Efficient algebraic solution of reaction-diffusion systems for the cardiac excitation process
A reaction-diffusion system, in a form of nonlinear degenerate parabolic system, which models the excitation process of a small block of cardiac tissue is considered. Classical algebraic approaches and previous formulations and methods are discussed. Numerical approximations for the corresponding variational formulation is obtained, and a new formulation which entails a convenient matrix structure for preconditioning is shown to be efficient in terms of computer time and memory. Convergence results are derived, and numerical experiments by a wide variety of techniques and iterative methods are reported and compared.
scientific article; zbMATH DE number 1787674