A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods. 1. Introduction. We describe a method for computing an incomplete factorization of the inverse of a general sparse matrix A 2 IR nn. The resulting...

The computational time required by interior-point methods is often dominated by the solution of linear systems of equations. An efficient specialized interior-point algorithm for primal block-angular problems has been used to solve these systems by combining Cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking constrai...

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...

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

A Newton-Krylov algorithm is presented for the compressible Navier-Stokes equations in three dimensions on unstructured grids. The algorithm uses a preconditioned matrix-free Krylov method to solve the linear system that arises in the Newton iterations. Incomplete factorization is used as the preconditioner, based on an approximate Jacobian matrix after the reverse Cuthill-McKee reordering of t...

In this paper an approach is proposed for preconditioning large general sparse matrices. This approach combines the scalability of explicit preconditioners with the preconditioning eeciency of incomplete factorizations. Several algorithms resulting from this approach are presented. Both the preconditioning eeciency and the cost of applying this preconditioner are tested. The experiments indicat...

A parallel implementation of the preconditioned conjugate residual (PCR) method is described. The method is used to solve the discretized generalised Stokes problem derived from the simulation of complex 2D axisymetrical hot metal forming process. We numerically show that the use of a simple diagonal block (BDS) preconditioner results in a high level of parallelism. Nevertheless in 2D, the iter...