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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2504.18699 |
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| _version_ | 1866912729187483648 |
|---|---|
| author | Bruno, Oscar Cao, Jinghao |
| author_facet | Bruno, Oscar Cao, Jinghao |
| contents | The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth kernels, this work presents a fast, high-order numerical methodology that extends the approach to singular kernels and non-smooth domains. The method relies on truncated Fourier expansions of a prescribed order for the characteristic function of the integration domain, as well as expansions for the products of characteristic functions and singular functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18699 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast Singular-Kernel Convolution on General Non-Smooth Domains via Truncated Fourier Filtering Bruno, Oscar Cao, Jinghao Numerical Analysis The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth kernels, this work presents a fast, high-order numerical methodology that extends the approach to singular kernels and non-smooth domains. The method relies on truncated Fourier expansions of a prescribed order for the characteristic function of the integration domain, as well as expansions for the products of characteristic functions and singular functions. |
| title | Fast Singular-Kernel Convolution on General Non-Smooth Domains via Truncated Fourier Filtering |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.18699 |