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Article: Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects

TitleMultilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects
Authors
KeywordsBoundary Integral Equation
Elastic Wave Scattering
Multilevel Fast Multipole Algorithm
Issue Date2009
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jcp
Citation
Journal Of Computational Physics, 2009, v. 228 n. 3, p. 921-932 How to Cite?
AbstractMultilevel fast multipole algorithm (MLFMA) is developed for solving elastic wave scattering by large three-dimensional (3D) objects. Since the governing set of boundary integral equations (BIE) for the problem includes both compressional and shear waves with different wave numbers in one medium, the double-tree structure for each medium is used in the MLFMA implementation. When both the object and surrounding media are elastic, four wave numbers in total and thus four FMA trees are involved. We employ Nyström method to discretize the BIE and generate the corresponding matrix equation. The MLFMA is used to accelerate the solution process by reducing the complexity of matrix-vector product from O (N2) to O (N log N) in iterative solvers. The multiple-tree structure differs from the single-tree frame in electromagnetics (EM) and acoustics, and greatly complicates the MLFMA implementation due to the different definitions for well-separated groups in different FMA trees. Our Nyström method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms. This feature is kept in the MLFMA by seeking the common near patches in different FMA trees and treating the involved near terms synergistically. Due to the high cost of the multiple-tree structure, our numerical examples show that we can only solve the elastic wave scattering problems with 0.3-0.4 millions of unknowns on our Dell Precision 690 workstation using one core. © 2008.
Persistent Identifierhttp://hdl.handle.net/10722/182757
ISSN
2015 Impact Factor: 2.556
2015 SCImago Journal Rankings: 2.167
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTong, MSen_US
dc.contributor.authorChew, WCen_US
dc.date.accessioned2013-05-02T05:16:44Z-
dc.date.available2013-05-02T05:16:44Z-
dc.date.issued2009en_US
dc.identifier.citationJournal Of Computational Physics, 2009, v. 228 n. 3, p. 921-932en_US
dc.identifier.issn0021-9991en_US
dc.identifier.urihttp://hdl.handle.net/10722/182757-
dc.description.abstractMultilevel fast multipole algorithm (MLFMA) is developed for solving elastic wave scattering by large three-dimensional (3D) objects. Since the governing set of boundary integral equations (BIE) for the problem includes both compressional and shear waves with different wave numbers in one medium, the double-tree structure for each medium is used in the MLFMA implementation. When both the object and surrounding media are elastic, four wave numbers in total and thus four FMA trees are involved. We employ Nyström method to discretize the BIE and generate the corresponding matrix equation. The MLFMA is used to accelerate the solution process by reducing the complexity of matrix-vector product from O (N2) to O (N log N) in iterative solvers. The multiple-tree structure differs from the single-tree frame in electromagnetics (EM) and acoustics, and greatly complicates the MLFMA implementation due to the different definitions for well-separated groups in different FMA trees. Our Nyström method has made use of the cancellation of leading terms in the series expansion of integral kernels to handle hyper singularities in near terms. This feature is kept in the MLFMA by seeking the common near patches in different FMA trees and treating the involved near terms synergistically. Due to the high cost of the multiple-tree structure, our numerical examples show that we can only solve the elastic wave scattering problems with 0.3-0.4 millions of unknowns on our Dell Precision 690 workstation using one core. © 2008.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jcpen_US
dc.relation.ispartofJournal of Computational Physicsen_US
dc.subjectBoundary Integral Equationen_US
dc.subjectElastic Wave Scatteringen_US
dc.subjectMultilevel Fast Multipole Algorithmen_US
dc.titleMultilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objectsen_US
dc.typeArticleen_US
dc.identifier.emailChew, WC: wcchew@hku.hken_US
dc.identifier.authorityChew, WC=rp00656en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.jcp.2008.10.003en_US
dc.identifier.scopuseid_2-s2.0-57649092469en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-57649092469&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume228en_US
dc.identifier.issue3en_US
dc.identifier.spage921en_US
dc.identifier.epage932en_US
dc.identifier.isiWOS:000262552500016-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridTong, MS=11839685700en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US

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