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Mixed precision sparse direct solver applied to 3D wave propagation


Efficient numerical simulation of wave propagation phenomena is needed in several applications such as seismic imaging, non-destructive testing, or helioseismology. In this work, we consider time-harmonic waves and the hybridizable discontinuous Galerkin discretization method, for which the efficiency of the wave propagator relies on the performance of finding the solution of systems of sparse linear equations. These systems have multiple sparse right-hand sides associated with several sources. This motivates the use of direct solvers which can efficiently reuse the LU factors to compute the solution of multiple right-hand sides at the cost however of a high memory footprint. Fortunately, matrices arising from the discretization of partial differential equations have been shown to have a low-rank property and the Block-Low Rank (BLR) format has been used to design fast direct solvers with reduced asymptotic complexity. In very recent work, the authors have described how the BLR LU factorization algorithm can benefit from mixed precision arithmetic. In the context of 3D frequency-domain wave equations, the BLR factorization in 32-bit single precision arithmetic has been shown to provide accurate enough solutions. In this talk, we will explain why and how we can exploit lower precision formats (such as 24 and 16 bit arithmetics) in the representation of BLR blocks, while preserving a satisfactory accuracy. This allows us to reduce the memory footprint of the solver by further compressing both the LU factor matrices and the working space without affecting the precision of the solution. The performance using recent features of the MUMPS sparse direct solver, including mixed precision, will be analyzed with large-scale 3D acoustic and elastic experiments using hawen software.
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hal-03887660 , version 1 (06-12-2022)


  • HAL Id : hal-03887660 , version 1


Patrick Amestoy, Alfredo Buttari, Florian Faucher, Jean-Yves L'Excellent, Matthieu Gerest, et al.. Mixed precision sparse direct solver applied to 3D wave propagation. 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2022), Jun 2022, Oslo, Norway. ⟨hal-03887660⟩
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