Simulating cardiac cell-by-cell electrophysiology involves resolving complex discontinuities at cellular interfaces, such as intercalated disks, and addressing the high computational demands of large-scale simulations. This talk presents a specialized framework employing parallel overlapping Schwarz algorithms with Generalized Dryjia-Smith-Widlund (GDSW) preconditioners, optimized for composite discontinuous Galerkin (DG) discretizations in cardiac electrophysiology applications. GDSW preconditioners provide an efficient strategy for accelerating convergence in iterative solvers by leveraging local eigenmode information to construct robust coarse spaces. This approach ensures rapid information exchange across subdomains while effectively managing the discontinuities introduced by heterogeneous cellular structures. The overlapping Schwarz framework is designed to balance computational efficiency with the accuracy needed to capture the fine electrical wave dynamics at the cellular level. Numerical performance evaluations on microscopic cardiac models highlight significant improvements in computational efficiency with respect to classical algebraic multigrid approaches, with reduced iteration counts and robust scalability across high-performance computing platforms. Applications include exploring the propagation of electrical waves through discontinuous myocardial tissue, as well as analyzing the effects of structural heterogeneities on conduction dynamics. This work extends recent advancements in domain decomposition and GDSW preconditioning to cardiac-specific problems, offering a scalable and efficient solution for cell-by-cell electrophysiology modeling.