Combined preconditioning with applications in reservoir simulation

Xiaozhe Hu, Shuhong Wu, Xiao Hui Wu, Jinchao Xu, Chen Song Zhang, Shiquan Zhang, Ludmil Zikatanov

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e., smoother) and (2) a preconditioner. The resulting preconditioner, which we refer to as a combined preconditioner, is much more robust and efficient than the iterative method and preconditioner when used in Krylov subspace methods. We prove that the combined preconditioner is positive definite and show estimates on the condition number of the preconditioned system. We combine an algebraic multigrid method and an incomplete factorization preconditioner to test the proposed framework on problems in petroleum reservoir simulation. Our numerical experiments demonstrate noticeable speed-up when we compare our combined method with the stand-alone algebraic multigrid method or the incomplete factorization preconditioner.

Original languageEnglish (US)
Pages (from-to)507-521
Number of pages15
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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