Computing singular and near-singular integrals over curved boundary elements: The strongly singular case
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910496260620288 |
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| author | Montanelli, Hadrien Collino, Francis Haddar, Houssem |
| author_facet | Montanelli, Hadrien Collino, Francis Haddar, Houssem |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17039 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Computing singular and near-singular integrals over curved boundary elements: The strongly singular case Montanelli, Hadrien Collino, Francis Haddar, Houssem Numerical Analysis 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. |
| title | Computing singular and near-singular integrals over curved boundary elements: The strongly singular case |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2309.17039 |