solver.…”

Section: Run-time Code Generationmentioning

confidence: 99%

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

Klöckner

Warburton

Hesthaven

2013

Lecture Notes in Earth System Sciences

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Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without compromising simulation stability. In a recent publication, we have shown that DG methods also adapt readily to execution on modern, massively parallel graphics processors (GPUs). A number of qualities of the method contribute to this suitability, reaching from locality of reference, through regularity of access patterns, to high arithmetic intensity. In this article, we illuminate a few of the more practical aspects of bringing DG onto a GPU, including the use of a Python-based metaprogramming infrastructure that was created specifically to support DG, but has found many uses across all disciplines of computational science. IntroductionDiscontinuous Galerkin methods [5,10,17,24] are, at first glance, a rather curious combination of ideas from Finite-Volume and Spectral Element methods. Up close, they are very much high-order methods by design. But instead of perpetuating the order increase like conventional global methods, at a certain level of detail, they switch over to a decomposition into computational elements and couple these el-

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Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure

Cited by 130 publications

References 32 publications

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

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