Results 1  10
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Fast Nonsymmetric Iterations and Preconditioning for NavierStokes Equations
 SIAM J. Sci. Comput
, 1994
"... Discretization and linearization of the steadystate NavierStokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded i ..."
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Cited by 74 (10 self)
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show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner. * This work was supported by the U. S. Army Research Office under grant DAAL0392G0016 and the U. S. National Science Foundation under grant ASC8958544
Iterative Solution Of The Helmholtz Equation By A SecondOrder Method
 SIAM J. Matrix Anal. Appl
, 1996
"... . The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The specific problem is the propagation of hydroacoustic waves in a twodimensional curvilinear duct. The problem is discretized with a secondorder accurate finitedifference method, resu ..."
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Cited by 21 (6 self)
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that the rate of convergence is high. Compared with band Gaussian elimination the preconditioned iterative method shows a significant gain in both storage requirement and arithmetic complexity. This research was supported by the U. S. National Science Foundationunder grant ASC8958544 and by the Swedish
Multigrid And Krylov Subspace Methods For The Discrete Stokes Equations
 INT. J. NUMER. METH. FLUIDS
, 1994
"... Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the perfo ..."
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Cited by 40 (3 self)
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Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several twodimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorizaton is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantages of being both independent of iteration parameters and widely applicable.
Perturbation Of Eigenvalues Of Preconditioned NavierStokes Operators
 CONSTRAINT PRECONDITIONING 19
, 1995
"... We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steadystate NavierStokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on p ..."
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Cited by 3 (1 self)
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We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steadystate NavierStokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.
USE OF LINEAR ALGEBRA KERNELS TO BUILD AN EFFICIENT FINITE ELEMENT SOLVER
, 1992
"... Abstract. For scientific codes to achieve good performance on computers with hierarchical memories, it is necessary that the ratio of memory references to arithmetic operations be low. In this paper, we show that Level 3 BLAS linear algebra kernels can be used to satisfy this requirement to produce ..."
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Cited by 1 (0 self)
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Abstract. For scientific codes to achieve good performance on computers with hierarchical memories, it is necessary that the ratio of memory references to arithmetic operations be low. In this paper, we show that Level 3 BLAS linear algebra kernels can be used to satisfy this requirement to produce an efficient implementation of a parallel finite element solver on a shared memory parallel computer with a fast cache memory.
F.: Domain decomposition algorithms for firstorder system least squares methods
 SIAM Journal of Scientific Computing. Dubois, Thierry, Francois Jauberteau, and Ye Zhou: Influences
, 1996
"... Least squares methods based on rstorder systems have been recently proposed and analyzed for secondorder elliptic equations and systems. They produce symmetric and positive de nite discrete systems by using standard nite element spaces, which are not required to satisfy the infsup condition. In t ..."
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Cited by 1 (0 self)
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Least squares methods based on rstorder systems have been recently proposed and analyzed for secondorder elliptic equations and systems. They produce symmetric and positive de nite discrete systems by using standard nite element spaces, which are not required to satisfy the infsup condition. In this paper, several domain decomposition algorithms for these rstorder least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin
On the Convergence of Line Iterative Methods for Cyclically Reduced NonSymmetrizable Linear Systems
, 1994
"... this paper, we extend this analysis, for constant coefficient problems, to the case where the reduced operator is not real symmetrizable. For centered differences this corresponds to the case where one cell Reynolds number is greater than one in absolute value and the other is less than one in absol ..."
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Cited by 3 (0 self)
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this paper, we extend this analysis, for constant coefficient problems, to the case where the reduced operator is not real symmetrizable. For centered differences this corresponds to the case where one cell Reynolds number is greater than one in absolute value and the other is less than one in absolute value. Although numerical experiments in [3] and [4] showed the method to be effective in this case, there were no analytic bounds on the convergence rate. The key observation is that the reduced matrix can always be transformed into a complex
INEXACT AND PRECONDITIONED UZAWA ALGORITHMS FOR SADDLE POINT PROBLEMS
, 1994
"... Variants of the Uzawa algorithm for solving symmetric indefinite linear systems are developed and analyzed. Each step of this algorithm requires the solution of a symmetric positivedefinite system of linear equations. It is shown that if this computation is replaced by an approximate solution produ ..."
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Variants of the Uzawa algorithm for solving symmetric indefinite linear systems are developed and analyzed. Each step of this algorithm requires the solution of a symmetric positivedefinite system of linear equations. It is shown that if this computation is replaced by an approximate solution produced by an arbitrary iterative method, then with relatively modest requirements on the accuracy of the approximate solution, the resulting inexact Uzawa algorithm is convergent, with a convergence rate close to that of the exact algorithm. In addition, it is shown that preconditioning can be used to improve performance. The analysis is illustrated and supplemented using several examples derived from mixed finite element discretization of the Stokes equations.
FAST NONSYMMETRIC ITERATIONS AND PRECONDITIONING FOR NAVIERSTOKES EQUATIONS*
"... Abstract. Discretization and linearization of the steadystate NavierStokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are ..."
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Abstract. Discretization and linearization of the steadystate NavierStokes equations gives rise to a nonsymmetric indefinite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization. We confirm and supplement these analytic results with a series of numerical experiments indicating that Krylov subspace iterative methods for nonsymmetric systems display rates of convergence that are independent of the mesh parameter. In addition, we show that preconditioning costs can be kept small by using iterative methods for some intermediate steps performed by the preconditioner. Key words. NavierStokes, iterative methods, preconditioners, Krylov subspace AMS subject classifications. 65F10, 65N12, 65N22, 65M60 1. Introduction. Consider the steadystate NavierStokes problem: given data f, find the velocity u and pressure p satisfying (1.1) 1v V2u + u(div u) + u. Vu + grad p f
DOMAIN DECOMPOSITION ALGORITHMS FOR FIRSTORDER SYSTEM LEAST SQUARES METHODS
"... Abstract. Firstorder system least squares methods have been recently proposed and analyzed for second order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces which are not required to satisfy the infsup condition. ..."
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Abstract. Firstorder system least squares methods have been recently proposed and analyzed for second order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces which are not required to satisfy the infsup condition. In this paper, several domain decomposition algorithms for these firstorder least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods. Therefore, domain decomposition algorithms provide parallel and scalable preconditioners also for least squares discretizations. Key words. Domain decomposition, firstorder system least squares.
Results 1  10
of
13