On a preconditioner for time domain boundary element methods

TL;DR

This paper introduces a new time stepping scheme for space-time boundary element methods that acts as an effective preconditioner or solver, improving efficiency and stability in wave scattering problems.

Contribution

A novel extrapolation-based time stepping scheme that enhances stability, reduces GMRES iterations, and can serve as a preconditioner or standalone solver for wave boundary element methods.

Findings

Proves stability and exactness with increasing degrees of freedom.

Reduces GMRES iterations significantly for screen problems.

Explores limitations for non-polynomial approximation spaces.

Abstract

We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of freedom and can be used either as a preconditioner, or as an efficient standalone solver for scattering problems with smooth solutions. It also significantly reduces the number of GMRES iterations for screen problems, with less regularity, and we explore its limitations for enriched methods based on non-polynomial approximation spaces.