EFFECTIVE NUMERICAL TECHNIQUES FOR THE SOLUTIONS OF ELECTROCARDIOLOGY EQUATIONS

The aim of this talk is to present some numerical techniques to solve the equa- tions arising in Electrocardiology. In particular we consider the Bidomain equations for the transmembrane and extracellular potentials coupled with the Luo-Rudy model that describes the ionic dynamics across the membrane at the cellular level. The Bidomain model consists of degenerate, quasi-linear, parabolic equations. It can be derived from a homogenization of the electrostatic laws for the potential in the intracellular and extracellular space. The Luo-Rudy model consists of a sti system of ordinary dierential equations. The intrinsic complexity of the coupled problem requires ad hoc numerical methods. In this talk we present a time- adaptive exponential scheme (2) for the time advancing, expressly devised to solve Luo-Rudy like models. Also we introduce a model-based block-triangular preconditioner (1) for the so- lution of the Bidomain system. Other strategies are presented; in particular we introduce a domain-decomposition approach (4), for the solution of a simplied model in regions where the high accuracy of the Bidomain is not needed (3).