A model-based block-triangular preconditioner for the Bidomain system in electrocardiology

Authors:
L. Gerardo-Giorda;L. Mirabella;F. Nobile;M. Perego;A. Veneziani
Affiliations:
Department of Mathematics and Computer Science, Emory University, 201 Dowman Drive, Atlanta, GA 30322, USA;Department of Mathematics and Computer Science, Emory University, 201 Dowman Drive, Atlanta, GA 30322, USA and MOX, Department of Mathematics, Politecnico di Milano, piazza L. da Vinci 32, 20133 M ...;MOX, Department of Mathematics, Politecnico di Milano, piazza L. da Vinci 32, 20133 Milano, Italy;Department of Mathematics and Computer Science, Emory University, 201 Dowman Drive, Atlanta, GA 30322, USA and MOX, Department of Mathematics, Politecnico di Milano, piazza L. da Vinci 32, 20133 M ...;Department of Mathematics and Computer Science, Emory University, 201 Dowman Drive, Atlanta, GA 30322, USA
Venue:
Journal of Computational Physics
Year:
2009

Citing 5
Cited 3

Efficient algebraic solution of reaction-diffusion systems for the cardiac excitation process

Journal of Computational and Applied Mathematics
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
On the Finite Element Solution of the Pure Neumann Problem

SIAM Review
New Nonoverlapping Domain Decomposition Methods for the Harmonic Maxwell System

SIAM Journal on Scientific Computing
Multilevel Additive Schwarz Preconditioners for the Bidomain Reaction-Diffusion System

SIAM Journal on Scientific Computing

Preconditioning the bidomain model with almost linear complexity

Journal of Computational Physics
Fast Structured AMG Preconditioning for the Bidomain Model in Electrocardiology

SIAM Journal on Scientific Computing
Parallel Multilevel Schwarz and Block Preconditioners for the Bidomain Parabolic-Parabolic and Parabolic-Elliptic Formulations

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	31.45

Visualization

Abstract

We introduce a preconditioner for the solution of the Bidomain system governing the propagation of action potentials in the myocardial tissue. The Bidomain model is a degenerate parabolic set of nonlinear reaction-diffusion equations. The nonlinear term describes the ion flux at the cellular level. The degenerate nature of the problem results in a severe ill conditioning of its discretization. Our preconditioning strategy is based on a suitable adaptation of the Monodomain model, a simplified version of the Bidomain one, which is by far simpler to solve, nevertheless is unable to capture significant features of the action potential propagation. The Monodomain preconditioner application to a non-symmetric formulation of the Bidomain system results at the algebraic level in a lower block-triangular preconditioner. We prove optimality of the preconditioner with respect to the mesh size, and corroborate our theoretical results with 3D numerical simulations both on idealized and real ventricle geometries.