In this paper we present a new incomplete LU decomposition which is based on an existing sparse direct solver. In contrast to many incomplete LU decompositions this ILU incorporates information about the inverse factors L−1 and U−1 which have direct influence on the dropping strategy. We demonstrate in several large scale examples that this implementation constructs a robust preconditioner.

The analysis of preconditioners based on incomplete Cholesky factorization in which the neglected (dropped) components are orthogonal to the approximations being kept is presented. General estimate for the condition number of the preconditioned system is given which only depends on the accuracy of individual approximations. The estimate is further improved if, for instance, only the newly compu...

We consider parallel preconditioning schemes to accelerate the convergence of Conjugate Gradients (CG) for sparse linear system solution. We develop methods for constructing and applying preconditioners on multiprocessors using incomplete factorizations with selective inversion for improved latency-tolerance. We provide empirical results on the efficiency, scalability and quality of our precond...

The efficient algorithm is presented for the analysis of electromagnetic scattering from composite structures with coexisting open and closed conductors. A hybrid combined-field integral equation-the improved electric-field integral equation (CFIE-IEFIE) formulation with the incomplete LU factorization (ILU) preconditioner is proposed. Numerical results are given to demonstrate that the efficie...

We show that a novel class of preconditioners, designed by Pravin Vaidya in 1991 but never before implemented, is remarkably robust and can outperform incomplete-Cholesky preconditioners. Our test suite includes problems arising from finitedifferences discretizations of elliptic PDEs in two and three dimensions. On 2D problems, Vaidya’s preconditioners often outperform drop-tolerance incomplete...

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...

We present a new parallelizable preconditioner that is used as the local component for a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attracting numerical behaviour and compare it to the regular BPS. Finally, to alleviate the construction cost of this new preconditioner, that requires the explicit computat...

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)...

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are formed as a means to solve rectangular matrices from linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed ...