Efficient solution of time‐domain boundary integral equations arising in sound‐hard scattering. (12th January 2016)

• Record Type: Journal Article
• Authors: Veit, Alexander; Merta, Michal; Zapletal, Jan; Lukáš, Dalibor
• Is Part Of: International journal for numerical methods in engineering. Volume 107:Number 5(2016)
• Page Start: 430
• Page End: 449
• Publication Date: 2016-01-12
• Subjects: variational methods -- wave equation -- boundary element method -- time domain -- retarded potential integral equation; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5187
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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 ∞ ‐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. Copyright © 2015 John Wiley & Sons, Ltd.