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A local target specific quadrature by expansion method for evaluation of layer potentials in 3D
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 365-392Article in journal (Refereed) Published
Abstract [en]

Accurate evaluation of layer potentials is crucial when boundary integral equation methods are used to solve partial differential equations. Quadrature by expansion (QBX) is a recently introduced method that can offer high accuracy for singular and nearly singular integrals, using truncated expansions to locally represent the potential. The QBX method is typically based on a spherical harmonics expansion which when truncated at order p has O(p2) terms. This expansion can equivalently be written with p terms, however paying the price that the expansion coefficients will depend on the evaluation/target point. Based on this observation, we develop a target specific QBX method, and apply it to Laplace's equation on multiply-connected domains. The method is local in that the QBX expansions only involve information from a neighborhood of the target point. An analysis of the truncation error in the QBX expansions is presented, practical parameter choices are discussed and the method is validated and tested on various problems.

Place, publisher, year, edition, pages
Academic Press, 2018. Vol. 364, p. 365-392
Keywords [en]
Exterior Dirichlet problem, Integral equations, Layer potentials, Multiply-connected domain, Quadrature by expansion, Spherical harmonics expansions
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-227521DOI: 10.1016/j.jcp.2018.03.006ISI: 000432481000017Scopus ID: 2-s2.0-85044166752OAI: oai:DiVA.org:kth-227521DiVA, id: diva2:1205921
Funder
Knut and Alice Wallenberg Foundation, KAW2014.0338Göran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish e‐Science Research Center
Note

QC 20180515

Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-06-13Bibliographically approved

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Tornberg, Anna-Karin

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  • apa
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