Multilevel Additive Schwarz Preconditioners for the Bidomain Reaction-Diffusion System

摘要: Multilevel additive Schwarz methods are analyzed and studied numerically for the anisotropic cardiac Bidomain model in three dimensions. This is most complete to date of bioelectrical activity heart tissue, consisting a degenerate parabolic system nonlinear reaction-diffusion equations coupled with stiff several ordinary differential describing ionic currents through cellular membrane. Due presence very different scales both space time, numerical discretization this by finite elements semi-implicit time produces ill-conditioned linear systems that must be solved at each step. The proposed multilevel algorithm employs hierarchy nested meshes overlapping preconditioners on level fully additive, hence parallel, within among levels. Convergence estimates proved resulting algorithm, showing its convergence rate independent number subdomains (scalability), mesh sizes levels (optimality). Several parallel tests Linux cluster confirm scalability optimality method, as well efficiency Cartesian deformed domains