Domain decomposition operator splitting for mimetic finite difference discretizations of non-stationary problems
In this paper, we propose reliable and efficient numerical methods for solving semilinear, time-dependent partial differential equations of reaction-diffusion type. The original problem is first integrated in time by using a linearly implicit fractional step Runge-Kutta method. This method takes advantage of a suitable partitioning of the diffusion operator based on domain decomposition techniques. The resulting semidiscrete problem is fully discretized by means of a mimetic finite difference method on quadrilateral meshes. Due to the previous splitting, the totally discrete scheme can be reduced to a set of uncoupled linear systems which can be solved in parallel. The overall algorithm is unconditionally stable and second-order convergent in both time and space. These properties are confirmed by numerical experiments. (C) 2010 Elsevier Ltd. All rights reserved.
domain decomposition operator splitting mimetic finite difference fractional steps parabolic problem