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An order optimal solver for the discretized bidomain equations. (English) Zbl 1199.65111

Summary: The electrical activity in the heart is governed by the bidomain equations. In this paper, we analyse an order optimal method for the algebraic equations arising from the discretization of this model. Our scheme is defined in terms of block Jacobi or block symmetric Gauss-Seidel preconditioners. Furthermore, each block in these methods is based on standard preconditioners for scalar elliptic or parabolic partial differential equations. Such preconditioners can be realized in terms of multigrid or domain decomposition schemes, and are thus readily available by applying ‘off-the-shelves’ software. Finally, our theoretical findings are illuminated by a series of numerical experiments.

MSC:

65F10 Iterative numerical methods for linear systems
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
92C05 Biophysics
65F08 Preconditioners for iterative methods
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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