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.

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

Domaines: Modélisation et 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⟩