High-Performance Parallel Solver for Integral Equations of Electromagnetics Based on Galerkin Method

Abstract

A new parallel solver for the volumetric integral equations (IE) of electrodynamics is presented. The solver is based on the Galerkin method, which ensures convergent numerical solution. The main features include: (i) memory usage eight times lower compared with analogous IE-based algorithms, without additional restrictions on the background media; (ii) accurate and stable method to compute matrix coefficients corresponding to the IE; and (iii) high degree of parallelism. The solver’s computational efficiency is demonstrated on a problem of magnetotelluric sounding of media with large conductivity contrast, revealing good agreement with results obtained using the second-order finite-element method. Due to the effective approach to parallelization and distributed data storage, the program exhibits perfect scalability on different hardware platforms.