Electromagnetic integral equations requiring small numbers of Krylov-subspace iterations

Integral equations requiring small numbers of Krylov-subspace iterations for two-dimensional penetrable scattering problems

This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations, which, as is established in this paper, are uniquely solvable Fredholm equations of the second kind, result from representations of fields as combinations of sin...

Fast, High-Order, Well-Conditioned Algorithms for the Solution of Three-Dimensional Acoustic and Electromagnetic Scattering Problems

We present a novel computational methodology based on Nyström discretizations to produce fast and very accurate solutions of acoustic and electromagnetic problems in small numbers of Krylov-subspace iterative solvers. At the heart of our approach are integral equation formulations that exhibit excellent spectral properties. In the case of scattering from perfectly conducting structures, and jus...

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

Fast Preconditioned Krylov Methods for Boundary Integral Equations in Electromagnetic Scattering

Well conditioned boundary integral equations for two-dimensional sound-hard scattering problems in domains with corners

We present several well-posed, well-conditioned integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We call these integral equations Direct Regularized Combined Field Integral Equations (DCFIE-R) formulations because (1) they consist of combinations of direct boundary integral equations of the ...