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Computing weakly singular and near-singular integrals in high-order boundary elements

Abstract : We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with high-order boundary elements. These are based on the computation of the preimage of the singularity in the reference element's space using Newton's method, singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy of our method for quadratic triangular elements with several numerical experiments, including the scattering by two nearby half-spheres.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03518653
Contributor : Hadrien Montanelli Connect in order to contact the contributor
Submitted on : Tuesday, January 11, 2022 - 2:34:59 PM
Last modification on : Friday, April 8, 2022 - 3:38:10 AM

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  • HAL Id : hal-03518653, version 1

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Hadrien Montanelli, Matthieu Aussal, Houssem Haddar. Computing weakly singular and near-singular integrals in high-order boundary elements. 2022. ⟨hal-03518653v1⟩

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