  We present a novel approach which aims at high-performance uncertainty
quantification for cardiac electrophysiology simulations. Employing the
monodomain equation to model the transmembrane potential inside the cardiac
cells, we evaluate the effect of spatially correlated perturbations of the
heart fibers on the statistics of the resulting quantities of interest. Our
methodology relies on a close integration of multilevel quadrature methods,
parallel iterative solvers and space-time finite element discretizations,
allowing for a fully parallelized framework in space, time and stochastics.
Extensive numerical studies are presented to evaluate convergence rates and to
compare the performance of classical Monte Carlo methods such as standard Monte
Carlo (MC) and quasi-Monte Carlo (QMC), as well as multilevel strategies, i.e.
multilevel Monte Carlo (MLMC) and multilevel quasi-Monte Carlo (MLQMC) on
hierarchies of nested meshes. Finally, we employ a recently suggested variant
of the multilevel approach for non-nested meshes to deal with a realistic heart
geometry.
