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

TL;DR

This paper introduces a highly efficient parallel solver for electromagnetic integral equations using the Galerkin method, significantly reducing memory usage and enhancing scalability for complex geophysical problems.

Contribution

The novel solver combines low memory consumption, accurate matrix coefficient computation, and high parallelism, advancing computational electromagnetics capabilities.

Findings

Memory usage is 8 times lower than similar algorithms.

The solver achieves high accuracy and stability.

Excellent scalability demonstrated on various hardware platforms.

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 the convergent numerical solution. The main features include: (i) the memory usage is 8 times lower, compared to analogous IE based algorithms, without additional restriction on the background media; (ii) accurate and stable method to compute matrix coefficients corresponding to the IE; (iii) high degree of parallelism. The solver's computational efficiency is shown on a problem of magnetotelluric sounding of the high conductivity contrast media. A good agreement with the results obtained with the second order finite element method is demonstrated. Due to effective approach to parallelization and distributed data storage the program exhibits perfect scalability on different hardware platforms.