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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.