COMPUTING SINGULAR AND NEAR-SINGULAR INTEGRALS OVER CURVED BOUNDARY ELEMENTS: THE STRONGLY SINGULAR CASE

Hadrien Montanelli; Francis Collino; Houssem Haddar

doi:10.1137/23M1605594

COMPUTING SINGULAR AND NEAR-SINGULAR INTEGRALS OVER CURVED BOUNDARY ELEMENTS: THE STRONGLY SINGULAR CASE

Hadrien Montanelli, Francis Collino, Houssem Haddar

Unité de Mathématiques Appliquées

Research output: Contribution to journal › Article › peer-review

Abstract

We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy and robustness of our method for quadratic basis functions and quadratic triangles by integrating it into a boundary element code and solving several scattering problems in three dimensions. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.

Original language	English
Pages (from-to)	A3756-A3778
Journal	SIAM Journal on Scientific Computing
Volume	46
Issue number	6
DOIs	https://doi.org/10.1137/23M1605594
Publication status	Published - 1 Jan 2024

Keywords

Helmholtz equation
boundary element method
continuation approach
homogeneous functions
integral equations
near-singular integrals

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10.1137/23M1605594

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title = "COMPUTING SINGULAR AND NEAR-SINGULAR INTEGRALS OVER CURVED BOUNDARY ELEMENTS: THE STRONGLY SINGULAR CASE",

abstract = "We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy and robustness of our method for quadratic basis functions and quadratic triangles by integrating it into a boundary element code and solving several scattering problems in three dimensions. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.",

keywords = "Helmholtz equation, boundary element method, continuation approach, homogeneous functions, integral equations, near-singular integrals",

author = "Hadrien Montanelli and Francis Collino and Houssem Haddar",

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AU - Haddar, Houssem

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N2 - We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy and robustness of our method for quadratic basis functions and quadratic triangles by integrating it into a boundary element code and solving several scattering problems in three dimensions. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.

AB - We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy and robustness of our method for quadratic basis functions and quadratic triangles by integrating it into a boundary element code and solving several scattering problems in three dimensions. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.

KW - Helmholtz equation

KW - boundary element method

KW - continuation approach

KW - homogeneous functions

KW - integral equations

KW - near-singular integrals

UR - https://www.scopus.com/pages/publications/105001741619

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ER -

COMPUTING SINGULAR AND NEAR-SINGULAR INTEGRALS OVER CURVED BOUNDARY ELEMENTS: THE STRONGLY SINGULAR CASE

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Keywords

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