Despite the fact that iterative solution techniques are recently gaining recognition among practitioners and finding their way into commercial software arena, the current state of the art in iterative methods remains unsatisfactory in many respects. Users of large production codes such as ANSYS, NASTRAN, ALGOR, SDRC, EMRC and ANSYS often observe many “bad” cases resulting from poorly conditione...

An efficient matrix solver is critical to the analytical placement. As the size of the matrix becomes huge, the multilevel methods tum out to be more efficient and more scalable. Algebraic Multigrid (AMG) is a multilevel technique to speedup the iterative matrix solver [lo]. We apply the algebraic multigrid method to solve the linear equations that arise from the analytical placement. A layout ...

Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficient finite element solution of some anisotropic problems, we hereby demonstrate that the processes...

In large-scale scienti c computing, linear sparse solver is one of the most time-consuming process. In GeoFEM, various types of preconditioned iterative method is implemented on massively parallel computers. It has been well-known that ILU(0) factorization is very e ective preconditioning method for iterative solver. But it's also well-known that this method requires global data dependency and ...

In this paper we derive a posteriori error estimates for the compositional model of multiphase Darcy flow in porous media, consisting of a system of strongly coupled nonlinear unsteady partial differential and algebraic equations. We show how to control the dual norm of the residual augmented by a nonconformity evaluation term by fully computable estimators. We then decompose the estimators int...

We consider the numerical solution of discretised Hamilton-Jacobi-Bellman (HJB) equations with applications in finance. For the discrete linear complementarity problem arising in American option pricing, we study a policy iteration method. We show, analytically and numerically, that, in standard situations, the computational cost of this approach is comparable to that of European option pricing...

We outline the basic features of a spectral multidomain penalty method (SMPM)based solver for the pressure Poisson equation (PPE) with Neumann boundary conditions, as encountered in the time-discretization of the incompressible Navier-Stokes equations. One one hand, the SMPM discretization enables robust under-resolved simulations without sacrificing high accuracy. On the other, the solution of...

We consider the computation of a few eigenvectors and corresponding eigen-values of a large sparse nonsymmetric matrix. In order to compute eigenvaluesin an isolated cluster around a given shift we apply shift-and-invert Arnoldi’smethod with and without implicit restarts. For the inner iterations we useGMRES as the iterative solver. The costs of the inexact solves are measured<l...

We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centersand in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver t...