Optimization and parallelization of the boundary element method for the wave equation in time domain

Bérenger Bramas 1, 2
Abstract : The time-domain BEM for the wave equation in acoustics and electromagnetism is used to simulatethe propagation of a wave with a discretization in time. It allows to obtain several frequencydomainresults with one solve. In this thesis, we investigate the implementation of an efficientTD-BEM solver using different approaches. We describe the context of our study and the TD-BEMformulation expressed as a sparse linear system composed of multiple interaction/convolutionmatrices. This system is naturally computed using the sparse matrix-vector product (SpMV). Wework on the limits of the SpMV kernel by looking at the matrix reordering and the behavior of ourSpMV kernels using vectorization (SIMD) on CPUs and an advanced blocking-layout on NvidiaGPUs. We show that this operator is not appropriate for our problem, and we then propose toreorder the original computation to get a special matrix structure. This new structure is called aslice matrix and is computed with a custom matrix/vector product operator. We present an optimizedimplementation of this operator on CPUs and Nvidia GPUs for which we describe advancedblocking schemes. The resulting solver is parallelized with a hybrid strategy above heterogeneousnodes and relies on a new heuristic to balance the work among the processing units. Due tothe quadratic complexity of this matrix approach, we study the use of the fast multipole method(FMM) for our time-domain BEM solver. We investigate the parallelization of the general FMMalgorithm using several paradigms in both shared and distributed memory, and we explain howmodern runtime systems are well-suited to express the FMM computation. Finally, we investigatethe implementation and the parametrization of an FMM kernel specific to our TD-BEM, and weprovide preliminary results.
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Bérenger Bramas. Optimization and parallelization of the boundary element method for the wave equation in time domain. Distributed, Parallel, and Cluster Computing [cs.DC]. Université de Bordeaux, 2016. English. ⟨NNT : 2016BORD0022⟩. ⟨tel-01306571⟩

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