Time-Domain BEM for the Wave Equation on Distributed-Heterogenous Architectures : a Blocking Approach

Abstract : The problem of time-domain BEM for the wave equation in acoustics and electromagnetism can be expressed as a sparse linear system composed of multiple interaction/convolution matrices. It can be solved using sparse matrix-vector products which are inefficient to achieve high Flop-rate whether on CPU or GPU. In this paper we extend the approach proposed in a previous work~\cite{bib:bramas} in which we re-order the computation to get a special matrices structure with one dense vector per row. This new structure is called a slice matrix and is computed with a custom matrix/vector product operator. In this study we present an optimized implementations of this operator on Nvidia GPU based on two blocking strategies. We explain how we can obtain multiple block-values from a slice and how these ones can be computed efficiently on GPU. We target heterogeneous nodes composed of CPU and GPU. In order to deal with the different efficiencies of the processing units we use a greedy heuristic that dynamically balances the work among the workers. We demonstrate the performance of our system by studying the quality of the balancing heuristic and the sequential Flop-rate of the blocked implementations. Finally, we validate our implementation with an industrial test case on 8 heterogeneous nodes each composed of 12 CPU and 3 GPU.
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https://hal.inria.fr/hal-01070069
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Submitted on : Wednesday, October 1, 2014 - 10:41:03 AM
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Bérenger Bramas, Olivier Coulaud, Guillaume Sylvand. Time-Domain BEM for the Wave Equation on Distributed-Heterogenous Architectures : a Blocking Approach. [Research Report] RR-8604, Inria Bordeaux Sud-Ouest; INRIA. 2014. ⟨hal-01070069⟩

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