Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability, but need to be used with an appropriate preconditioner (e.g., ILU, AMG, Gauss-Seidel, etc.) for proper convergence. The choice of an effective preconditioner is highly problem dependent. We propose a novel fully algebraic...

We propose variants of the modified incomplete Cholesky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

In this paper we implement the element-by-element preconditioner and inexact Newton-Krylov methods (developed in the past) for solving stabilized computational fluid dynamics (CFD) problems with spectral methods. Two different approaches are implemented for speeding up the process of solving both steady and unsteady incompressible Navier-Stokes equations. The first approach concerns the applica...

The aim of this article is to shows that hierarchical matrices (H-matrices) provide a means to efficiently precondition linear systems arising from the streamline diffusion finite-element method applied to convection-dominated problems. Approximate inverses and approximate LU decompositions can be computed with logarithmic-linear complexity in the standard Hmatrix format. Neither the complexity...

A novel algorithm for computing the incomplete-LU and Cholesky factorization with 0 fill-in on a graphics processing unit (GPU) is proposed. It implements the incomplete factorization of the given matrix in two phases. First, the symbolic analysis phase builds a dependency graph based on the matrix sparsity pattern and groups the independent rows into levels. Second, the numerical factorization...

This paper presents a systematic comparison of recently developed iterative methods for solving nonsymmetric linear equations arising from the numerical simulation of semiconductor processing. A non comprehensive survey of the literature concerning iterative solvers is given including theoretical studies as well as current articles on practical applications. In particular, we consider the conju...

We present an efficient implicit time stepping method for Discontinuous Galerkin discretizations of the compressible Navier-Stokes equations on unstructured meshes. The Local Discontinuous Galerkin method is used for the discretization of the viscous terms. For unstructured meshes, the Local Discontinuous Galerkin method is known to produce non-compact discretizations. In order to circumvent th...

We propose a preconditioning technique that is applicable in a “black box” fashion to linear systems arising from second order scalar elliptic PDEs discretized by finite differences or finite elements with nodal basis functions. This technique is based on an algebraic multilevel scheme with coarsening by aggregation. We introduce a new aggregation method which, for the targeted class of applica...

This paper discusses performance optimization on the dynamical core of global numerical weather prediction model in Global/Regional Assimilation and Prediction System (GRAPES). GRAPES is a new generation of numerical weather prediction system developed and currently used by Chinese Meteorology Administration. The computational performance of the dynamical core in GRAPES relies on the efficient ...

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the ...