Spectral Simulations of Electromagnetic Wave Scattering

Yang, Baolin; Gottlieb, David; Hesthaven, Jan S.

doi:10.1006/jcph.1997.5686

Cited by 138 publications

(111 citation statements)

References 8 publications

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“…Finally, it may be noted that comparison of similar sets of boundary conditions (characteristic boundary condition, PML, and stretching/filtering) have been made in the context of electromagnetic wave scattering [13,34]. There it was found that PML and stretching/ filtering layers gave similar results, in both cases superior to characteristic-based conditions.…”

Section: Propagation Of a Nearly Linear Acoustic Pulsementioning

confidence: 95%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

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Section: Propagation Of a Nearly Linear Acoustic Pulsementioning

confidence: 95%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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“…On the other hand, guided by the consideration of numerical algorithms, various domain decomposition approaches have been proposed. Since the spectral methods which can delivery strikingly high accuracy are unfortunately quite inflexible to handle complex geometries, recently, the development of the domain decomposition pseudospectral or spectral methods has attracted much attentions [39][40][41][42][43]. A block pseudospectral (BPS) method was successfully developed for one-(1D) and two-dimensional (2D) electromagnetic problems by using overlapping or composite grids to achieve a highly accurate coupling of subdomains [39,40].…”

Section: Introductionmentioning

confidence: 99%

“…Remarkably, innovative ways to appropriately enforce the physical jump conditions at material interfaces are presented by using fictitious points (FPs) [39,40]. At present, multidomain methods [41][42][43] are some of the best available approaches for handling complex geometries in CEM.…”

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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“…Recently, the pseudospectral time-domain (PSTD) method has been developed and successfully applied to solve various problems of practical interest, such as determining the electromagnetic scattering by objects placed in an open space [14][15][16][17][18][19][20][21] and investigating the scattering of two-dimensional (2D) cylinders buried in a half space with a planar [22,23] or an undulating surface [23]. This method has been systematically presented in [24].…”

Section: Introductionmentioning

confidence: 99%

A Monte-Carlo MPSTD Analysis of Scattering From Cylinders Buried Below a Random Periodic Rough Surface

Dai¹,

Liu²,

Xu³

2013

PIER B

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Abstract-The analysis of scattering of objects buried below a random rough surface is of practical interest. In reality, the random rough surface may be of an extensive periodic structure. To deal with this more realistic situation, this paper presents a Monte-Carlo MPSTD numerical technique developed for investigating the scattering of a cylinder buried below a random periodic rough surface. The computation model is formulated in two steps. In the first step, only the random rough surface is considered and the periodic boundary condition (PBC) is enforced at the two ends of a period of the rough surface. Then, in the second step, a cylinder is placed below the random rough surface and the interaction between the buried cylinder and the rough surface is taken into account. In each of the two steps, the fields are computed employing the MPSTD algorithm developed in the authors' previous work. Sample numerical results are presented and validated.

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Spectral Simulations of Electromagnetic Wave Scattering

Cited by 138 publications

References 8 publications

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

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

A Monte-Carlo MPSTD Analysis of Scattering From Cylinders Buried Below a Random Periodic Rough Surface

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