TY - JOUR

T1 - An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects

AU - Lai, Jun

AU - O'Neil, Michael

N1 - Funding Information:
Research was supported in part by the Funds for Creative Research Groups of NSFC (No. 11621101), the Major Research Plan of NSFC (No. 91630309), NSFC grant No. 11871427 and The Fundamental Research Funds for the Central Universities.Research was supported in part by the Office of Naval Research under award numbers #N00014-17-1-2059 and #N00014-17-1-2451.
Publisher Copyright:
© 2019 Elsevier Inc.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

AB - Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

KW - Body of revolution

KW - Dielectric media

KW - Electromagnetics

KW - Fast Fourier transform

KW - Müller's integral equation

KW - Penetrable media

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U2 - 10.1016/j.jcp.2019.04.005

DO - 10.1016/j.jcp.2019.04.005

M3 - Article

AN - SCOPUS:85064327913

SN - 0021-9991

VL - 390

SP - 152

EP - 174

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -