A BDDC Preconditioner for the EMI-Model in three Dimensions
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We consider the EMI (Extracellular space, cell Membrane and Intracellular space) model, which has been at the core of the EuroHPC project MICROCARD. Throughout the course of this project, Balancing Domain Decomposition by Constraints (BDDC) preconditioners have been proven to be an efficient choice for composite Discontinuous Galerkin (DG) type discretizations of cardiac cell-by-cell models and a theoretical analysis of this method have been presented in two dimensions. Here, a key step was the careful construction of extended dual and primal spaces for the degrees of freedom, allowing for continuous mapping in the BDDC splitting while still honoring the discontinuities across cell boundaries as they occur in the EMI model. This talk discusses the theoretical analysis in three dimensions as well as some practical results and implementation details.