Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions

TL;DR

This paper develops adaptive mesh refinement techniques for the wave equation with Neumann boundary conditions, using boundary element methods and a posteriori error estimates to improve computational efficiency and accuracy.

Contribution

It introduces space-time adaptive boundary element methods for the wave equation with Neumann conditions, based on residual-based a posteriori error estimates, which is a novel approach.

Findings

Adaptive mesh refinement improves accuracy in wave simulations.

Numerical experiments demonstrate the effectiveness of the adaptive methods.

The approach enhances computational efficiency for boundary element solutions.

Abstract

This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive versions of a space-time boundary element method are presented, based on a reliable a posteriori error estimate of residual type. Numerical experiments illustrate the performance of the proposed approach.