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An adaptive kernel-split quadrature method for parameter-dependent layer potentials
KTH, Sweden.ORCID iD: 0000-0002-0434-2580
KTH, Sweden.ORCID iD: 0000-0001-7425-8029
Karolinska Institutet, Solna, Sweden.ORCID iD: 0000-0002-4290-1670
2022 (English)In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 48, no 2, article id 12Article in journal (Refereed) Published
Abstract [en]

Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer potentials belonging to the modified Helmholtz, modified biharmonic, and modified Stokes equations. These equations depend on a parameter, denoted alpha, and kernel-split quadrature loses its accuracy rapidly when this parameter grows beyond a certain threshold. This paper describes an algorithm that remedies this problem, using per-target adaptive sampling of the source geometry. The refinement is carried out through recursive bisection, with a carefully selected rule set. This maintains accuracy for a wide range of the parameter alpha, at an increased cost that scales as log alpha. Using this algorithm allows kernel-split quadrature to be both accurate and efficient for a much wider range of problems than previously possible.

Place, publisher, year, edition, pages
Springer Nature , 2022. Vol. 48, no 2, article id 12
Keywords [en]
Integral equations, Partial differential equations, Layer potentials, Modified Helmholtz equation, Modified Stokes equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-64994DOI: 10.1007/s10444-022-09927-5ISI: 000766563600001Scopus ID: 2-s2.0-85126240977OAI: oai:DiVA.org:mdh-64994DiVA, id: diva2:1818742
Available from: 2022-03-25 Created: 2023-12-12Bibliographically approved

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Fryklund, Fredrikaf Klinteberg, LudvigTornberg, Anna-Karin

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