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Spectral Deferred Correction Methods for Adaptive Electro-Mechanical Coupling in Cardiac Simulation

Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 22)

Abstract

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.

Keywords

Biomedical science Cardiac electro-mechanical coupling Cardiovascular system Multiphysics problem Spatio-temporal adaptivity 

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Zuse Institute BerlinBereich Numerische MathematikBerlin-DahlemGermany
  2. 2.Department of MathematicsUniversity of MilanMilanoItaly

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