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In this work, a parallel three-dimensional solver for numerical simulations in com-
putational electrocardiology is introduced and studied. The solver is based on the
anisotropic Bidomain cardiac model, consisting of a system of two degenerate parabolic
reaction–diffusion equations describing the intra and extracellular potentials of the
myocardial tissue. This model includes intramural fiber rotation and anisotropic con-
ductivity coefficients that can be fully orthotropic or axially symmetric around the
fiber direction. The solver also includes the simpler anisotropic Monodomain model,
consisting of only one reaction–diffusion equation. These cardiac models are coupled with
a membrane model for the ionic currents, consisting of a system of ordinary differential
equations that can vary from the simple FitzHugh–Nagumo (FHN) model to the more
complex phase-I Luo–Rudy model (LR1). The solver employs structured isoparametric
Q1 finite elements in space and a semi-implicit adaptive method in time. Parallelization
and portability are based on the PETSc parallel library. Large-scale computations with
up to O(107 ) unknowns have been run on parallel computers, simulating excitation and
repolarization phenomena in three-dimensional domains
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