A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

Charles L. Epstein; Leslie Greengard; Michael O'Neil

doi:10.1016/j.jcp.2019.02.041

A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

Charles L. Epstein, Leslie Greengard, Michael O'Neil

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω→0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

Original language	English (US)
Pages (from-to)	205-229
Number of pages	25
Journal	Journal of Computational Physics
Volume	387
DOIs	https://doi.org/10.1016/j.jcp.2019.02.041
State	Published - Jun 15 2019

Keywords

Body of revolution
Generalized Debye sources
Maxwell's equations
Penetrable media
Perfect electric conductor
Second-kind integral equations

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2019.02.041

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title = "A high-order wideband direct solver for electromagnetic scattering from bodies of revolution",

abstract = "The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω→0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nystr{\"o}m discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.",

keywords = "Body of revolution, Generalized Debye sources, Maxwell's equations, Penetrable media, Perfect electric conductor, Second-kind integral equations",

author = "Epstein, {Charles L.} and Leslie Greengard and Michael O'Neil",

note = "Funding Information: Research supported in part by NSF award DMS-1507396.Research supported in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program award FA9550-10-1-0180.Research supported in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program award FA9550-10-1-0180 and the Office of Naval Research under awards N00014-17-1-2059 and N00014-17-1-2451. Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.jcp.2019.02.041",

language = "English (US)",

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AU - Epstein, Charles L.

AU - Greengard, Leslie

AU - O'Neil, Michael

N1 - Funding Information: Research supported in part by NSF award DMS-1507396.Research supported in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program award FA9550-10-1-0180.Research supported in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR under NSSEFF Program award FA9550-10-1-0180 and the Office of Naval Research under awards N00014-17-1-2059 and N00014-17-1-2451. Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω→0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

AB - The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric conductors and dielectric bodies. Furthermore, these representations, and resulting integral equations, are fully stable in the static limit as ω→0 in multiply connected geometries. In this paper, we present the first high-order accurate solver based on this representation for bodies of revolution. The resulting solver uses a Nyström discretization of a one-dimensional generating curve and high-order integral equation methods for applying and inverting surface differentials. The accuracy and speed of the solvers are demonstrated in several numerical examples.

KW - Body of revolution

KW - Generalized Debye sources

KW - Maxwell's equations

KW - Penetrable media

KW - Perfect electric conductor

KW - Second-kind integral equations

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

A high-order wideband direct solver for electromagnetic scattering from bodies of revolution

Abstract

Keywords

ASJC Scopus subject areas

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