H. A. Van-der and . Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci

, Stat. Comput, vol.13, issue.2, pp.631-644, 1992.

Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput, vol.7, issue.3, pp.856-869, 1986.

S. T. Barnard, L. M. Bernardo, and H. D. Simon, An MPI implementation of the SPAI preconditioner on the t3E, Int. J. High Perform. Comput. Appl, vol.13, pp.107-128, 1999.

A. Brandt, S. F. Mccormick, and J. W. Ruge, Algebraic Multigrid (AMG) for Sparse Matrix Equations, p.21

A. H. Baker, T. Gamblin, M. Schulz, and U. M. Yang, Challenges of scaling algebraic multigrid across modern multicore architectures, p.23

, Distributed Processing Symposium (IPDPS), pp.275-286, 2011.

J. Park, M. Smelyanskiy, U. M. Yang, D. Mudigere, and P. Dubey, High-performance algebraic multigrid solver optimized for multi-core based 25 distributed parallel systems, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p.26

, SC '15, vol.54, pp.1-54, 2015.

V. Dolean, P. Jolivet, and F. Nataf, An Introduction to Domain Decomposition Methods, Society for Industrial and Applied Mathematics, p.28
URL : https://hal.archives-ouvertes.fr/cel-01100932

, PA, 2015.

N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein et al., A robust two-level domain decomposition preconditioner for systems of 30

C. R. Pdes and . Math, , vol.349, pp.1255-1259, 2011.

J. M. Gratien, An abstract object oriented runtime system for heterogeneous parallel architecture, Parallel and Distributed Processing, vol.32
URL : https://hal.archives-ouvertes.fr/hal-00788293

, Symposium Workshops PhD Forum (IPDPSW), pp.1203-1212, 2013.

F. Broquedis, J. Clet-ortega, S. Moreaud, N. Furmento, B. Goglin et al., hwloc: a generic framework for managing 34 hardware affinities in HPC applications, PDP 2010 -the 18th Euromicro International Conference on Parallel, p.35

. Computing, . Pisa, . Ieee, and . Italy, , 2010.

Y. Saad, Iterative Methods for Sparse Linear Systems, p.37, 2003.

J. Magras, P. Quandalle, and P. Bia, High-performance reservoir simulation with parallel ATHOS, SPE Reservoir Simulation Symposium, 2001.

J. Gratien, T. Guignon, J. Magras, P. Quandalle, and O. M. Ricois, Scalability and load balancing problems in parallel reservoir simulation, SPE Reservoir Simulation Symposium, vol.40, 2007.

E. Chow and A. Patel, Fine-grained parallel incomplete LU factorization, SIAM J. Sci. Comput, vol.37, issue.2, pp.169-193, 2015.

R. D. Falgout, J. E. Jones, and U. M. Yang, The design and implementation of hypre, a library of parallel high performance preconditioners

, Numerical Solution of Partial Differential Equations on Parallel Computers, pp.267-294, 2006.

C. Feng, S. Shu, and X. Yue, An improvement to the OpenMP version of BoomerAMG, High Performance Computing: 46 8th CCF Conference, HPC 2012, pp.1-11, 2012.

H. A. Schwarz, Uber einen grenzubergang durch alternierendes verfahren, vol.1870, pp.272-286

I. Aavatsmark, T. Barkve, Ø. Bøe, and T. Mannseth, Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media, J, p.50

, Comput. Phys, vol.127, issue.1, pp.2-14, 1996.

R. Eymard, C. Guichard, R. Herbin, and R. Masson, Vertex-centred discretization of multiphase compositional Darcy flows on general meshes
URL : https://hal.archives-ouvertes.fr/hal-01238550

. Geosci, , vol.16, pp.987-1005, 2012.

F. Boyer, F. Hubert, and S. Krell, Nonoverlapping Schwarz algorithm for solving two-dimensional m-DDFV schemes, IMA J. Numer. Anal, vol.30, issue.4, pp.1062-1100, 2010.

J. Droniou, R. Eymard, T. Gallouët, and R. Herbin, A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume 56 methods, Math. Models Methods Appl. Sci, vol.20, issue.02, pp.265-295, 2010.

J. Droniou, R. Eymard, and R. Herbin, Gradient schemes: generic tools for the numerical analysis of diffusion equations, ESAIM Math. Model. Numer
URL : https://hal.archives-ouvertes.fr/hal-01150517

, Anal, vol.50, issue.3, pp.749-781, 2016.

G. Guennebaud and B. Jacob, Eigen v3, 2010.

M. Christie and M. Blunt, Tenth SPE comparative solution project: A comparison of upscaling techniques, SPE Reserv. Eval. Eng, vol.4, issue.2, p.61, 2001.

P. Jolivet, F. Hecht, F. Nataf, and C. Prud'homme, Scalable domain decomposition preconditioners for heterogeneous elliptic problems, SC13 -63 International Conference for High Performance Computing, Networking, Storage and Analysis, vol.80, pp.1-80, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00939957

J. M. Tang, R. Nabben, C. Vuik, and Y. A. Erlangga, Comparison of two-level preconditioners derived from deflation, domain decomposition and 66 multigrid methods, J. Sci. Comput, vol.39, issue.3, pp.340-370, 2009.

M. W. Gee, C. M. Siefert, J. J. Hu, R. S. Tuminaro, and M. G. Sala, ML 5.0 Smoothed Aggregation User's Guide

M. Blatt and P. Bastian, The iterative solver template library, International Workshop on Applied Parallel Computing, pp.666-675, 2006.

P. Petsc-home, , 2018.

P. Trilinos-home, , 2018.

V. Minden, B. Smith, and M. G. Knepley, Preliminary implementation of PETSc using GPUs, GPU Solutions to Multi-Scale Problems in Science and Engineering, vol.5, pp.131-140, 2013.


M. Kreutzer, J. Thies, M. Röhrig-zöllner, A. Pieper, F. Shahzad et al., GHOST: building blocks 7 for high performance sparse linear algebra on heterogeneous systems, Int. J. Parallel Program, vol.45, issue.5, pp.1046-1072, 2017.

R. D. Blumofe, C. F. Joerg, B. C. Kuszmaul, C. E. Leiserson, K. H. Randall et al., Cilk: An efficient multithreaded runtime system, J. Parallel Distrib, vol.9

, Comput, vol.37, issue.1, pp.55-69, 1996.

E. Ayguadé, R. M. Badia, P. Bellens, D. Cabrera, A. Duran et al., , p.11

R. Mayo, J. M. Pérez, J. Planas, and E. S. Quintana-ortí, Extending OpenMP to survive the heterogeneous multi-core era, Int. J. Parallel Program, vol.38, p.12

, , pp.440-459, 2010.

C. Augonnet, S. Thibault, R. Namyst, and P. Wacrenier, StarPU: a unified platform for task scheduling on heterogeneous multicore architectures, p.14
URL : https://hal.archives-ouvertes.fr/inria-00384363

, Concurr. Comput. Pract. Exp, vol.23, issue.2, pp.187-198, 2011.

J. V. Lima, T. Gautier, V. Danjean, B. Raffin, and N. Maillard, Design and analysis of scheduling strategies for multi-CPU and multi-GPU architectures
URL : https://hal.archives-ouvertes.fr/hal-01132037