A new Newton-Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs. However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. The developed preconditioner is...

We introduce a multi-level restricted Schwarz preconditioner with a special coarse-to-fine interpolation and show numerically that the new preconditioner works extremely well for some difficult large systems of linear equations arising from some optimization problems constrained by the incompressible Navier-Stokes equations. Performance of the preconditioner is reported for parameters including...

Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained. Then, these algorithms are used for computing a block ILU preconditioner for the block tridiagonal linear system of equations. Some numerical results are given to show the robustness and efficiency of the preconditioner. The performance of the proposed preconditioner is compared with...

‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wave length components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an e cient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition...

A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh size...

We propose a new two-level nonlinear additive Schwarz preconditioned inexact Newton algorithm (ASPIN). The two-level nonlinear preconditioner combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. Our parallel numerical results based on a lid-driven cavity incompressible flow problem show that the new two-level ASPIN is nearly scalable with respect...

The natural preconditioner defined by local potentials is effective in the truncated Newton method for minimizing large scale biomolecular potential energy functions. This paper extends its definition, and proposes an algorithm for generating the sparse pattern of the preconditioner from the primary structure of a molecular system with N atoms. It shows that the implementation of the new compre...

In this paper we introduce a Relaxed Dimensional Factorization (RDF) preconditioner for saddle point problems. Properties of the preconditioned matrix are analyzed and compared with those of the closely related Dimensional Splitting (DS) preconditioner recently introduced by Benzi and Guo [7]. Numerical results for a variety of finite element discretizations of both steady and unsteady incompre...