A multi-level preconditioned iterative method based on a multi-level block ILU factoriza-tion preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coef-cient matrices usually have several rows with zero diagonal values that may cause stability diiculty in standard ILU factoriza...

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...

Incomplete LU factorization (ILU) techniques are a well-known class of preconditioners, often used in conjunction with Krylov accelerators for the iterative solution of linear systems of equations. However, for certain problems, ILU factorizations can yield factors that are unstable, and in some cases quite dense. Reordering techniques based on permuting the matrix prior to performing the facto...

A Newton-Krylov method is developed for the solution of the steady compressible Navier-Stokes 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 (Block-ILU(0)) is also presented as a precond...

Standard preconditioning techniques based on incomplete LU (ILU) factorizations offer a limited degree of parallelism, in general. A few of the alternatives advocated so far consist of either using some form of polynomial preconditioning, or applying the usual ILU factorization to a matrix obtained from a multicolor ordering. In this paper we present an incomplete factorization technique based ...

A recently proposed Minimum Discarded Fill (MDF ) ordering (or pivoting) technique is e ective in nding high quality ILU (`) preconditioners, especially for problems arising from unstructured nite element grids. This algorithm can identify anisotropy in complicated physical structures and orders the unknowns in a \preferred" direction. However, the MDF ordering is costly, when ` increases. In t...

The standard incomplete LU (ILU) preconditioners often fail for general sparse in-deenite 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 met...

A new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory. This technique combines Kronecker product approximation and wavelet sparsification for the Kronecker product factors. The user is only required to supply a procedure for computation of each entry of the given matrix. ...

An efficient numerical bifurcation and continuation method for the Navier–Stokes equations in cylindrical geometries is presented and applied to a nontrivial fluid dynamics problem, the flow in a cylindrical container driven by differential rotation. The large systems that result from discretizing the Navier–Stokes equations, especially in regimes where inertia is important, necessitate the use...

A Newton–Krylov method is developed for the solution of the steady compressible Navier– Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast ...