Efficient Solution of Time-Domain Boundary Integral Equations Arising in Sound-Hard Scattering

TL;DR

This paper presents an efficient, parallelized numerical method for solving time-domain boundary integral equations related to sound-hard scattering, demonstrating good scalability and reduced computational time through advanced preconditioning.

Contribution

It introduces a space-time Galerkin method with smooth basis functions, analyzes system matrix structure, and develops effective preconditioning strategies for large-scale parallel computations.

Findings

Good parallel scalability up to 1000 cores

Significant reduction in computational time with algebraic preconditioning

Effective convergence and accuracy in numerical experiments

Abstract

We consider the efficient numerical solution of the three-dimensional wave equation with Neumann boundary conditions via time-domain boundary integral equations. A space-time Galerkin method with $C^\infty$-smooth, compactly supported basis functions in time and piecewise polynomial basis functions in space is employed. We discuss the structure of the system matrix and its efficient parallel assembly. Different preconditioning strategies for the solution of the arising systems with block Hessenberg matrices are proposed and investigated numerically. Furthermore, a C++ implementation parallelized by OpenMP and MPI in shared and distributed memory, respectively, is presented. The code is part of the boundary element library BEM4I. Results of numerical experiments including convergence and scalability tests up to a thousand cores on a cluster are provided. The presented implementation shows good parallel scalability of the system matrix assembly. Moreover, the proposed algebraic preconditioner in combination with the FGMRES solver leads to a significant reduction of the computational time.