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Sweeping preconditioner for 3D Helmholtz equation
Department of Mathematics, The University of Texas at Austin, Austin, USA.
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: Society of Exploration Geophysicists. Expanded Abstracts with Biographies, ISSN 1052-3812, Vol. 30, no 1, 3158-3163 p.Article in journal (Refereed) Published
Abstract [en]

TheHelmholtz equation describes wave propagation in the frequency domain and,as such, can be used for seismic imaging and fullwaveform inversion. We present two novel preconditioners for the efficientsolution of the Helmholtz equation in three dimensions. Both methodsfollow the general structure of constructing an approximate LDLt factorizationby eliminating the unknowns layer by layer starting from anabsorbing layer or boundary condition. In the first approach, werepresent the Schur complement matrices of the factorization in thehierarchical matrix framework. In the second approach, applying each Schurcomplement matrix is equivalent to solving a quasi-2D problem withthe multifrontal method. These preconditioners have linear application cost, andthe preconditioned iterative solvers converge in a number of iterationsthat is essentially independent of the number of unknowns orthe frequency. Numerical results on realistic 3D seismic models toconfirm the efficiency of these methods.

Place, publisher, year, edition, pages
Society of Exploration Geophysicists , 2011. Vol. 30, no 1, 3158-3163 p.
Keyword [en]
3D; Frequency-domain; Full waveform inversion; Wave equation; Wave propagation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-72025DOI: 10.1190/1.3627851Scopus ID: 2-s2.0-84857565162OAI: oai:DiVA.org:kth-72025DiVA: diva2:487171
Note
QC 20120217Available from: 2012-01-31 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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  • de-DE
  • en-GB
  • en-US
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  • nn-NB
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  • Other locale
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Output format
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