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Efficient Preconditioners (efficient + preconditioner)

Distribution by Scientific Domains
Engineering60%
Mathematics and Statistics40%

Selected Abstracts

Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003
U. Langer
Abstract This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first-kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so-called grey-box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Efficient preconditioning techniques for finite-element quadratic discretization arising from linearized incompressible Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010
A. El Maliki
Abstract We develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier,Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor,Hood element P2,P1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r,(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P1,P2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003
U. Langer
Abstract This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first-kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so-called grey-box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Some preconditioners for the CFIE equation of electromagnetism

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008
David P. Levadoux
Abstract We present three weak parametrices of the operator of the combined field integral equation (CFIE). An interesting feature of these parametrices is that they are compatible with different discretization strategies and hence allow for the construction of efficient preconditioners dedicated to the CFIE. Their numerical analysis shows that a regularization process acting at the continuous level of the equation is also effective at the discrete level if the mesh size tends to zero. First numerical tests confirm this effect and preconditioning is observed indeed. Furthermore, we show that the underlying operator of CFIE satisfies a uniform discrete Inf,Sup condition that allows one to predict an original convergence result for the numerical solution of CFIE to the exact one. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Inverse Toeplitz preconditioners for Hermitian Toeplitz systems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2005
Fu-Rong Lin
Abstract In this paper we consider solving Hermitian Toeplitz systems Tnx=b by using the preconditioned conjugate gradient (PCG) method. Here the Toeplitz matrices Tn are assumed to be generated by a non-negative continuous 2,-periodic function ,, i.e. Tn=,,n[,]. It was proved in (Linear Algebra Appl. 1993; 190:181) that if , is positive then the spectrum of ,,n[1/,],,n[,] is clustered around 1. We prove that the trigonometric polynomial q (s,2, cf. (2) and (3)) converges to 1/, uniformly as n,, under the condition that 1/, is in Wiener class. It follows that the computational cost of the PCG method can be reduced by replacing 1/, with q, where Nefficient preconditioners for Tn when , has finite zeros of even orders. We prove that with our preconditioners, the preconditioned matrix has spectrum clustered around 1. It follows that the PCG methods converge very fast when applied to solve the preconditioned systems. Numerical results are given to demonstrate the efficiency of our preconditioners. Copyright © 2004 John Wiley & Sons, Ltd. [source]