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Article: Nyström method for elastic wave scattering by three-dimensional obstacles

TitleNyström method for elastic wave scattering by three-dimensional obstacles
Authors
KeywordsBoundary Integral Equation
Elastic Wave Scattering
Nyström Method
Issue Date2007
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jcp
Citation
Journal Of Computational Physics, 2007, v. 226 n. 2, p. 1845-1858 How to Cite?
AbstractNyström method is developed to solve for boundary integral equations (BIE's) for elastic wave scattering by three-dimensional obstacles. To generate the matrix equation from a BIE, Nyström method applies a quadrature rule to the integrations of smooth integrands over a discretized element directly and chooses the values of the unknown function at quadrature points as the system's unknowns to be solved. This leads to a simple procedure to form the off-diagonal entries of matrix by simply evaluating the integrands without numerical integrations. For the diagonal or near diagonal entries corresponding to the integrals over a singular or near-singular element where the kernels are singular or near singular, we develop a systematic singularity treatment technique, known as the local correction scheme, based on the linear approximation of elements. The scheme differs from the singularity regularization or subtraction technique used in the boundary element method (BEM). It applies the series expansion of scalar Green's function to the kernels and derives analytical solutions for the strongly singular integrals under the Cauchy principal value like (CPV-like) sense. Since the approach avoids the need for reformulating the BIE for singularity removal in BEM and solves for the Somigliana's equation directly, it is easy to implement and efficient in calculation. Numerical examples are used to demonstrate its robustness. © 2007 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/182734
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.accessioned2013-05-02T05:16:38Z-
dc.date.available2013-05-02T05:16:38Z-
dc.date.issued2007en_US
dc.identifier.citationJournal Of Computational Physics, 2007, v. 226 n. 2, p. 1845-1858en_US
dc.identifier.issn0021-9991en_US
dc.identifier.urihttp://hdl.handle.net/10722/182734-
dc.description.abstractNyström method is developed to solve for boundary integral equations (BIE's) for elastic wave scattering by three-dimensional obstacles. To generate the matrix equation from a BIE, Nyström method applies a quadrature rule to the integrations of smooth integrands over a discretized element directly and chooses the values of the unknown function at quadrature points as the system's unknowns to be solved. This leads to a simple procedure to form the off-diagonal entries of matrix by simply evaluating the integrands without numerical integrations. For the diagonal or near diagonal entries corresponding to the integrals over a singular or near-singular element where the kernels are singular or near singular, we develop a systematic singularity treatment technique, known as the local correction scheme, based on the linear approximation of elements. The scheme differs from the singularity regularization or subtraction technique used in the boundary element method (BEM). It applies the series expansion of scalar Green's function to the kernels and derives analytical solutions for the strongly singular integrals under the Cauchy principal value like (CPV-like) sense. Since the approach avoids the need for reformulating the BIE for singularity removal in BEM and solves for the Somigliana's equation directly, it is easy to implement and efficient in calculation. Numerical examples are used to demonstrate its robustness. © 2007 Elsevier Inc. All rights reserved.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.subjectNyström Methoden_US
dc.titleNyström method for elastic wave scattering by three-dimensional obstaclesen_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.2007.06.013en_US
dc.identifier.scopuseid_2-s2.0-34548674928en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-34548674928&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume226en_US
dc.identifier.issue2en_US
dc.identifier.spage1845en_US
dc.identifier.epage1858en_US
dc.identifier.isiWOS:000250209700032-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridTong, MS=11839685700en_US
dc.identifier.scopusauthoridChew, WC=36014436300en_US

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