On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912856271749120 |
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| author | Harbrecht, Helmut von Rickenbach, Remo |
| author_facet | Harbrecht, Helmut von Rickenbach, Remo |
| contents | The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are asymptotically optimal, meaning that any target accuracy can be achieved at a computational expense that stays proportional to the number of degrees of freedom (within the setting determined by an underlying wavelet basis) that would ideally be necessary for realising that target accuracy if full knowledge about the unknown solution were given. As we consider anisotropic wavelet bases, we can achieve higher convergence rates compared to the standard, isotropic setting. Especially, edge singularities of anisotropic nature can be resolved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates Harbrecht, Helmut von Rickenbach, Remo Numerical Analysis The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are asymptotically optimal, meaning that any target accuracy can be achieved at a computational expense that stays proportional to the number of degrees of freedom (within the setting determined by an underlying wavelet basis) that would ideally be necessary for realising that target accuracy if full knowledge about the unknown solution were given. As we consider anisotropic wavelet bases, we can achieve higher convergence rates compared to the standard, isotropic setting. Especially, edge singularities of anisotropic nature can be resolved. |
| title | On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.06938 |