A parallel fast multipole method for a space-time boundary element method for the heat equation

TL;DR

This paper introduces a parallel fast multipole method tailored for a space-time boundary element approach to the heat equation, achieving high efficiency through innovative parallelization and vectorization techniques.

Contribution

It presents a novel parallelization strategy exploiting temporal structure, combining distributed, task-based, and SIMD parallelism for the heat equation boundary element method.

Findings

High parallel efficiency observed in numerical tests.

Effective exploitation of temporal structure for parallelization.

Combines distributed, shared memory, and SIMD parallelism.

Abstract

We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an efficient distributed parallelization with respect to time and with a one-directional communication pattern. On top, we apply a task-based shared memory parallelization and SIMD vectorization. In the numerical tests we observe high efficiencies of our parallelization approach.