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ALGEBRAIC DOMAIN DECOMPOSITION METHODS FOR HIGHLY HETEROGENEOUS PROBLEMS
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DOI：10.1137/110842648.png)
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We consider the solution of linear systems arising from porous media flow simulations with high heterogeneities. Using a Newton algorithm to handle the nonlinearity leads to solving 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 solution 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.
Keyword:
domain decomposition method
deflation
high performance computing
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Multiscale finite element methods for high-contrast problems using local spectral basis functions
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