A space-time adaptive boundary element method for the wave equation

TL;DR

This paper develops a space-time adaptive boundary element method for wave equations, enhancing mesh refinement techniques to improve accuracy and convergence in acoustic scattering problems.

Contribution

It introduces a novel adaptive boundary element procedure with residual-based error indicators for wave equations, addressing algorithmic challenges and demonstrating improved convergence.

Findings

Enhanced convergence rates observed in numerical experiments.

Effective local tensor-product mesh refinements.

Improved performance for problems with singularities.

Abstract

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for acoustic soft-scattering problems with local tensor-product refinements of the space-time mesh. We discuss the algorithmic challenges and investigate the proposed method in numerical experiments. In particular, we study the performance and improved convergence rates with respect to the energy norm for problems dominated by spatial, temporal or traveling singularities of the solution. The efficiency of the considered rigorous and heuristic a posteriori error indicators is discussed.