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Convergence Characteristics (convergence + characteristic)
Selected AbstractsFast computation evolutionary programming algorithm for the economic dispatch problemEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 1 2006P. Somasundaram Abstract This paper essentially aims to propose a new EP based algorithm for solving the ED problem. The ED problem is solved using EP with system lambda as decision variable and power mismatch as fitness function. The algorithm is made fast through judicious modifications in initialization of the parent population, offspring generation and selection of the normal distribution curve. The proposed modifications reduce the search region progressively and generate only effective offsprings. The proposed algorithm is tested on a number of sample systems with quadratic cost function and also on a 10-unit system with piecewise quadratic cost function. The computational results reveal that the proposed algorithm has an excellent convergence characteristic and is superior to other EP based methods in many respects. Copyright © 2005 John Wiley & Sons, Ltd. [source] Error estimates in 2-node shear-flexible beam elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2003Gajbir Singh Abstract The objective of the paper is to report the investigation of error estimates/or convergence characteristics of shear-flexible beam elements. The order and magnitude of principal discretization error in the usage of various types beam elements such as: (a) 2-node standard isoparametric element, (b) 2-node field-consistent/reduced integration element and (c) 2-node coupled-displacement field element, is assessed herein. The method employs classical order of error analyses that is commonly used to evaluate the discretization error of finite difference methods. The finite element equilibrium equations at any node are expressed in terms of differential equations through the use of Taylor series. These differential equations are compared with the governing equations and error terms are identified. It is shown that the discretization error in coupled-field elements is the least compared to the field-consistent and standard finite elements (based on exact integration). Copyright © 2003 John Wiley & Sons, Ltd. [source] Optimal transportation meshfree approximation schemes for fluid and plastic flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010B. Li Abstract We develop an optimal transportation meshfree (OTM) method for simulating general solid and fluid flows, including fluid,structure interaction. The method combines concepts from optimal transportation theory with material-point sampling and max-ent meshfree interpolation. The proposed OTM method generalizes the Benamou,Brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries and constitutive behavior. The OTM method enforces mass transport and essential boundary conditions exactly and is free from tension instabilities. The OTM method exactly conserves linear and angular momentum and its convergence characteristics are verified in standard benchmark problems. We illustrate the range and scope of the method by means of two examples of application: the bouncing of a gas-filled balloon off a rigid wall; and the classical Taylor-anvil benchmark test extended to the hypervelocity range. Copyright © 2010 John Wiley & Sons, Ltd. [source] A variational r -adaption and shape-optimization method for finite-deformation elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Thoutireddy Abstract This paper is concerned with the formulation of a variational r -adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configurational forces for isoparametric elements and non-linear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and non-linear elastic bodies; and the optimization of the shape of elastic inclusions. Copyright © 2004 John Wiley & Sons, Ltd. [source] A variational multiscale Newton,Schur approach for the incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2010D. Z. Turner Abstract In the following paper, we present a consistent Newton,Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier,Stokes equations in three dimensions. The main contributions of this work are a systematic study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton,Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier,Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows. Copyright © 2009 John Wiley & Sons, Ltd. [source] A modification of the artificial compressibility algorithm with improved convergence characteristicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2007Frank Muldoon Abstract The artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven-cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward-facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley & Sons, Ltd. [source] On coupling the Reynolds-averaged Navier,Stokes equations with two-equation turbulence model equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2006Seungsoo Lee Abstract Two methods for coupling the Reynolds-averaged Navier,Stokes equations with the q,, turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier,Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds-averaged Navier,Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization-alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two- and three-dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] Block preconditioners for the discrete incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3-4 2002Howard C. Elman Abstract We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier,Stokes equations. For steady-state problems, we show that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. These characteristics are directly correlated with the convergence properties of iterative solvers, with convergence rates independent of mesh size and only mildly dependent on viscosity. For evolutionary problems, we show that implicit treatment of the time derivatives leads to systems for which convergence is essentially independent of viscosity. Copyright © 2002 John Wiley & Sons, Ltd. [source] Systematic Study of Selected Diagonalization Methods for Configuration Interaction MatricesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 13 2001Matthew L. Leininger Abstract Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two-vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large-scale CI matrices by eliminating the need to ever store more than three expansion vectors (bi) and associated matrix-vector products (,i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal-storage, single-vector method of Olsen is found to be a reasonable alternative for obtaining energies of well-behaved systems to within ,Eh accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10,10Eh) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on-the-fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant-based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574,1589, 2001 [source] Asymptotic expansions of multiply scattered surface currentsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007*Article first published online: 29 FEB 200, Fatih Ecevit We have recently uncovered the convergence characteristics of multiple scattering iterations for "two-dimensional" as well as "three-dimensional scalar (acoustics)" scattering models in the high-frequency regime. As we have demonstrated, a most distinctive property of these latermodels, compared to their two-dimensional counterparts, is the dependence of corresponding asymptotic expansions on the relative angle of rotation between the principal axes of the successive reflection points of the optical rays. Concerning the case of fully "three-dimensional vector (electromagnetic)" scattering problems, here we show that the vectorial nature of the problem, in turn, gives rise to new additional complex structure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||