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With the ultimate goal of designing a scalable parallel preconditioner for reservoir simulation problems, we combine domain decomposition ideas (prove suitable for parallelization) with incomplete factorizations (which are standard in reservoir simulation) at subdomain level. We introduce an ILU(k)-based two-level domain decomposition preconditioner and compare its performance with a two-level ILU(k)-Block-Jacobi preconditioner.

An algebraic ILU(k) based two-level domain decomposition preconditioner