Improving the Parallel Efficiency of Tau3P, a Parallel Electromagnetic Field Solver

Michael Wolf, University of Illinois

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At the Stanford Linear Accelerator Center, I developed a parallel time domain electromagnetic solver (Tau3P) that has been successful in modeling large accelerator structures. However, during the development of Tau3P, I had difficulties obtaining good parallel efficiency for large numbers of processors. One difficulty is that Tau3P uses a discrete surface integral (DSI) method on unstructured meshes with both orthogonal and nonorthogonal elements. In this formulation, partitions consisting of nonorthogonal elements have many more nonzeros than partitions with the same number of strictly orthogonal elements. This complicates loadbalancing. Another difficulty is the extreme sparsity of the matrices. Due to this sparsity, each processor must contain many rows to mitigate the effects of communication. However, agglomerating too many rows per processor will reduce potential parallelism by limiting the number of processors. If communication for this problem could be reduced, it would become less difficult to obtain high parallel efficiency for large numbers of processors.

I am researching the use of mesh partitioning techniques in an attempt to reduce this communication and improve parallel efficiency in Tau3P. From these techniques, I have obtained improved parallel efficiency in Tau3P and have learned what partitioning techniques work well for these types of problems. This summer I hope to explore additional mesh partitioning techniques in order to improve the parallel efficiency further. In addition to this partitioning work, I have begun to focus on the communication patterns in Tau3P in an attempt to reduce this communication overhead and increase parallel performance. I have examined different modes of MPI communication and the effects they have on the parallel efficiency. Also, I have begun examining how the order of the computation and communication stages affects the parallel efficiency of the parallel numerical algorithms in Tau3P.

Abstract Author(s): Michael Wolf<br />Ali Pinar<br />Esmond Ng