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" An efficient parallel algorithm for solving time dependent partial differential equations " When solving time dependent partial differential equations on parallel computers using non-overlapping domain decomposition method, one often needs numerical boundary conditions between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the solution algorithms. In this presentation, a brief review of the latest development in parallel processing for computational simulations will be given, followed by stability and accuracy analysis of the existing methods for generating numerical boundary conditions, and discussions of a new approach based on explicit predictors and implicit correctors. Numerical results will be presented to demonstrate significant improvement in stability and accuracy using the new approach. |