A Parallel Algorithm Based on Additive Schwarz Domain Decomposition Method for Parabolic Problems

In this paper, we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems. We introduce an additive Schwarz domain decomposition method for parabolic differential equations and also consider the dependence of convergence rates of the algorithm on parameters of time step and space-mesh. The resulting preconditioned linear system of equations is solved by the conjugate gradient method and the algorithm is parallel. Finally we give a numerical example.