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

23 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. © 2013 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)507-521
Number of pages15
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - Jul 9 2013
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

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


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