Integral Equation Methods for Electrostatics, Acoustics, and Electromagnetics in Smoothly Varying, Anisotropic Media

[EN] 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.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.Imbert-Gérard, L.; Vico Bondía, F.; Greengard, L.; Ferrando Bataller, M. (2019). Integral Equation Methods for Electrostatics, Acoustics, and Electromagnetics in Smoothly Varying, Anisotropic Media. SIAM Journal on Numerical Analysis. 57(3):1020-1035. https://doi.org/10.1137/18M1187039S1020103557