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Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
- Source :
- Multiscale Modeling & Simulation. 9:686-710
- Publication Year :
- 2011
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2011.
-
Abstract
- 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 $LDL^t$ 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 indefinite 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.<br />Comment: 25 pages
- Subjects :
- Variable coefficient
Helmholtz equation
Preconditioner
Ecological Modeling
Mathematical analysis
65F08, 65N22, 65N80
MathematicsofComputing_NUMERICALANALYSIS
General Physics and Astronomy
General Chemistry
High Frequency Waves
Mathematics::Numerical Analysis
Computer Science Applications
symbols.namesake
Modeling and Simulation
Green's function
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
symbols
Mathematics - Numerical Analysis
Mathematics
Subjects
Details
- ISSN :
- 15403467 and 15403459
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Multiscale Modeling & Simulation
- Accession number :
- edsair.doi.dedup.....7df007dff3424e6fd3140ba5a90609d2