The ILU method for finite-element discretizations
Journal of Computational and Applied Mathematics
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Generalized approximate inverse finite element matrix techniques
Neural, Parallel & Scientific Computations
Towards a fast parallel sparse symmetric matrix-vector multiplication
Parallel Computing - Linear systems and associated problems
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Journal of Computational Physics
Parallel Approximate Finite Element Inverse Preconditioning on Distributed Systems
ISPDC '04 Proceedings of the Third International Symposium on Parallel and Distributed Computing/Third International Workshop on Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks
Diagonally-striped matrices and approximate inverse preconditioners
Journal of Computational and Applied Mathematics
Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Parallel solution of sparse linear systems arising in advection–diffusion problems
Euro-Par'05 Proceedings of the 11th international Euro-Par conference on Parallel Processing
Adaptive Pattern Research for Block FSAI Preconditioning
SIAM Journal on Scientific Computing
Hi-index | 7.29 |
Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency E"p^* larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that E"p^* for p in the upper range may be much improved if PCG-FSAI is implemented on CLX.