TY - JOUR
T1 - Integral equation methods for electrostatics, acoustics, and electromagnetics in smoothly varying, anisotropic media
AU - Imbert-Gerard, Lise Marie
AU - Vico, Felipe
AU - Greengard, Leslie
AU - Ferrando, Miguel
N1 - Funding Information:
∗Received by the editors May 14, 2018; accepted for publication (in revised form) March 4, 2019; published electronically May 7, 2019. http://www.siam.org/journals/sinum/57-3/M118703.html Funding: The work of the authors was partially supported by the Spanish Ministry of Science and Innovation under project TEC2016-78028-C3-3-P and the U.S. Department of Energy under grant DE-FG02-86ER53223. †Department of Mathematics, University of Maryland, College Park, MD 20742 (lmig@math. umd.edu). ‡Instituto de Telecomunicaciones y Aplicaciones Multimedia (ITEAM), Universidad Politècnica de València, 46022 València, Spain ([email protected], [email protected]). §Courant Institute, New York University, and Flatiron Institute, Simons Foundation, New York, NY 10012 ([email protected]).
Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics
PY - 2019
Y1 - 2019
N2 - We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic, or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [F. Vico, L. Greengard, M. Ferrando, J. Comput. Phys., 323 (2016), pp. 191–203] to discretize and apply the relevant integral operators.
AB - We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic, or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [F. Vico, L. Greengard, M. Ferrando, J. Comput. Phys., 323 (2016), pp. 191–203] to discretize and apply the relevant integral operators.
KW - Acoustics
KW - Anisotropic media
KW - Electromagnetics
KW - Electrostatics
KW - Inhomogeneous media
KW - Integral equations
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U2 - 10.1137/18M1187039
DO - 10.1137/18M1187039
M3 - Article
AN - SCOPUS:85069808123
SN - 0036-1429
VL - 57
SP - 1020
EP - 1035
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 3
ER -