In this paper, we consider linear systems arising in static tire equilibrium computation. The heterogeneous material properties, nonlinear constraints, and a 3D nite element formulation make the linear systems arising in tire design diicult to solve by iterative methods. An analysis of matrix characteristics attempts to explain this negative eeect. This paper focuses on two preconditioning tech...

This paper tests a number of ILU-type preconditioners for solving indeenite linear systems which arise from complex applications such as Computational Fluid Dynamics. Both point and block preconditioners are considered. The paper focuses on ILU factorization which can be computed with high accuracy by allowing liberal amounts of ll-in. A number of strategies for enhancing the stability of the f...

We present an algebraic structured preconditioner for the iterative solution of large sparse linear systems. The preconditioner is based on a multifrontal variant of sparse LU factorization used with nested dissection ordering. Multifrontal factorization amounts to a partial factorization of a sequence of logically dense frontal matrices, and the preconditioner is obtained if structured factori...

We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete ...

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear nite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact nite-di erence Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz me...

In this paper Rannacher-Turek non-conforming rotated bilinear finite elements are applied for the numerical solution of second order elliptic boundary value problems. The preconditioned conjugate gradient method is used for the iterative solution of the arising linear algebraic system. A locally optimized construction for an M-matrix approximation of the global stiffness matrix is the first ste...

The present paper is dedicated to the preconditioning of boundary element matrices in wavelet coordinates. We investigate the incomplete Cholesky factorization for a pattern which includes also the coefficients of all off-diagonal bands associated with the level-level-interactions. The pattern is chosen in such a way that the incomplete Cholesky factorization is computable in log-linear complex...

Incomplete LU factorizations are among the most eeective preconditioners for solving general large, sparse linear systems arising from practical engineering problems. This paper shows how an ILU factorization may be easily computed in sparse skyline storage format, as opposed to traditional row-by-row schemes. This organization of the factorization has many advantages, including its amenability...

Incomplete LU factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indeenite matrices. However, their failure rate is still too high for them to be useful as black-box library software for general matrices. Besides fatal breakdowns due to zero pivots, the major causes of failure are inaccuracy, and instability of the triangular solves. When ...

A class of parallel incomplete factorization preconditionings for the solution of large linear systems is investigated. The approach may be regarded as a generalized domain decomposition method. Adjacent subdomains have to communicate during the setting up of the precon-ditioner, and during the application of the preconditioner. Overlap is not necessary to achieve high performance. Fill-in leve...