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 stand-alone algebraic multigrid method or the incomplete factorization preconditioner.
Original language | English (US) |
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Pages (from-to) | 507-521 |
Number of pages | 15 |
Journal | Multiscale Modeling and Simulation |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - 2013 |
All Science Journal Classification (ASJC) codes
- General Chemistry
- Modeling and Simulation
- Ecological Modeling
- General Physics and Astronomy
- Computer Science Applications