Clustered Edge-By-Edge Preconditioners For Non-Symmetric Finite Element Equations

. In this paper we present new preconditioners for implicit edge-based computations inspired on the concept of clustered element-by-element preconditioners. These new globally defined preconditioners employ product decompositions of clusters of edges matrices obtained from the grouping of edges into superedges. A performance study of these new preconditioners is performed on the CRAY J90 parallel computer. We analyse several flow problems discretized by the SUPG formulation using GMRES as iterative driver. Catabriga, Martins, Coutinho and Alves 1 INTRODUCTION Parallel supercomputers are nowadays widely used in large-scale finite element flow simulations. Several examples may be found, for instance, in Tezduyar. 1 In such large-scale problems, the solution of nonlinear systems of equations involving millions of unknowns may be required. In these cases, Krylov space based iterative update techniques 2 are used for the solution of the equation systems arising from finite element di..

Some Finite Element Computational Strategies for Large-Scale Flow Problems in High Performance Computers

In this paper we present some computational strategies tailored for the Finite Element solution of large-scale flow problems in high performance computers. Reduced Integration techniques and edge-based data structures are studied. We also introduce new preconditioners for implicit schemes based on superedges clustering. The performance of these new computational strategies is evaluated on the Cray J90 and SGI/Origin 2000 parallel computers. 1 Introduction Parallel supercomputers are widely used in large-scale finite element flow simulation [1]. Because the supercomputer architecture is different than uniprocessor computer, the performance of this machine increase when the codes are designed to take advantage of the new design. Low order elements are used in finite element analysis by their simplicity and adaptability to any domain. For these kind of elements we present here some finite element computational strategies for large-scale flow problems [2]. These strategies are separated..

An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors [24]. In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented