Linearly scalable fast direct solver based on proxy surface method for two-dimensional elastic wave scattering by cavity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929740160434176 |
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| author | Matsumoto, Yasuhiro Maruyama, Taizo |
| author_facet | Matsumoto, Yasuhiro Maruyama, Taizo |
| contents | This paper proposes an $O(N)$ fast direct solver for two-dimensional elastic wave scattering problems. The proxy surface method is extended to elastodynamics to obtain shared coefficients for low-rank approximations from discretized integral operators. The proposed method is a variant of the Martinsson-Rokhlin-type fast direct solver. Our variant avoids the explicit computation of the inverse of the coefficient matrix, thereby reducing the required number of matrix-matrix multiplications. Numerical experiments demonstrate that the proposed solver has a complexity of $O(N)$ in the low-frequency range and has a highly parallel computation efficiency with a strong scaling efficiency of 70\%. Furthermore, multiple right-hand sides can be solved efficiently; specifically, when solving problems with 180 right-hand side vectors, the processing time per vector from the second vector onward was approximately 28,900 times faster than that for the first vector. This is a key advantage of fast direct methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linearly scalable fast direct solver based on proxy surface method for two-dimensional elastic wave scattering by cavity Matsumoto, Yasuhiro Maruyama, Taizo Numerical Analysis This paper proposes an $O(N)$ fast direct solver for two-dimensional elastic wave scattering problems. The proxy surface method is extended to elastodynamics to obtain shared coefficients for low-rank approximations from discretized integral operators. The proposed method is a variant of the Martinsson-Rokhlin-type fast direct solver. Our variant avoids the explicit computation of the inverse of the coefficient matrix, thereby reducing the required number of matrix-matrix multiplications. Numerical experiments demonstrate that the proposed solver has a complexity of $O(N)$ in the low-frequency range and has a highly parallel computation efficiency with a strong scaling efficiency of 70\%. Furthermore, multiple right-hand sides can be solved efficiently; specifically, when solving problems with 180 right-hand side vectors, the processing time per vector from the second vector onward was approximately 28,900 times faster than that for the first vector. This is a key advantage of fast direct methods. |
| title | Linearly scalable fast direct solver based on proxy surface method for two-dimensional elastic wave scattering by cavity |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.18026 |