Approximated implicit time-stepping schemes in a distributed memory parallel environment

The recently proposed Minimal Residential Approximate Implicit (MRAI) schemes have been developed as cheaper and parallelizable alternatives for implicit time stepping. For an implicit scheme of interest, the approach is based on the use of a restricted number of GMRES iterations to solve the implicit (linearized) system. The main difference with the conventional use of iterative techniques is that the convergence of the iterative process is not checked, but the step size of the scheme is adjusted adaptively for stability. Since the GMRES process is relatively easy to parallelize, the MRAI schemes are also well parallelizable. On platforms as the Cray T3E and IBM SP2, the MRAI codes show similar speed-ups as for explicit schemes, while the stability descretized heat equation. Speed-up results for the Cray T3E and IBM SP2 are reported and analysed