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Adaptive local multigrid methods for solving time-harmonic eddy-current problems

IEEE TRANSACTIONS ON MAGNETICS 2006年第2期42卷 309-318页

作者： Sterz, O Hauser, A Wittum, G CST GmbH D-64289 Darmstadt Germany Heidelberg Univ IWR D-69120 Heidelberg Germany

The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive multigrid scheme for time-harmonic eddy currents. Numerical experiments show that the standard multigrid scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.

关键词： adaptive mesh-refinement eddy currents edge elements finite-element methods frequency domain local multigrid methods red-green refinement

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Multigrid methods for the three-dimensional simulation of nonlinear magnetomechanical systems

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IEEE TRANSACTIONS ON MAGNETICS 2002年第3期38卷 1497-1511页

作者： Schinnerl, M Schöberl, J Kaltenbacher, M Lerch, R Univ Erlangen Nurnberg Dept Sensor Technol D-91058 Erlangen Germany Univ Linz Dept Numerical Math & Optimizat A-4040 Linz Austria

We present a recently developed multigrid calculation scheme for coupled magnetomechanical systems. The scheme allows the efficient calculation of three-dimensional (3-D) dynamic rigid motions as well as deformations of nonmagnetic and ferromagnetic materials in a magnetic field. Thereby, the 3-D mechanical problem is discretized with nodal elements and the 3-D magnetic problem with edge elements. Both finite element meshes may be chosen independently and thus can be separately adapted to the physical requirements of the mechanical and magnetic fields. Fast multigrid solution techniques can solve large scaled 3-D problems within very short CPU times. Three examples demonstrate the efficiency of the developed scheme.

关键词： Eddy currents edge elements finite-element methods magnetomechanical systems moving bodies multigrid methods

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THE SIMPLIFIED HYBRID-COMBINED methods FOR LAPLACE EQUATION WITH SINGULARITIES

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1990年第2期29卷 171-193页

作者： LI, ZC BUI, TD CONCORDIA UNIV DEPT COMP SCIMONTREAL H3G 1M8QUEBECCANADA

In Li and Liang (1983), the simplified hybrid-combined method is presented for combining the Ritz-Galerkin method and the finite-element method. In this paper we will apply this method to solve singularity problems of Laplace's equation. Error bounds and stability analyses will be provided while taking into account the integration approximation along the coupling boundary. A significant coupling relation between the Ritz-Galerkin and the finite-element method has been found for the Laplace equation with singularities. An optimal rate of convergence has also been achieved. Numerical experiments have been carried out for solving the benchmark problem: Motz's problem to verify the theoretical results.

关键词： Singularity problems combined methods hybrid methods finite-element methods the Ritz-Galerkin methods elliptic boundary value problems

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Deformation analysis of induction machines by means of analytical and numerical methods

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IEEE TRANSACTIONS ON MAGNETICS 2008年第6期44卷 1498-1501页

作者： Schlensok, Christoph van Riesen, Dirk van der Giet, Michael Hameyer, Kay Bosch Rexroth AG D-97816 Lohr Germany Rhein Westfal TH Aachen Inst Elect Machines D-52062 Aachen Germany

The estimation and calculation of the acoustic sound of electric machinery is of high interest. Various approaches have been presented relying either on analytical or on numerical models. In general, the analytical models are based on the electromagnetic-field theory, and the results are compared to measurements. Numerical models allow for the separation of different exciting forces stemming from various effects. In the studied case of an induction machine (IM) with squirrel-cage rotor the three following effects are taken into account in the analytical model: the fundamental field, saturation, and eccentricity. Nevertheless, the numerical results have to be verified. Hence, they are compared to the physically based analytical results. The radiated noise depends directly on the surface's deformation of the machine. Therefore, the analysis is focused on the structure-dynamic vibrations. The combined analysis presented here, allows for the reduction of vibrations and noise optimizing the coupling of stator and housing. The studied IM's housing is mounted with six spiral-steel springs to the stator. With the presented method the impact of different numbers of pins is analyzed.

关键词： audible noise deformation finite-element methods induction machine (IM) structure dynamics vibrations

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Comparison of numerical methods for modeling of superconductors

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IEEE TRANSACTIONS ON MAGNETICS 2002年第2期38卷 849-852页

作者： Stavrev, S Grilli, F Dutoit, B Nibbio, N Vinot, E Klutsch, I Meunier, G Tixador, P Yang, YF Martinez, E Swiss Fed Inst Technol EPFL EL LANOS CH-1015 Lausanne Switzerland Inst Natl Polytech Grenoble INPG LEG F-38042 Grenoble France Univ Southampton Sch Engn IoC Southampton SO17 1BJ Hants England

Different finite-element method (FEM) formulations have been developed in order to model the electromagnetic behavior of type-II superconductors. This paper presents a comparison between simulations with A-V formulation models implemented in two FEM software packages (FLUX2D and FLUX3D) and a numerical method based on analytical model for superconductors in applied magnetic field. These models can be used for superconductors with complex geometry and power-law current-voltage characteristics. Simulated is a 37-filamentary tape with applied transport current in self-field and alternating current (ac) magnetic field parallel to the wide side of the tape. A good agreement is found between the ac-loss and current distributions obtained with the different models.

关键词： AC losses finite-element methods numerical analysis superconducting materials

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Estimating the Inf-Sup Constant in Reduced Basis methods for Time-Harmonic Maxwell's Equations

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2015年第11期63卷 3549-3557页

作者： Hess, Martin W. Grundel, Sara Benner, Peter Max Planck Inst Dynam Complex Tech Syst D-39106 Magdeburg Germany

The reduced basis method (RBM) generates low-order models of parametrized partial differential equations. These allow for the efficient evaluation of parametrized models in many-query and real-time contexts. We use the RBM to generate low-order models of microscale models under variation of frequency, geometry, and material parameters. In particular, we focus on the efficient estimation of the discrete stability constant used in the reducced basis error estimation. A good estimation of the discrete stability constant is a challenging problem for Maxwell's equations, but is needed to yield rigorous bounds on the model approximation error. We therefore test and compare

关键词： Electromagnetic (EM) fields finite-element methods numerical analysis reduced-order systems

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S-domain methods for simultaneous time and frequency characterization of electromagnetic devices

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1998年第9期46卷 1277-1290页

作者： Bracken, JE Su, DK Cendes, ZJ Ansoft Corp Pittsburgh PA 15219 USA

An efficient procedure is developed for simultaneously characterizing the time-domain and frequency-domain behavior of electromagnetic devices. The procedure works in the complex-frequency plane-called the s-domain-and provides an analytical expression for the behavior of the device at any frequency and for any transient excitation. This analytical expression is obtained by first evaluating a reduced-order model of the poles and zeros of the device. These poles and zeros are then used to characterize the device in terms of rational polynomials in the s-domain. Two different methods for evaluating reduced-order models are presented. One is called asymptotic waveform evaluation (AWE) and is combined,vith the finite-element method;the other is called adaptive Lanzcos-Pade sweep (ALPS) and is combined with the boundary-element method. The resulting reduced-order models provide the frequency-domain behavior of the device over a broad bandwidth. Using the Laplace transform, these reduced-order models also provide the time-domain behavior. Several numerical examples have been run using commercial electronic design automation (EDA) software to demonstrate that this solution procedure is a highly efficient and accurate way to characterize the electromagnetic performance of real-life devices.

关键词： electromagnetic analysis electromagnetic transient analysis finite-element methods Maxwell's equations reduced-order systems

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Fast computational methods for large-scale eddy-current computation

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IEEE TRANSACTIONS ON MAGNETICS 2002年第2期38卷 529-532页

作者： Rubinacci, G Tamburrino, A Ventre, S Villone, F Univ Studi Cassino EURATOM Assoc DAEIMI Lab Computat ElectromagnetENEACREATE I-03043 Cassino Italy

In this paper, we present a technique for solving largescale problems arising from the discretization of an integral formulation for three-dimensional eddy current problems in the magnetoquasi-static limit using edge-element-based shape functions. The proposed approach is in the framework of the precorrected fast Fourier transform method (PFFTM) that allows to compute the product of the full stiffness matrix with a vector in O(N log N) operations. A key point of standard PFFTM is the introduction of point-like sources defined onto a regular grid to approximate an arbitrary current density in the conductor and to compute the large distance interactions by FFT. Point-like sources are not suitable for representing solenoidal current densities as required for eddy currents problems. In this paper, edge-element-based shape functions onto the regular grid are introduced instead of the point-like sources. This allows us to improve the approximation (solenoidal current densities are approximated by solenoidal basis functions) and to reduce further the computational cost.

关键词： eddy currents fast algorithms finite-element methods integral equations

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A generalized bpx multigrid framework covering nonnested v-cycle methods (vol 76, pg 137, 2007)

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MATHEMATICS OF COMPUTATION 2007年第260期76卷 2251-2251页

作者： Duan, Huo-Yuan Gao, Shao-Qin Tan, Roger C. E. Zhang, Shangyou Natl Univ Singapore Dept Math Singapore 117543 Singapore Hebei Univ Coll Math & Comp Baoding Peoples R China Univ Delaware Dept Math Sci Newark DE 19716 USA

More than a decade ago, Bramble, Pasciak and Xu developed a framework inanalyzing the multigrid methods with nonnested spaces or non-inherited quadratic forms. It wassubsequently known as the BPX multigrid framework, which was widely used in the analysis ofmultigrid and domain decomposition methods. However, the framework has an apparent limit in theanalysis of nonnested V-cycle methods, and it produces a variable V-cycle, or nonuniform convergencerate V-cycle methods, or other nonoptimal results in analysis thus far. This paper completes along-time effort in extending the BPX multigrid framework so that it truly covers the nonnestedV-cycle. We will apply the extended BPX framework to the analysis of many V-cycle nonnestedmultigrid methods. Some of them were proven previously only for two-level and W-cycle *** numerical results are presented to support the theoretical analysis of this paper.

关键词： V-cycle nonnested multigrid method finite-element methods FULL ELLIPTICREGULARITY BOUNDARY-VALUE-PROBLEMS STOKES EQUATIONS CONVERGENCE ALGORITHMS INDEfinite SPACES GRIDS

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MULTIGRID methods FOR THE SOLUTION OF POISSON EQUATION IN A THICK SPHERICAL-SHELL

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SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1991年第3期12卷 681-694页

作者： KARPIK, SR PELTIER, WR

Two multigrid methods designed for the solution of a finite-element discretization of Poisson's equation in spherical geometry are presented and compared. One of these, based upon an approximate local least-squares inverse (LS1), has been previously reported by J. R. Baumgardner and P. O. Frederickson [SIAM J. Numer. Anal., 22 (1985), pp. 1107-1115];the other, developed by the authors, employs a "mass lumped" line Jacobi smoothing procedure that is entirely new. The new method is shown to be both more economical and considerably more robust than that based upon the LS1 smoothing iteration.

关键词： MULTIGRID methods ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS finite-element methods

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