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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)152-174
Number of pages23
JournalJournal of Computational Physics
Volume390
DOIs
StatePublished - Aug 1 2019

Fingerprint

Electromagnetic Scattering
electromagnetic scattering
fast Fourier transformations
Fast Fourier transforms
Integral equations
integral equations
Integral Equations
Invert
Scattering
recursive functions
Recursion Formula
Physical Modeling
Gaussian Quadrature
Adaptive Mesh
Materials Science
Geometry
Metamaterials
Separation of Variables
Maxwell equations
Materials science

Keywords

  • Body of revolution
  • Dielectric media
  • Electromagnetics
  • Fast Fourier transform
  • Müller's integral equation
  • Penetrable media

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects. / Lai, Jun; O'Neil, Michael.

In: Journal of Computational Physics, Vol. 390, 01.08.2019, p. 152-174.

Research output: Contribution to journalArticle

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