We develop a drop-threshold incomplete Cholesky preconditioner which uses blocked data structures and computational kernels for improved performance on computers with one or more levels of cache memory. The techniques are similar to those used for Cholesky factorization in sparse direct solvers. We report on the performance of our preconditioned conjugate gradient solver on sparse linear system...

AILU: A Preconditioner Based on the Analytic Factorization of the Elliptic Operator Martin J. Gander and Frederic Nataf Department of Mathematics, McGill University, Montreal, Canada and CMAP, CNRS UMR7641, Ecole Polytechnique, Palaiseau, France We investigate a new type of preconditioner for large systems of linear equations stemming from the discretization of elliptic symmetric partial differ...

We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct loca...

Aerodynamic flows involve features with a wide range of spatial and temporal scales which need to be resolved in order to accurately predict desired engineering quantities. While computational fluid dynamics (CFD) has advanced considerably in the past 30 years, the desire to perform more complex, higher-fidelity simulations remains. Present day CFD simulations are limited by the lack of an effi...

A new multilevel preconditioner is proposed for the iterative solution of two dimensional discrete second order elliptic PDEs. It is based a recursive block incomplete factorization of the system matrix partitioned in a two-by-two block form, in which the submatrix related to the rst block of unknowns in approximated by a MILU(0) factorization, and the Schur complement computed from a diagonal ...

In optimizing the iteration parameters of the SIMPLE-like numerical procedure, a genetic algorithm (GA) which searches for a minimum calculation time in a space of iteration numbers was developed. A methodology has been presented for the numerical solution of natural convection in a squeezed cavity at Rayleigh number of 10 and Pr number of 10.0. The pressure correction equation was employed in ...

This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate LDLt factorization by eliminating the unknowns layer by layer starting from an absorbing layer or boundary condition. The central idea of this paper is to approximate ...

The standard Incomplete LU (ILU) preconditioners often fail for general sparse indeenite matrices because they give rise tòunstable' factors L and U. In such cases, it may be attractive to approximate the inverse of the matrix directly. This paper focuses on approximate inverse preconditioners based on minimizing kI?AMk F , where AM is the preconditioned matrix. An iterative descent-type method...