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Iteration Scheme (iteration + scheme)
Selected AbstractsCore loss estimation in three-phase transformer using vector hysteresis model and classical loss model incorporated in 2D magnetodynamicsEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2003O. Deblecker This paper deals with the computation of the magnetic field and core loss in a three-phase three-limb transformer at no-load. The computational algorithm consists of the vector hysteresis model incorporated in 2D magneto-dynamics via the differential reluctivity tensor. The hysteretic nonlinearity is handled by a simple iteration scheme. The eddy-current losses in the laminated steel core are accounted for by considering an additional conductivity matrix in the FE equations. The magnetisation-dependant vector Preisach model with an analytical expression for the distribution function is adopted for describing the hysteretic constitutive law in the rolling and transverse directions of the laminations. The parameters and mean field term are fitted on the basis of a set of BH-symmetric (quasistatic) loops. Numerical results are presented that confirm the effectiveness of the proposed method for the no-load simulation of the transformer in the transient and the steady-states. [source] Numerical stability of unsteady stream-function vorticity calculationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2003E. Sousa Abstract The stability of a numerical solution of the Navier,Stokes equations is usually approached by con- sidering the numerical stability of a discretized advection,diffusion equation for either a velocity component, or in the case of two-dimensional flow, the vorticity. Stability restrictions for discretized advection,diffusion equations are a very serious constraint, particularly when a mesh is refined in an explicit scheme, so an accurate understanding of the numerical stability of a discretization procedure is often of equal or greater practical importance than concerns with accuracy. The stream-function vorticity formulation provides two equations, one an advection,diffusion equation for vorticity and the other a Poisson equation between the vorticity and the stream-function. These two equations are usually not coupled when considering numerical stability. The relation between the stream-function and the vorticity is linear and so has, in principle, an exact inverse. This allows an algebraic method to link the interior and the boundary vorticity into a single iteration scheme. In this work, we derive a global time-iteration matrix for the combined system. When applied to a model problem, this matrix formulation shows differences between the numerical stability of the full system equations and that of the discretized advection,diffusion equation alone. It also gives an indication of how the wall vorticity discretization affects stability. Despite the added algebraic complexity, it is straightforward to use MATLAB to carry out all the matrix operations. Copyright © 2003 John Wiley & Sons, Ltd. [source] A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Kwang-Soo Kim Abstract This paper describes and compares two vorticity-based integral approaches for the solution of the incompressible Navier,Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot,Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well-established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity-based methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Annular liquid jets at high Reynolds numbersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003G. Georgiou Abstract The flow of annular liquid jets at high Reynolds numbers is analysed by means of the finite element method and the full-Newton iteration scheme. Results have been obtained for various values of the inner to the outer diameter ratio and for non-zero surface tension, using extremely long meshes. The annular film moves far from the symmetry axis at low values of the Reynolds number. At higher Reynolds numbers, the film moves towards the axis of symmetry and appears close to very far downstream, forming a round jet. Asymptotic results for the radius of the resulting round jet are provided. Copyright © 2003 John Wiley & Sons, Ltd. [source] Adaptive geometry and process optimization for injection molding using the kriging surrogate model trained by numerical simulationADVANCES IN POLYMER TECHNOLOGY, Issue 1 2008Yuehua Gao Abstract An adaptive optimization method based on the kriging surrogate model has been developed to intelligently determine the optimal geometric dimensions and processing parameters for minimizing warpage in injection-molded components. The kriging surrogate model is a statistics-based interpolated technique that provides the approximate functional relationship between warpage and factors that influence warpage. In this study, it is used to be first trained by,and later replaced,the full-fledged, time-consuming numerical simulation in the optimization process. Based on this surrogate model, an adaptive iteration scheme that takes into account the predicted uncertainty is performed to improve the accuracy of the surrogate model while finding the optimum solution. The optimization process starts with a small number of initial training sample points and then adds additional key points during iterations by evaluating the correlations among the candidate points. As an example of validation and application, optimization of geometric dimensions and processing parameters for a box-shape part with different and stepwise wall thicknesses has been performed. The results demonstrate the feasibility and effectiveness of the proposed optimization method. © 2008 Wiley Periodicals, Inc. Adv Polym Techn 27:1,16, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20116 [source] Nonlinear actuation model for lateral electrostatically-actuated DC-contact RF MEMS series switchesMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2007A. Lázaro Abstract In this work, a nonlinear model to predict actuation characteristics in lateral electrostatically-actuated DC-contact MEMS switches is proposed. In this case a parallel-plate approximation cannot be applied. The model is based on the equilibrium equation for an elastic beam. It is demonstrated that the contribution of fringing fields is essential. The model relies on finite-difference discretization of the structures, applying boundary conditions and is solved with a Gauss-Seidel relaxation iteration scheme. Its usefulness is demonstrated in a series MEMS switch with lateral interdigital electrostatic actuation. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1238,1241, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22450 [source] Radial basis collocation method and quasi-Newton iteration for nonlinear elliptic problemsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2008H.Y. Hu Abstract This work presents a radial basis collocation method combined with the quasi-Newton iteration method for solving semilinear elliptic partial differential equations. The main result in this study is that there exists an exponential convergence rate in the radial basis collocation discretization and a superlinear convergence rate in the quasi-Newton iteration of the nonlinear partial differential equations. In this work, the numerical error associated with the employed quadrature rule is considered. It is shown that the errors in Sobolev norms for linear elliptic partial differential equations using radial basis collocation method are bounded by the truncation error of the RBF. The combined errors due to radial basis approximation, quadrature rules, and quasi-Newton and Newton iterations are also presented. This result can be extended to finite element or finite difference method combined with any iteration methods discussed in this work. The numerical example demonstrates a good agreement between numerical results and analytical predictions. The numerical results also show that although the convergence rate of order 1.62 of the quasi-Newton iteration scheme is slightly slower than rate of order 2 in the Newton iteration scheme, the former is more stable and less sensitive to the initial guess. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] An iterative method for the reconstruction of a stationary flowNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007Tomas Johansson Abstract In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source] Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary conditionCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2009Yuri Trakhinin We study the free boundary problem for the equations of compressible Euler equations with a vacuum boundary condition. Our main goal is to recover in Eulerian coordinates the earlier well-posedness result obtained by Lindblad [11] for the isentropic Euler equations and extend it to the case of full gas dynamics. For technical simplicity we consider the case of an unbounded domain whose boundary has the form of a graph and make short comments about the case of a bounded domain. We prove the local-in-time existence in Sobolev spaces by the technique applied earlier to weakly stable shock waves and characteristic discontinuities [5, 12]. It contains, in particular, the reduction to a fixed domain, using the "good unknown" of Alinhac [1], and a suitable Nash-Moser-type iteration scheme. A certain modification of such an approach is caused by the fact that the symbol associated to the free surface is not elliptic. This approach is still directly applicable to the relativistic version of our problem in the setting of special relativity, and we briefly discuss its extension to general relativity. © 2009 Wiley Periodicals, Inc. [source] FEM simulation of turbulent flow in a turbine blade passage with dynamical fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009Lixiang Zhang Abstract Results are described from a combined mathematical modeling and numerical iteration schemes of flow and vibration. We consider the coupling numerical simulations of both turbulent flow and structure vibration induced by flow. The methodology used is based on the stabilized finite element formulations with time integration. A fully coupled model of flow and flow-induced structure vibration was established using a hydride generalized variational principle of fluid and solid dynamics. The spatial discretization of this coupling model is based on the finite element interpolating formulations for the fluid and solid structure, while the different time integration schemes are respectively used for fluid and solid structure to obtain a stabilized algorithm. For fluid and solid dynamics, Hughes' predictor multi-corrector algorithm and the Newmark method are monolithically used to realize a monolithic solution of the fully coupled model. The numerical convergence is ensured for small deformation vibrating problems of the structure by using different time steps for fluid and solid, respectively. The established model and the associated numerical methodology developed in the paper were then applied to simulate two different flows. The first one is the lid-driven square cavity flow with different Reynolds numbers of 1000, 400 and 100 and the second is the turbulent flows in a 3-D turbine blade passage with dynamical fluid,structure interaction. Good agreement between numerical simulations and measurements of pressure and vibration acceleration indicates that the finite element method formulations developed in this paper are appropriate to deal with the flow under investigation. Copyright © 2009 John Wiley & Sons, Ltd. [source] Ishikawa iterative process with errors for nonlinear equations of generalized monotone type in Banach spacesMATHEMATISCHE NACHRICHTEN, Issue 10 2005Ljubomir B. Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D , X , 2D be a multi-valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||