Attention-based hybrid solvers for linear equations that are geometry aware
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917842462441472 |
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| author | Versano, Idan Turkel, Eli |
| author_facet | Versano, Idan Turkel, Eli |
| contents | We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust preconditioner for problems defined by different geometries without further fine-tuning or additional data mining. We demonstrate our method for the Helmholtz equation, which is used to solve problems in electromagnetics and acoustics; the Helmholtz equation is not positive definite, and with absorbing boundary conditions, it is not symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Attention-based hybrid solvers for linear equations that are geometry aware Versano, Idan Turkel, Eli Numerical Analysis We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust preconditioner for problems defined by different geometries without further fine-tuning or additional data mining. We demonstrate our method for the Helmholtz equation, which is used to solve problems in electromagnetics and acoustics; the Helmholtz equation is not positive definite, and with absorbing boundary conditions, it is not symmetric. |
| title | Attention-based hybrid solvers for linear equations that are geometry aware |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.13341 |