Pennacchio, Micol; Simoncini, Valeria Fast structured AMG preconditioning for the bidomain model in electrocardiology. (English) Zbl 1227.92034 SIAM J. Sci. Comput. 33, No. 2, 721-745 (2011). Summary: The electrical activity of the heart may be modeled by a nonlinear system of partial differential equations known as the bidomain model. Due to the rapid variations in the electrical field, accurate simulations require a fine-scale discretization of the equations and consequently the solution of large severely ill-conditioned linear systems at each time step. Solving these systems is a major bottleneck of the whole simulation. We propose a highly effective preconditioning strategy for a general and popular three-dimensional formulation of the problem. A theoretical analysis of the preconditioned matrix ensuring mesh independence of the spectrum is also described. Numerical comparisons with state-of-the-art approaches confirm the effectiveness of our preconditioning technique. Finally, we show that an equivalent but less exercised formulation provides the best performance, in terms of CPU time. Cited in 10 Documents MSC: 92C50 Medical applications (general) 92C05 Biophysics 35Q92 PDEs in connection with biology, chemistry and other natural sciences 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 92C30 Physiology (general) Keywords:reaction-diffusion system; iterative methods; algebraic multigrid Software:COMSOL; HSL_MI20; AGMG; HSL PDFBibTeX XMLCite \textit{M. Pennacchio} and \textit{V. Simoncini}, SIAM J. Sci. Comput. 33, No. 2, 721--745 (2011; Zbl 1227.92034) Full Text: DOI