Coarse Grid Correction Operator Splitting for Parabolic Partial Differential Equations
Operator Splitting | domain decomposition | Coarse Grid Correction
We develop a two-level splitting method for the numerical solution of parabolic partial differential equations (PDE). Instead of using the backward Euler method, we use an operator splitting scheme to advance the system of equations obtained from the spatial discretization of the PDE. The split operators are derived from a domain decomposition technique based on a partition of unity of the spatial domain. The analysis and numerical results show that the discretization error is of second order in space and of first order in time, however, it deteriorates when the number of subdomains increases and when the overlap between the subdomains decreases. To overcome this drawback we introduce a coarse grid correction scheme at each time step. The numerical results obtained with the coarse grid correction show that the discretization errors are smaller than the ones obtained from the one-level operator splitting method.