Parallel algorithms for computational continuum dynamics

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Department of Mathematical Sciences


The numerical solution of many problems in continuum dynamics is seriously limited by the computation rates attainable on computers with serial architecture. Parallel processing machines can achieve much higher rates. However, the greatest potential of the new architectures can be realized only through the derivation of parallel algorithms. That is, computational work must be partitioned into independent sequences of calculations. This research was undertaken to develop parallel algorithms for explicit and implicit, Lagrangian and Eulerian finite difference schemes for computational continum dynamics in one spatial dimension. First, the explicit conservation equations in the Lagrangian reference frame were readily reformulated for concurrent processing. Second, an implicit solution was derived for these equations. The parallelism is achieved via a block implicit numerical scheme. Third, a rezoning algorithm was employed with each Lagrangian integration step to transform the mesh back to the Eulerian reference frame. The algorithmic development path lead to a parallelization of the processing in blocks of the finite discretization zones. At each step of this research project, the derived numerical methods provided effective algorithms for exploiting the architectural advantages of a MIMD machine such as the HEP H1000 (Heterogeneous Element Processor) computer. The computational timing data show significant speed-up with the number of processes.

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Applied Mathematics and Computation