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Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems

Abstract : Controlled-source electromagnetic (CSEM) surveying becomes a widespreadmethod for oil and gaz exploration, which requires fast and efficient software for invertinglarge-scale EM datasets. In this context, one often needs to solve sparse systems of linearequations with a large number of sparse right-hand sides, each corresponding to a giventransmitter position. Sparse direct solvers are very attractive for these problems, especiallywhen combined with low-rank approximations which significantly reduce the complexityand the cost of the factorization. In the case of thousands of right-hand sides, the timespent in the sparse triangular solve tends to dominate the total simulation time and herewe propose several approaches to reduce it. A significant reduction is demonstrated formarine CSEM application by utilizing the sparsity of the right-hand sides (RHS) and ofthe solutions that results from the geometry of the problem. Large gains are achievedby restricting computations at the forward substitution stage to exploit the fact that theRHS matrix might have empty rows (vertical sparsity) and/or empty blocks of columnswithin a non-empty row (horizontal sparsity). We also adapt the parallel algorithms thatwere designed for the factorization to solve-oriented algorithms and describe performanceoptimizations particularly relevant for the very large numbers of right-hand sides of theCSEM application. We show that both the operation count and the elapsed time for thesolution phase can be significantly reduced. The total time of CSEM simulation can bedivided by approximately a factor of 3 on all the matrices from our set (from 3 to 30million unknowns, and from 4 to 12 thousands RHSs).
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https://hal.inria.fr/hal-01912713
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Submitted on : Monday, November 5, 2018 - 3:59:16 PM
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  • HAL Id : hal-01912713, version 1

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Patrick Amestoy, Sebastien de la Kethulle de Ryhove, Jean-Yves l'Excellent, Gilles Moreau, Daniil Shantsev. Efficient use of sparsity by direct solvers applied to 3D controlled-source EM problems. [Research Report] RR-9220, Inria Grenoble Rhône-Alpes; LIP - ENS Lyon. 2018, pp.26. ⟨hal-01912713⟩

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