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Parallelization Strategies for ElementbyElement PCG Solver using HPF for Unstructured FE Applications on Linux clusters
"... Parallel implementation of an unstructured Finite Element (FE) solver using the Preconditioned Conjugate Gradient (PCG) Method is described here. High Performance Fortran (HPF) has been used with the implementation based on a 32node Pentium II 350MHz cluster running LINUX. The PCG solver is set up ..."
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Parallel implementation of an unstructured Finite Element (FE) solver using the Preconditioned Conjugate Gradient (PCG) Method is described here. High Performance Fortran (HPF) has been used with the implementation based on a 32node Pentium II 350MHz cluster running LINUX. The PCG solver is set up
Solution Of Structured Systems Of Linear Equations Using ElementByElement Preconditioners
, 1995
"... We consider the solution of the n by n system of linear equations, Ax = b, where A is both sparse and structured so that it may be expressed as A = p X i=1 A i : Sparse structured linear systems arise in many applications. The elementary matrices A i are of low rank, and are usually sparse s ..."
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Cited by 2 (2 self)
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so that their nonzero entries may be represented as a small, dense block. We assume that A is a large and normally positive definite symmetric matrix. The solution technique considered is the conjugate gradient method using a range of ElementByElement (EBE) preconditioners that were introduced
On the Use of ElementbyElement Preconditioners to Solve Large Scale Partially Separable Optimization Problems
"... We study the solution of largescale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the allpervasive property of partial separability, first studied by Griewank and Toint (1982b). A typical minimizationmethod for nonlinear optimi ..."
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Cited by 8 (5 self)
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. Numerical experiments indicate the effectiveness of these preconditioners on largescale examples. Keywords: largescale problems, unconstrained optimization, elememtbyelement preconditioners, conjugategradients. AMS(MOS) subject classifications: 65F05, 65F10, 65F15, 65F50, 65K05, 90C30. Also appeared
ELEMENTBYELEMENT PARALLEL COMPUTATION OF INCOMPRESSIBLE NAVIER{STOKES EQUATIONS IN THREE DIMENSIONS
"... Abstract. Development of a stable nite element model for solving steady incompressible viscous °uid °ows in three dimensions is the main theme of the present study. For stability reasons, weighting functions are designed in favor of eld variables on the upstream side. For accuracy reasons, it is r ..."
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{Babuska{Brezzi (LBB) stability condition. To resolve diculties arising from asymmetry and indeniteness in the resulting largesize matrix equations, we abandon the eliminationlike solution solver because the storage demand exceeds the ability of our hardware to solve for threedimensional problems. A modern
On the Preprocessing of Sparse Unassembled Linear Systems for Efficient Solution Using Elementbyelement Preconditioners
, 1996
"... this paper, we consider this preprocessing step in detail. ..."
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Cited by 2 (1 self)
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this paper, we consider this preprocessing step in detail.
Finiteelement preconditioning of GNI spectral methods
 SIAM J. Sci. Comput
"... Several old and new finiteelement preconditioners for nodalbased spectral discretizations of −∆u = f in the domain Ω = (−1, 1)d (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computation ..."
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Cited by 9 (2 self)
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on the Galerkin approach with Numerical Integration (GNI) at the LegendreGaussLobatto (LGL) nodes in the domain. The preconditioning matrices rely on either P1 or Q1 or Q1,NI (i.e., with Numerical Integration) finite elements on meshes whose vertices coincide with the LGL nodes used 1 for the spectral
ALGEBRAIC MULTILEVEL PRECONDITIONING IN THREEDIMENSIONAL Hpdivq SPACE
"... Abstract. An algebraic multilevel iteration method for solving system of linear algebraic equations arising in threedimensional Hpdivq space is presented. The algorithm is developed for the discrete problem obtained by using the space of lowest order RaviartThomasNedelec elements. The theoretical ..."
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Abstract. An algebraic multilevel iteration method for solving system of linear algebraic equations arising in threedimensional Hpdivq space is presented. The algorithm is developed for the discrete problem obtained by using the space of lowest order RaviartThomasNedelec elements
SPARSKIT: a basic tool kit for sparse matrix computations  Version 2
, 1994
"... . This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boei ..."
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Cited by 317 (22 self)
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. This paper presents the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate exchange of software and data between researchers in sparse matrix computations. Our starting point is the Harwell/Boeing collection of matrices for which we provide a number of tools. Among other things the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, performing basic linear algebra operations with sparse matrices and so on. Work done partly at CSRD, university of Illinois and partly at RIACS (NASA Ames Research Center). Current address: Computer Science Dept., University of Minnesota, Minneapolis, MN 55455. This work was supported in part by the NAS Systems Division, via Cooperative Agreement NCC 2387 between NASA and the University Space Research Association (USRA) and in part by the Department of Energy under grant DEFG02...
ThreeDimensional FiniteElement Analyses: Implications for Computer Architectures
 In Proceedings of Supercomputing '91
, 1991
"... The computationallyintensive step of the finite element method is the solution of a linear system of equations. Very large and very sparse system matrices result from threedimensional finiteelement applications. The sparsity must be exploited for efficient use of memory and computational componen ..."
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Cited by 2 (0 self)
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The computationallyintensive step of the finite element method is the solution of a linear system of equations. Very large and very sparse system matrices result from threedimensional finiteelement applications. The sparsity must be exploited for efficient use of memory and computational
Anisotropic Finite Elements: Local Estimates and Applications
, 1999
"... The solution of elliptic boundary value problems my have... ..."
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Cited by 122 (6 self)
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The solution of elliptic boundary value problems my have...
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