Computing singular and near-singular integrals over curved boundary elements: The strongly singular case

2023/09/29 by Hadrien Montanelli, Montanelli, Hadrien, Francis Collino +3 · 1 citation
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2309.17039

openalex publication_date 2023/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 3D. We also give numerical evidence that the utilization of curved boundary elements enhances computational efficiency compared to conventional planar elements.

Cited by

• Convergence rates of curved boundary element methods for the 3D Laplace and Helmholtz equations

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