Iterative domain decomposition algorithms for the solution of singularly perturbed parabolic problems

A combination of a time discretization and domain decomposition methods for the solution of singularly perturbed semilinear parabolic problems is considered. On this basis, iterative algorithms suitable for parallelization are constructed. Convergence properties of these algorithms are established. The implementation of the algorithms on a shared memory multiprocessor is examined. Numerical results for a test singularly perturbed problem are presented.