Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

Ani Anciaux-Sedrakian, Peter Gottschling, Jean-Marc Gratien, Thomas Guignon
IFP Energies nouvelles, 1-4 avenue de Bois-Preau, 92852 Rueil-Malmaison Cedex France
Oil & Gas Science and Technology – Rev. IFP Energies nouvelles, 2014


   author={Anciaux-Sedrakian, Ani and Gottschling, Peter and Gratien, Jean-Marc and Guignon, Thomas},

   title={Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures},



   journal={Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles},



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In the pastfew years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO2 geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is "are current algorithms and software able to use these new technologies efficiently?" The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU- consuming part of such simulators. This paper proposes a survey on various solver and preconditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some preconditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation.
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