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Journal Articles SIAM Journal on Scientific Computing Year : 2013

Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems

Abstract

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.
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Dates and versions

hal-00611997 , version 1 (27-07-2011)
hal-00611997 , version 2 (19-02-2013)

Identifiers

  • HAL Id : hal-00611997 , version 2

Cite

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⟩
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