The solution of singularly perturbed parabolic problems by parallel algorithms combining Crank-Nicolson scheme and overlapping Schwarz methods (Q1963104)

Parallel algorithms combining a time discretization and overlapping domain decomposition methods are applied to the solution of singularly perturbed parabolic problems. Two domain decomposition methods are considered: the method with two-color ordering of subdomains and the method with additional ``correcting'' problems. Modifications of the methods are considered using time extrapolation on subdomain interfaces. Convergence properties of the algorithms are established at the differential level. Numerical results for a test singularly perturbed parabolic problem are described.