Space-time multilevel quadrature methods and their application for cardiac electrophysiology

Bader, Seif Ben and Harbrecht, Helmut and Krause, Rolf and Multerer, Michael and Quaglino, Alessio and Schmidlin, Marc. (2021) Space-time multilevel quadrature methods and their application for cardiac electrophysiology. Preprints Fachbereich Mathematik, 2021 (13).


Official URL: https://edoc.unibas.ch/82976/

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Schmidlin, Marc
Item Type:Preprint
Publisher:Universität Basel
edoc DOI:
Last Modified:07 May 2021 13:45
Deposited On:07 May 2021 13:45

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