High-order corrected trapezoidal rules for a class of singular integrals

We present a family of high-order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of increasing smoothness. The quadratures are based on the trapezoida...

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Bibliographic Details
Published in:Advances in computational mathematics 2023-08, Vol.49 (4), Article 60
Main Authors: Izzo, Federico, Runborg, Olof, Tsai, Richard
Format: Article
Language:English
Subjects:
Boundary integral formulations
Closest point projection
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Integrals
Level set methods
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nodes
Quadratures
Series expansion
Singular integrals
Singularities
Smoothness
Taylor series
Trapezoidal rules
Visualization
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Summary:We present a family of high-order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of increasing smoothness. The quadratures are based on the trapezoidal rule, with the quadrature weights for Cartesian nodes close to the singularity judiciously corrected based on the expansion. High-order accuracy can be achieved by utilizing a sufficient number of correction nodes around the singularity to approximate the terms in the series expansion. The derived quadratures are applied to the implicit boundary integral formulation of surface integrals involving the Laplace layer kernels.
ISSN:1019-7168
1572-9044
1572-9044
DOI:10.1007/s10444-023-10060-0