Fourier Methods Applicable in the Numerical Solution of Electromagnetic Time-Domain Scattering Problems

This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two spatial dimensions. The proposed methodology relies on convolution quadrature (CQ) schemes and the recently introduced windowed Green function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is used to transform the problem into a finite number of (complex) frequency-domain problems posed, in our case, on the domains containing unbounded penetrable interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method—which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Nyström or boundary element Helmholtz integral equation solvers capable of handling complex wavenumbers with large imaginary part. A high-order Nyström method based on Alpert's quadrature rules is used here. A variety of CQ schemes and numerical examples, including wave propagation in open waveguides as well as scattering from multiple layered media, demonstrate the capabilities of the proposed approach.

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The method of auxiliary sources for two dimensional time domain scattering problems

Trans Black Sea Region Symposium on Applied Electromagnetism ◽

10.1109/aem.1996.873037 ◽

2005 ◽

Cited By ~ 1

Author(s):

R. Jobava ◽

R. Zaridze ◽

D. Karkashadze ◽

G. Bit-Babik ◽

Ph. Shubitidze

Keyword(s):

Time Domain ◽

Two Dimensional ◽

Scattering Problems ◽

Method Of Auxiliary Sources ◽

Time Domain Scattering

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Diffraction theory of frequency- and time-domain scattering by weakly aperiodic truncated thin-wire gratings

Journal of the Optical Society of America A ◽

10.1364/josaa.11.001291 ◽

1994 ◽

Vol 11 (4) ◽

pp. 1291 ◽

Cited By ~ 48

Author(s):

Leopold B. Felsen ◽

Lawrence Carin

Keyword(s):

Time Domain ◽

Diffraction Theory ◽

Thin Wire ◽

Time Domain Scattering ◽

Wire Gratings

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An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-10-2012-0272 ◽

2013 ◽

Vol 33 (1/2) ◽

pp. 116-125

Author(s):

Zhongming Bai ◽

Xikui Ma ◽

Xu Zhuansun ◽

Qi Liu

Keyword(s):

Finite Difference ◽

Numerical Solution ◽

Fourth Order ◽

Time Domain ◽

Fdtd Method ◽

Time Domain Method ◽

Integration Time ◽

Precise Integration ◽

Content Type ◽

Domain Method

Purpose – The purpose of the paper is to introduce a perfectly matched layer (PML) absorber, based on Berenger's split field PML, to the recently proposed low-dispersion precise integration time domain method using a fourth-order accurate finite difference scheme (PITD(4)). Design/methodology/approach – The validity and effectiveness of the PITD(4) method with the inclusion of the PML is investigated through a two-dimensional (2-D) point source radiating example. Findings – Numerical results indicate that the larger time steps remain unchanged in the procedure of the PITD(4) method with the PML, and meanwhile, the PITD(4) method employing the PML is of the same absorbability as that of the finite-difference time-domain (FDTD) method with the PML. In addition, it is also demonstrated that the later time reflection error of the PITD(4) method employing the PML is much lower than that of the FDTD method with the PML. Originality/value – An efficient application of PML in fourth-order precise integration time domain method for the numerical solution of Maxwell's equations.

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