Premium
Efficient solution of time‐domain boundary integral equations arising in sound‐hard scattering
Author(s) -
Veit Alexander,
Merta Michal,
Zapletal Jan,
Lukáš Dalibor
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5187
Subject(s) - preconditioner , solver , basis function , domain decomposition methods , piecewise , galerkin method , boundary element method , mathematics , boundary (topology) , matrix (chemical analysis) , generalized minimal residual method , boundary value problem , finite element method , computational science , computer science , mathematical analysis , linear system , mathematical optimization , physics , materials science , composite material , thermodynamics
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.