Sparse symmetric indefinite linear systems of equations arise in numerous practical applications. In many situations, an iterative method is the method of choice but a preconditioner is normally required for it to be effective. In this paper, the focus is on a class of incomplete factorization algorithms that can be used to compute preconditioners for symmetric indefinite systems. A limited mem...

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...

Consider the solution of large sparse symmetric positive de nite linear systems using the preconditioned conjugate gradient method. On sequential architectures, incomplete Cholesky factorizations provide ef13 fective preconditioning for systems from a variety of application domains, some of which may have widely di ering preconditioning requirements. However, incomplete factorization based prec...

Consider the solution of large sparse symmetric positive de nite linear systems using the preconditioned conjugate gradient method. On sequential architectures, incomplete Cholesky factorizations provide effective preconditioning for systems from a variety of application domains, some of which may have widely di ering preconditioning requirements. However, incomplete factorization based precond...

Incomplete LU factorization is a valuable preconditioning approach for sparse iterative solvers. An “ideal” but inefficient preconditioner for the iterative solution of Ax = b is A−1 itself. This paper describes a preconditioner based on sparse approximations to partitioned representations of A−1, in addition to the results of implementation of the proposed method in a shared memory parallel en...

The purpose of our work is to provide a method which exploits the parallel blockwise algorithmic approach used in the framework of high performance sparse direct solvers in order to develop robust preconditioners based on a parallel incomplete factorization. The idea is then to define an adaptive blockwise incomplete factorization that is much more accurate (and numerically more robust) than th...

A multigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code DANCIR This code simulates a wide variety of semiconductor devices by numerically solving the drift di usion equations The most time consuming aspect of the simulation is the solution of three linear systems within each iteration of the Gummel method The original version of DANCIR use...

F11DNF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose F11DNF computes an incomplete LU factorization of a complex sparse non-Hermitian matrix, represented in coordinate storage format. This factorization may be used as a preconditioner in combination w...

In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR( s ) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner imp...

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...