A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912643513581568 |
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| author | Goebel, Fritz Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Weiser, Martin Scacchi, Simone Anzt, Hartwig |
| author_facet | Goebel, Fritz Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Weiser, Martin Scacchi, Simone Anzt, Hartwig |
| contents | We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions Goebel, Fritz Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Weiser, Martin Scacchi, Simone Anzt, Hartwig Numerical Analysis 65N55, 65M55, 65F08, 65F10, 92C30 We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments. |
| title | A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions |
| topic | Numerical Analysis 65N55, 65M55, 65F08, 65F10, 92C30 |
| url | https://arxiv.org/abs/2502.07722 |