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Sweeping preconditioner for the helmholtz equation: hierarchical matrix representation
Department of Mathematics, The University of Texas at Austin, Austin, USA.
Department of Mathematics, The University of Texas at Austin, Austin, USA.
2011 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 64, no 5, 697-735 p.Article in journal (Refereed) Published
Abstract [en]

The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including very-high-frequency problems. The first central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundary condition. Given this specific order of factorization, the second central idea is to represent the intermediate matrices in the hierarchical matrix framework. In two dimensions, both the construction and the application of the preconditioners are of linear complexity. The generalized minimal residual method (GMRES) solver with the resulting preconditioner converges in an amazingly small number of iterations, which is essentially independent of the number of unknowns. This approach is also extended to the three-dimensional case with some success. Numerical results are provided in both two and three dimensions to demonstrate the efficiency of this new approach.

Place, publisher, year, edition, pages
Wiley&Sons , 2011. Vol. 64, no 5, 697-735 p.
Keyword [en]
DOMAIN DECOMPOSITION METHOD; FAST DIRECT SOLVER; LINEAR-SYSTEMS; MULTIFRONTAL METHOD; 2 DIMENSIONS; SCATTERING; INDEFINITE; ALGORITHM; APPROXIMATION; EXTRAPOLATION
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-72096DOI: 10.1002/cpa.20358ISI: 000287163300003OAI: oai:DiVA.org:kth-72096DiVA: diva2:487185
Note
QC 20120217Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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Engquist, Björn
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CiteExportLink to record
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