Colloquia Patavina: Multilevel Schwarz methods for cardiac reaction, diffusion models and applications


Martedi' 3 Novembre 2009 alle ore 16:00 in aula 1A/150 della Torre Archimede il Professor Luca Franco Pavarino dell'Universita' di Milano terra' una conferenza della serie Colloquia Patavina.

La Commissione Colloquia
M.A. Garuti, M. Pavon, M. Pitteri, F. Rossi

Multilevel Schwarz methods for cardiac reaction, diffusion models and applications

Luca Franco Pavarino (Universita' di Milano)

Research on the electrophysiology of the heart has progressed greatly in the last decades, producing a vast body of knowledge ranging from the microscopic description of ion channels of the cellular membrane to the macroscopic properties of the anisotropic propagation of excitation and repolarization fronts in the whole heart. Multiscale models have proven very useful in the study of these complex phenomena, progressively including more detailed features of each component in more refined mathematical models with appropriate space and time scales. One of the major challenges in contemporary electrophysiology is the integration of these sophisticated sub-models into a global model that is able to reproduce efficiently the bioelectrical activity of the heart.
We present here recent results obtained in our research group by integrating two of the most advanced models in electrocardiology, the anisotropic Bidomain cardiac model, a degenerate system of two parabolic reaction-diffusion equations, and the Luo-Rudy (LR) ionic model, a system of several ordinary differential equations. The numerical resolution of the coupled Bidomain - LR system is computationally very expensive, because of the interaction of the different scales in space and time, the degenerate nature of the PDEs involved and the very severe ill-conditioning of the discrete systems arising at each time step. We will present efficient parallel Bidomain solvers based on Imex methods in time and finite element methods in space; the key to obtaining a scalable large-scale solver is the use of multilevel overlapping additive Schwarz preconditioner for the Krylov space iterative solver employed at each time step.
Several numerical simulations in three dimensions on Linux clusters allow to study the evolution of the cardiac potentials in normal and reentry dynamics with unprecedented resolution of the relevant space and time scales.

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