Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems

Pascal Have (1) , Roland Masson (1) , Frédéric Nataf (2, 3) , Mikolaj Szydlarski (2, 4) , Hua Xiang (5) , Tao Zhao (2)

1 IFPEN - IFP Energies nouvelles
2 LJLL - Laboratoire Jacques-Louis Lions
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
4 GRAND-LARGE - Global parallel and distributed computing
5 Department of Mathematics [Wuhan]

We consider the solving of linear systems arising from porous media flow simulations with high heterogeneities. Using a Newton algorithm to handle the non-linearity leads to the solving of a sequence of linear systems with different but similar matrices and right hand sides. The parallel solver is a Schwarz domain decomposition method. The unknowns are partitioned with a criterion based on the entries of the input matrix. This leads to substantial gains compared to a partition based only on the adjacency graph of the matrix. From the information generated during the solving of the first linear system, it is possible to build a coarse space for a two-level domain decomposition algorithm that leads to an acceleration of the convergence of the subsequent linear systems. We compare two coarse spaces: a classical approach and a new one adapted to parallel implementation.

Domaines: Analyse numérique [math.NA]

Pascal Have, Roland Masson, Frédéric Nataf, Mikolaj Szydlarski, Hua Xiang, et al.. Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems. SIAM Journal on Scientific Computing, 2013, 35 (3), pp.C284-C302. ⟨hal-00611997v2⟩