Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
2011 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 9, no 2, 686-710 p.Article in journal (Refereed) Published
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate LDLt factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate the Schur complement matrices of the factorization using moving perfectly matched layers (PMLs) introduced in the interior of the domain. Applying each Schur complement matrix is equivalent to solving a quasi-1D problem with a banded LU factorization in the 2D case and to solving a quasi-2D problem with a multifrontal method in the 3D case. The resulting preconditioner has linear application cost, and the preconditioned iterative solver converges in a number of iterations that is essentially independent of the number of unknowns or the frequency. Numerical results are presented in both two and three dimensions to demonstrate the efficiency of this new preconditioner.
Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2011. Vol. 9, no 2, 686-710 p.
Helmholtz equation; perfectly matched layers; high frequency waves; preconditioners; LDL(t) factorization; Green's function; multifrontal methods; optimal ordering
IdentifiersURN: urn:nbn:se:kth:diva-71917DOI: 10.1137/100804644ISI: 000292291100007OAI: oai:DiVA.org:kth-71917DiVA: diva2:487114
QC 201202172012-01-312012-01-312012-02-17Bibliographically approved