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

Integral Equation Methods in Electromagnetic Scattering from Anisotropic Media

We investigate scattering of time-harmonic electromagnetic waves by an anisotropic inhomogeneous medium. The problem is equivalently transformed into a system of strongly singular integral equations. Uniqueness and existence of a solution is shown and we examine the regularity of the solution by means of integral equations. We also prove the analyticity of the scattered eld with respect to the ...

Electrostatics of Anisotropic Inclusions in Anisotropic Media

There are many ways to solve potential problems for anisotropic mixtures. The nite element method is a popular choice with great exibility that gives the solution in the entire computational domain. EEective medium approximation is a simpler option that only estimates eeective properties. Interface integral equation methods is a third class of methods that has been studied for a long time, but ...

A Differential Forms Approach to Electromagnetics in Anisotropic Media

Fast integral equation solvers on Graphics Processing Units for Electromagnetics

This paper presents a comprehensive survey on current status of integral equation solvers implemented on parallel computing systems accelerated by graphics processing units (GPUs) and proposes several key points for efficiently utilizing this type of fundamentally different processors to accelerate several categories of algorithms used by today’s integral equation solvers. Three spatial interpo...

Boundary Integral Methods in Low Frequency Acoustics

Abstract This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its relations to the interior eigenvalue value problems of the Laplacian. Based on the integral representations, we study the asymptotic behaviors of the solutions to the bound...