Integral equation methods for electrostatics, acoustics and electromagnetics in smoothly varying, anisotropic media
This work provides a unified framework for solving scattering problems in complex media, which is important for computational electromagnetics and acoustics, but the approach is incremental as it modifies classical formulations.
The paper presents well-conditioned integral equation methods for solving electrostatic, acoustic, and electromagnetic scattering problems in anisotropic, inhomogeneous media, demonstrating efficient iterative solutions with FFT-based discretization.
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 [1] to discretize and apply the relevant integral operators.