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

  • Martin WeiserEmail author
  • Simone Scacchi
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 22)


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.


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


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© 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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