@misc{WeiserScacchi, author = {Weiser, Martin and Scacchi, Simone}, title = {Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-50695}, abstract = {We investigate spectral deferred correction (SDC) methods for time stepping and their interplay with spatio-temporal adaptivity, applied to the solution of the cardiac electro-mechanical coupling model. This model consists of the Monodomain equations, a reaction-diffusion system modeling the cardiac bioelectrical activity, coupled with a quasi-static mechanical model describing the contraction and relaxation of the cardiac muscle. The numerical approximation of the cardiac electro-mechanical coupling is a challenging multiphysics problem, because it exhibits very different spatial and temporal scales. Therefore, spatio-temporal adaptivity is a promising approach to reduce the computational complexity. SDC methods are simple iterative methods for solving collocation systems. We exploit their flexibility for combining them in various ways with spatio-temporal adaptivity. The accuracy and computational complexity of the resulting methods are studied on some numerical examples.}, language = {en} } @inproceedings{WeiserScacchi, author = {Weiser, Martin and Scacchi, Simone}, title = {Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation}, series = {G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014}, booktitle = {G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014}, publisher = {Springer}, doi = {10.1007/978-3-319-23413-7_42}, pages = {321 -- 328}, abstract = {We investigate spectral deferred correction (SDC) methods for time stepping and their interplay with spatio-temporal adaptivity, applied to the solution of the cardiac electro-mechanical coupling model. This model consists of the Monodomain equations, a reaction-diffusion system modeling the cardiac bioelectrical activity, coupled with a quasi-static mechanical model describing the contraction and relaxation of the cardiac muscle. The numerical approximation of the cardiac electro-mechanical coupling is a challenging multiphysics problem, because it exhibits very different spatial and temporal scales. Therefore, spatio-temporal adaptivity is a promising approach to reduce the computational complexity. SDC methods are simple iterative methods for solving collocation systems. We exploit their flexibility for combining them in various ways with spatio-temporal adaptivity. The accuracy and computational complexity of the resulting methods are studied on some numerical examples.}, language = {en} } @article{HuynhCheginiPavarinoetal., author = {Huynh, Ngoc and Chegini, Fatemeh and Pavarino, Luca and Weiser, Martin and Scacchi, Simone}, title = {Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model}, series = {SIAM Journal on Scientific Computing}, volume = {45}, journal = {SIAM Journal on Scientific Computing}, number = {6}, pages = {A2836 -- A2857}, abstract = {A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow 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 have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing 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.}, language = {en} } @inproceedings{CheginiFroehlyHuynhetal., author = {Chegini, Fatemeh and Froehly, Algiane and Huynh, Ngoc Mai Monica and Pavarino, Luca and Potse, Mark and Scacchi, Simone and Weiser, Martin}, title = {Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution}, series = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, booktitle = {10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023}, doi = {10.23967/c.coupled.2023.004}, abstract = {The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes.}, language = {en} }