Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation

Please always quote using this URN: urn:nbn:de:0297-zib-50695
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  • We investigate spectral deferred correction (SDC) methods for time stepping and their interplay with spatio-temporal adaptivity, applied to the solution of the cardiac electro-mechanical coupling model. This model consists of the Monodomain equations, a reaction-diffusion system modeling the cardiac bioelectrical activity, coupled with a quasi-static mechanical model describing the contraction and relaxation of the cardiac muscle. The numerical approximation of the cardiac electro-mechanical coupling is a challenging multiphysics problem, because it exhibits very different spatial and temporal scales. Therefore, spatio-temporal adaptivity is a promising approach to reduce the computational complexity. SDC methods are simple iterative methods for solving collocation systems. We exploit their flexibility for combining them in various ways with spatio-temporal adaptivity. The accuracy and computational complexity of the resulting methods are studied on some numerical examples.

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Author:Martin Weiser, Simone Scacchi
Document Type:ZIB-Report
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M70 Spectral, collocation and related methods
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Date of first Publication:2014/06/20
Series (Serial Number):ZIB-Report (14-22)
ISSN:1438-0064