Combinative preconditioning based on Relaxed Nested Factorization and Tangential Filtering preconditioner

Pawan Kumar (1) , Laura Grigori (1) , Frédéric Nataf (2) , Qiang Niu (3)

1 GRAND-LARGE - Global parallel and distributed computing
2 LJLL - Laboratoire Jacques-Louis Lions
3 Xiamen University

The problem of solving block tridiagonal linear systems arising from the discretization of PDE is considered. The nested factorization preconditioner introduced by [J. R. Appleyard and I. M. Cheshire, {\it Nested Factorization}, SPE 12264, presented at the Seventh SPE Symposium on Reservoir Simulation, San Francisco, 1983] is an effective preconditioner for certain class of problems and a similar method is implemented in Schlumerger's Eclipse oil reservoir simulator. In this paper, a relaxed version of Nested Factorization preconditioner is proposed as a replacement to ILU(0). Indeed, the proposed preconditioner is SPD and leads to a stable splitting if the input matrix is S.P.D.\,. For ILU(0), equivalent properties hold if the input matrix is a M-matrix. Moreover it has no storage cost. Effective multiplicative/additive preconditioning is achieved in combination with Tangential filtering preconditioner with the filter vector chosen as vector of $ones$. Numerical tests are carried out with both additive and multiplicative combinations. With this setup the new preconditioner is as robust as the combination of ILU(0) with tangential filtering preconditioner.

Keywords: preconditioner; linear system; frequency filtering decomposition; GMRES; nested factorization; incomplete LU; eigenvalues

Domains: Modeling and Simulation

Pawan Kumar, Laura Grigori, Frédéric Nataf, Qiang Niu. Combinative preconditioning based on Relaxed Nested Factorization and Tangential Filtering preconditioner. [Research Report] RR-6955, INRIA. 2009. ⟨inria-00392881⟩