It is well known that standard incomplete factorization (IC) methods exist for M-matrices 14] and that modiied incomplete factorization (MIC) methods exist for weakly diagonally dominant matrices 8]. The restriction to these classes of matrices excludes many realistic general applications to discretized partial diieren-tial equations. We present a technique to avoid this problem by making an in...

In this paper we analyze a preconditioner for mixed finite element systems arising in the approximation of a second order lliptic problem with Neumann boundary conditions by triangular non-conforming elements. This problem stems from the so called rojection methods for the unsteady Navier–Stokes equations and is one of the most computationally intensive parts of the method. he present study is ...

This paper presents an investigation into fault tolerance for the fine-grained parallel algorithm for computing an incomplete LU factorization. Results concerning the convergence of the algorithm with respect to the occurrence of faults, and the impact of any sub-optimality in the produced incomplete factors in Krylov subspace solvers are given. Numerical tests show that the simple algorithmic ...

In this paper, we investigate GPU based parallel triangular solvers systematically. The parallel triangular solvers are fundamental to incomplete LU factorization family preconditioners and algebraic multigrid solvers. We develop a new matrix format suitable for GPU devices. Parallel lower triangular solvers and upper triangular solvers are developed for this new data structure. With these solv...

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...

In this paper, we present SILCA-Newton-Krylov, a new method for accurate, efficient and robust timedomain VLSI circuit simulation. Similar to SPICE, SILCA-Newton-Krylov uses time-difference and Newton-Raphson for solving nonlinear differential equations from circuit simulation. But different from SPICE, SILCA-Newton-Krylov explores a preconditioned flexible generalized minimal residual (FGMRES)...

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 ...

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 ...

Funding Information Russian Science Foundation, Grant/Award Number: 14-31-00024 Summary The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier–Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov–Galerkin finite element method for the Oseen problem leads to the system of algebraic equati...