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Scalable BDDC algorithms for cardiac electromechanical coupling. (English) Zbl 1368.92005
Lee, Chang-Ock (ed.) et al., Domain decomposition methods in science and engineering XXIII. Proceedings of the 23rd international conference, Jeju Island, Korea, July 6–10, 2015. Cham: Springer (ISBN 978-3-319-52388-0/hbk; 978-3-319-52389-7/ebook). Lecture Notes in Computational Science and Engineering 116, 261-268 (2017).
Summary: The spread of electrical excitation in the cardiac muscle and the subsequent contraction-relaxation process is quantitatively described by the cardiac electromechanical coupling model. The electrical model consists of the Bidomain system, which is a degenerate parabolic system of two nonlinear partial differential equations (PDEs) of reaction-diffusion type, describing the evolution in space and time of the intra- and extracellular electric potentials. The PDEs are coupled through the reaction term with a stiff system of ordinary differential equations (ODEs), the membrane model, which describes the flow of the ionic currents through the cellular membrane and the dynamics of the associated gating variables. The mechanical model consists of the quasi-static finite elasticity system, modeling the cardiac tissue as a nearly-incompressible transversely isotropic hyperelastic material, and coupled with a system of ODEs accounting for the development of biochemically generated active force.
For the entire collection see [Zbl 1371.65003].
Reviewer: Reviewer (Berlin)

MSC:
92-08 Computational methods for problems pertaining to biology
92C30 Physiology (general)
92C10 Biomechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
Software:
BoomerAMG; PCBDDC; PETSc
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References:
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