This paper addresses the problem of computing preconditioners for solving linear systems of equations with a sequence of slowly varying matrices. This problem arises in many important applications. For example, a common situation in computational fluid dynamics, is when the equations change only slightly, possibly in some parts of the physical domain. In such situations it is wasteful to recomp...

Non-orthogonal spline wavelets are developed for Galerkin BEM. The proposed wavelets have compact supports and closed-form expressions. Besides of it, one can choose arbitrarily the order of vanishing moments of the wavelets independently of order of B-splines. Sparse coefficient matrices are obtained by truncating the small elements a priori. The memory requirement and computational time can b...

Standard (single-level) incomplete factorization preconditioners are known to successfully accelerate Krylov subspace iterations for many linear systems. The classical Modified Incomplete LU (MILU) factorization approach improves the acceleration given by (standard) ILU approaches, by modifying the non-unit diagonal in the factorization to match the action of the system matrix on a given vector...

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...

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...

Application demands and grand challenges in numerical simulation require for both highly capable computing platforms and efficient numerical solution schemes. Power constraints and further miniaturization of modern and future hardware give way for multiand manycore processors with increasing fine-grained parallelism and deeply nested hierarchical memory systems – as already exemplified by recen...

A Newton-Krylov method is developed for the solution of the steady compressible NavierStokes equations using a Discontinuous Galerkin (DG) discretization on unstructured meshes. An element Line-Jacobi preconditioner is presented which solves a block tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (BlockILU(0)) is also presented as a precondit...

The fields scattered by dielectric objects placed inside parallel-plate waveguides and periodic structures in two dimensions may efficiently be computed via a finitedifference frequency-domain (FDFD) method. This involves large, sparse linear systems of equations that may be solved using preconditioned Krylov subspace methods. Our preconditioners involve fast discrete trigonometric transforms a...

Numerical performance of two different preconditioning approaches, modified SSOR (MSSOR) preconditioner and incomplete factorization with zero fill-in (ILU0) preconditioner, is compared for the iterative solution of symmetric indefinite linear systems arising from finite element discretization of the Biot’s consolidation equations. Numerical results show that the nodal ordering affect the perfo...

We propose an incomplete multifrontal LU-factorization (IMF) preconditioner that extends supernodal multifrontal methods to incomplete factorizations. It can be used as a preconditioner in a Krylov-subspace method to solve large-scale sparse linear systems with an element structure; e.g., those arising from a finite element discretization of a partial differential equation. The fact that the el...