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Combined Preconditioning with Applications in Reservoir Simulation

Authors
  • Hu, Xiaozhe
  • Wu, Shuhong
  • Wu, Xiao-Hui
  • Xu, Jinchao
  • Zhang, Chen-Song
  • Zhang, Shiquan
  • Zikatanov, Ludmil
Type
Preprint
Publication Date
Feb 15, 2013
Submission Date
May 28, 2012
Identifiers
arXiv ID: 1205.6113
Source
arXiv
License
Yellow
External links

Abstract

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 standalone algebraic multigrid method or the incomplete factorization preconditioner.

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