A hybrid interpolation ACA accelerated method for parabolic boundary integral operators
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911981873659904 |
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| author | Ambikasaran, Sivaram Khan, Ritesh Tausch, Johannes Wang, Sihao |
| author_facet | Ambikasaran, Sivaram Khan, Ritesh Tausch, Johannes Wang, Sihao |
| contents | We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-lower triangular and hence can be solved by block forward elimination. For the fast evaluation of the history part, the matrix is subdivided into a family of sub-matrices according to the temporal separation. Separated blocks are approximated by Chebyshev interpolation of the heat kernel in time. For the spatial variable, we propose an adaptive cross approximation (ACA) framework to obtain a data-sparse approximation of the entire matrix. We analyse how the ACA tolerance must be adjusted to the temporal separation and present numerical results for a benchmark problem to confirm the theoretical estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hybrid interpolation ACA accelerated method for parabolic boundary integral operators Ambikasaran, Sivaram Khan, Ritesh Tausch, Johannes Wang, Sihao Numerical Analysis 65R20, 68F55, 68U05 We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-lower triangular and hence can be solved by block forward elimination. For the fast evaluation of the history part, the matrix is subdivided into a family of sub-matrices according to the temporal separation. Separated blocks are approximated by Chebyshev interpolation of the heat kernel in time. For the spatial variable, we propose an adaptive cross approximation (ACA) framework to obtain a data-sparse approximation of the entire matrix. We analyse how the ACA tolerance must be adjusted to the temporal separation and present numerical results for a benchmark problem to confirm the theoretical estimates. |
| title | A hybrid interpolation ACA accelerated method for parabolic boundary integral operators |
| topic | Numerical Analysis 65R20, 68F55, 68U05 |
| url | https://arxiv.org/abs/2408.04080 |