Based on the work of Wang and Li [A new preconditioned AOR iterative method for L-matrices, J. Comput. Appl. Math. 229 (2009) 47-53], in this paper, a new preconditioner for the AOR method is proposed for solving linear systems whose coefficient matrix is an L-matrix. Several comparison theorems are shown for the proposed method with two preconditioners. It follows from the comparison results t...

This study develops an OpenMP scheme to parallel the preconditioned conjugate gradient methods (PCG) in shared memory computers. The proposed method is simple and systematic, so a minor change in traditional PCG methods may produce effective parallelism. At first, the global stiffness matrix is renumbered in order to produce a parallel three-line form matrix, and a subroutine only needs to be c...

In this paper we are concerned with the spectral analysis of the sequence of preconditioned matrices {P−1 n An(a, m1,m2, k)}n, where n = (n1, n2), N(n) = n1n2 and where An(a, m1, m2 , k) ∈ RN(n)×N(n) is the symmetric two-level matrix coming from a high–order Finite Difference (FD) discretization of the problem

A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous...

A recently developed robust Algebraic Multigrid (AMG) method for the efficient solution of 3D nonlinear electrostatic and magnetostatic field problems will be presented. The method is directed to large matrix equations which arise from finite element (FE) discretization where AMG is used as a preconditioner in the Preconditioned Conjugate Gradient (PCG) method. Numerical results will demonstrat...

Three-dimensional device simulations of sidewall trench-isolated MOSFETs involve Linear systems of equations that are extremely ill-conditioned if the geometric channel length exceeds 2pm. Since conventional preconditioned iterative methods tend to fail in such cases we have implemented a robust iterative linear solver using a hierarchy of incomplete factorizations of the coefficient matrix.

A preconditioned conjugate gradient method was implemented into an iteration on a program for data estimation of breeding values, and its convergence characteristics were studied. An algorithm was used as a reference in which one fixed effect was solved by Gauss-Seidel method, and other effects were solved by a second-order Jacobi method. Implementation of the preconditioned conjugate gradient ...

In this paper, we apply the preconditioned Lanczos (PL) method to compute the minimum eigenvalue of a symmetric positive definite Toeplitz matrix. The sine transform-based preconditioner is used to speed up the convergence rate of the PL method. The resulting method involves only Toeplitz and sine transform matrix-vector multiplications and hence can be computed efficiently by fast transform al...

A preconditioned five-equation two-phase model coupled with an interface sharpening technique is introduced for simulation of a wide range of multiphase flows with both high and low Mach regimes. Harten-Lax-van Leer-Contact (HLLC) Riemann solver is implemented for solving the discretized equations while tangent of hyperbola for interface capturing (THINC) interface sharpening method is applied ...

In many statistical applications one must solve linear systems corresponding to large, dense, and possibly irregularly structured covariance matrices. These matrices are often illconditioned; for example, the condition number increases at least linearly with respect to the size of the matrix when observations of a random process are obtained from a fixed domain. This paper discusses a precondit...