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Transfer Operators (transfer + operators)
Selected AbstractsOn the Approximation of Transport Phenomena , a Dynamical Systems ApproachGAMM - MITTEILUNGEN, Issue 1 2009Michael Dellnitz Abstract Transport phenomena are studied in a large variety of dynamical systems with applications ranging from the analysis of fluid flow in the ocean and the predator-prey interaction in jelly-fish to the investigation of blood flow in the cardiovascular system. Our approach to analyze transport is based on the methodology of so-called transfer operators associated with a dynamical system since this is particularly suitable. We describe the approach and illustrate it by two real world applications: the computation of transport for asteroids in the solar system and the approximation of macroscopic structures in the Southern Ocean (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A node-based agglomeration AMG solver for linear elasticity in thin bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2009Prasad S. Sumant Abstract This paper describes the development of an efficient and accurate algebraic multigrid finite element solver for analysis of linear elasticity problems in two-dimensional thin body elasticity. Such problems are commonly encountered during the analysis of thin film devices in micro-electro-mechanical systems. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. A new node-based agglomeration scheme is proposed for computationally efficient, aggressive and yet effective generation of coarse grids. It is demonstrated that the use of appropriate finite element discretization along with the proposed algebraic multigrid process preserves the rigid body modes that are essential for good convergence of the multigrid solution. Several case studies are taken up to validate the approach. The proposed node-based agglomeration scheme is shown to lead to development of sparse and efficient intergrid transfer operators making the overall multigrid solution process very efficient. The proposed solver is found to work very well even for Poisson's ratio >0.4. Finally, an application of the proposed solver is demonstrated through a simulation of a micro-electro-mechanical switch. Copyright © 2008 John Wiley & Sons, Ltd. [source] Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003U. 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] Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2002Mark Adams Abstract Multigrid has been a popular solver method for finite element and finite difference problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often difficult or impossible for the application to provide coarse grids, is not as well understood. In particular, methods that are designed to require only data that are easily available in most finite element applications (i.e. fine grid data), constructing the grid transfer operators and coarse grid operators internally, are of practical interest. We investigate three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: (1) non-nested geometric multigrid, (2) smoothed aggregation, and (3) plain aggregation algebraic multigrid. This paper evaluates the effectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom. Published in 2002 by John Wiley & Sons, Ltd. [source] Workers' Remittances to India: An Examination of Transfer Cost and EfficiencyINTERNATIONAL MIGRATION, Issue 5 2010Bhupal Singh Regarding the time efficiency of remittance transfer channels to India, the evidence suggests that traditional banking instruments are relatively inefficient as compared to the new information technology-enabled products. Transfer arrangement of the Indian banks with overseas exchange houses has reduced the settlement cycle and the cost. Both the banks and money transfer operators (MTOs) are able to keep the transaction cycle low through the use of information technology-enabled formats. Given that the average cost curve of the banks is located to the right of the average cost curve of the MTOs, greater potential exists for the improvement in overall efficiency of the two entities, particularly through the sharing of messaging and the access and disbursement networks to reduce the overhead cost. The estimates of error correction model reveal that the transaction fee and payment infrastructure are significant determinants of remittance flows, underscoring the scope of policy measures in influencing remittance inflows. The estimates indicate that over the medium to long-term horizon, transaction cost emerges as the most dominant variable explaining the variation in remittances. The payments infrastructure also explains about 10 per cent variation in remittances over the medium-term. The impulse response analysis further reveals that the favourable shocks to transaction fees and the payments infrastructure cause steady improvement in remittance inflows over the medium-term horizon, thus underlining the importance of cost and efficiency in affecting the workers' remittances. [source] Algebraic multigrid and 4th-order discrete-difference equations of incompressible fluid flowNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2010R. Webster Abstract This paper investigates the effectiveness of two different Algebraic Multigrid (AMG) approaches to the solution of 4th-order discrete-difference equations for incompressible fluid flow (in this case for a discrete, scalar, stream-function field). One is based on a classical, algebraic multigrid, method (C-AMG) the other is based on a smoothed-aggregation method for 4th-order problems (SA-AMG). In the C-AMG case, the inter-grid transfer operators are enhanced using Jacobi relaxation. In the SA-AMG case, they are improved using a constrained energy optimization of the coarse-grid basis functions. Both approaches are shown to be effective for discretizations based on uniform, structured and unstructured, meshes. They both give good convergence factors that are largely independent of the mesh size/bandwidth. The SA-AMG approach, however, is more costly both in storage and operations. The Jacobi-relaxed C-AMG approach is faster, by a factor of between 2 and 4 for two-dimensional problems, even though its reduction factors are inferior to those of SA-AMG. For non-uniform meshes, the accuracy of this particular discretization degrades from 2nd to 1st order and the convergence factors for both methods then become mesh dependent. Copyright © 2009 John Wiley & Sons, Ltd. [source] An algebraic generalization of local Fourier analysis for grid transfer operators in multigrid based on Toeplitz matricesNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2010M. Donatelli Abstract Local Fourier analysis (LFA) is a classical tool for proving convergence theorems for multigrid methods (MGMs). In particular, we are interested in optimal convergence, i.e. convergence rates that are independent of the problem size. For elliptic partial differential equations (PDEs), a well-known optimality result requires that the sum of the orders of the grid transfer operators is not lower than the order of the PDE approximated. Analogously, when dealing with MGMs for Toeplitz matrices, a well-known optimality condition concerns the position and the order of the zeros of the symbols of the grid transfer operators. In this work we show that in the case of elliptic PDEs with constant coefficients, the two different approaches lead to an equivalent condition. We argue that the analysis for Toeplitz matrices is an algebraic generalization of the LFA, which allows to deal not only with differential problems but also for instance with integral problems. The equivalence of the two approaches gives the possibility of using grid transfer operators with different orders also for MGMs for Toeplitz matrices. We give also a class of grid transfer operators related to the B-spline's refinement equation and study their geometric properties. Numerical experiments confirm the correctness of the proposed analysis. Copyright © 2010 John Wiley & Sons, Ltd. [source] An algebraic multigrid method for finite element discretizations with edge elementsNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 3 2002S. Reitzinger Abstract This paper presents an algebraic multigrid method for the efficient solution of the linear system arising from a finite element discretization of variational problems in H0(curl,,). The finite element spaces are generated by Nédélec's edge elements. A coarsening technique is presented, which allows the construction of suitable coarse finite element spaces, corresponding transfer operators and appropriate smoothers. The prolongation operator is designed such that coarse grid kernel functions of the curl-operator are mapped to fine grid kernel functions. Furthermore, coarse grid kernel functions are ,discrete' gradients. The smoothers proposed by Hiptmair and Arnold, Falk and Winther are directly used in the algebraic framework. Numerical studies are presented for 3D problems to show the high efficiency of the proposed technique. Copyright © 2002 John Wiley & Sons, Ltd. [source] | |||||||||||||