Well-conditioned dipole-type method of fundamental solutions: derivation and its mathematical analysis
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911974438207488 |
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| author | Sakakibara, Koya |
| author_facet | Sakakibara, Koya |
| contents | In this paper, we examine the dipole-type method of fundamental solutions, which can be conceptualized as a discretization of the "singularity-removed" double-layer potential. We present a method for removing the ill-conditionality, which was previously considered a significant challenge, and provide a mathematical analysis in the context of disk regions. Moreover, we extend the proposed method to the general Jordan region using conformal mapping, demonstrating the efficacy of the proposed method through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-conditioned dipole-type method of fundamental solutions: derivation and its mathematical analysis Sakakibara, Koya Numerical Analysis 65N80, 65N35, 65N12, 35J05, 35J08 In this paper, we examine the dipole-type method of fundamental solutions, which can be conceptualized as a discretization of the "singularity-removed" double-layer potential. We present a method for removing the ill-conditionality, which was previously considered a significant challenge, and provide a mathematical analysis in the context of disk regions. Moreover, we extend the proposed method to the general Jordan region using conformal mapping, demonstrating the efficacy of the proposed method through numerical experiments. |
| title | Well-conditioned dipole-type method of fundamental solutions: derivation and its mathematical analysis |
| topic | Numerical Analysis 65N80, 65N35, 65N12, 35J05, 35J08 |
| url | https://arxiv.org/abs/2408.00212 |