Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909457985830912 |
|---|---|
| author | Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Franco Weiser, Martin Scacchi, Simone |
| author_facet | Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Franco Weiser, Martin Scacchi, Simone |
| contents | A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. Unlike classical Bidomain and Monodomain cardiac models, which rely on homogenized descriptions of cardiac tissue at the macroscopic level, the cell-by-cell models enable the representation of individual cardiac cells, cell aggregates, damaged tissues, and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models exhibit discontinuous global solutions across the cell boundaries. Therefore, the proposed BDDC preconditioner employs appropriate dual and primal spaces with additional constraints to transfer information between cells (subdomains) without affecting the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12295 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model Huynh, Ngoc Mai Monica Chegini, Fatemeh Pavarino, Luca Franco Weiser, Martin Scacchi, Simone Numerical Analysis 65N55, 65M55, 65F10, 92C30 A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. Unlike classical Bidomain and Monodomain cardiac models, which rely on homogenized descriptions of cardiac tissue at the macroscopic level, the cell-by-cell models enable the representation of individual cardiac cells, cell aggregates, damaged tissues, and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models exhibit discontinuous global solutions across the cell boundaries. Therefore, the proposed BDDC preconditioner employs appropriate dual and primal spaces with additional constraints to transfer information between cells (subdomains) without affecting the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters. |
| title | Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model |
| topic | Numerical Analysis 65N55, 65M55, 65F10, 92C30 |
| url | https://arxiv.org/abs/2212.12295 |