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

2025/08/17 by Aimi, Alessandra, Di Credico, Giulia, Gimperlein, Heiko +1 · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.12332

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.

Citations

• A space-time adaptive boundary element method for the wave equation
• Stable least-squares space-time boundary element methods for the wave equation
• Asymptotically constant-free and polynomial-degree-robust a posteriori estimates for space discretizations of the wave equation
• A new approach to space-time boundary integral equations for the wave equation
• Efficient Solution of Time-Domain Boundary Integral Equations Arising in Sound-Hard Scattering
• A fully discrete Calderon Calculus for the two-dimensional elastic wave equation
• Adaptive Time Discretization for Retarded Potentials
• Damped energy-norm a posteriori error estimates for fully discrete approximations of the wave equation using C2-reconstructions with the leapfrog scheme

Cited by

• A space-time adaptive boundary element method for the wave equation
• A posteriori error estimates and space-adaptive mesh refinements for time-dependent scattering problems

Related

• A space-time adaptive boundary element method for the wave equation
• A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
• A new approach to space-time boundary integral equations for the wave equation
• Stable least-squares space-time boundary element methods for the wave equation
• Adaptive FEM with explicit time integration for the wave equation