An adaptive Hybridizable Discontinuous Galerkin approach for cardiac electrophysiology

Autor: Hoermann, Julia M., Bertoglio, Cristóbal, Kronbichler, Martin, Pfaller, Martin R., Chabiniok, Radomir, Wall, Wolfgang A.
Přispěvatelé: Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), University of Groningen [Groningen], Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Imaging Sciences and Biomedical Engineering Division [London], Guy's and St Thomas' Hospital [London]-King‘s College London, Université Paris-Saclay, Institute for Computational Mechanics, Technical University of Munich, Garching, Germany, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Zdroj: International Journal for Numerical Methods in Biomedical Engineering
International Journal for Numerical Methods in Biomedical Engineering, John Wiley and Sons, 2018, 34 (5), e2959 (20 p.). ⟨10.1002/cnm.2959⟩
International Journal for Numerical Methods in Biomedical Engineering, 2018, 34 (5), e2959 (20 p.). ⟨10.1002/cnm.2959⟩
ISSN: 2040-7939
2040-7947
Popis: International audience; Cardiac electrophysiology simulations are numerically challenging due to the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the Hybridizable Discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle p-adaptivity reduces the average number of degrees of freedom by 95% compared to the non-adaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.
Databáze: OpenAIRE
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