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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 84 (1999), S. 143-171 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N15, 65N30, 65N50, 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. A residual based error estimator for the approximation of linear elliptic boundary value problems by nonconforming finite element methods is introduced and analyzed. In particular, we consider mortar finite element techniques restricting ourselves to geometrically conforming domain decomposition methods using P1 approximations in each subdomain. Additionally, a residual based error estimator for Crouzeix-Raviart elements of lowest order is presented and compared with the error estimator obtained in the more general mortar situation. It is shown that the computational effort of the error estimator can be considerably reduced if the special structure of the Lagrange multiplier is taken into account.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0332-1649
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Purpose - We present a method for the simulation of the dynamical behavior of a coupled magneto-mechanical system given in terms of a conductor moving through an electromagnetic field. Design/methodology/approach - For the magnetic part, we consider a model based on an electric vector and a magnetic scalar potential, whereas the mechanical part is modelled by the equation of a rigid body motion. A weak coupling is employed: at each time step the resulting forces are calculated yielding the new displacement of the conductor. Findings - Numerical results are given for the simulation of an electromagnetic brake with axisymmetric geometry. They indicate that the proposed method is especially well suited for eddy current problems involving moving conductors. Research limitations/implications - Further research should be undertaken toward the application of the proposed method to real 3D problems. Originality/value - The spatial discretization of the problem relies on the use of two independent triangulations to approximate the two involved potentials. Whereas the scalar magnetic potential is discretized by means of nodal H1-conforming finite elements on a grid covering the global computational domain, the vector electric potential is approximated by Hcurl-conforming edge elements on another grid only covering the conductor. The coupling between the two grids is accomplished via the mortar finite element method. At each time step, only the coupling matrix has to be reassembled, all other involved matrices remain the same. Moreover, no remeshing is necessary when the conductor changes its position. The paper should be valuable for any researcher interested in the numerical simulation of eddy current problems.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2021-03-16
    Language: English
    Type: article , doc-type:article
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  • 4
    Publication Date: 2014-02-26
    Description: The focus of this paper is on the efficient solution of boundary value problems involving the double-- curl operator. Those arise in the computation of electromagnetic fields in various settings, for instance when solving the electric or magnetic wave equation with implicit timestepping, when tackling time--harmonic problems or in the context of eddy--current computations. Their discretization is based on on N\'ed\'elec's {\bf H(curl}; $\Omega$)--conforming edge elements on unstructured grids. In order to capture local effects and to guarantee a prescribed accuracy of the approximate solution adaptive refinement of the grid controlled by a posteriori error estimators is employed. The hierarchy of meshes created through adaptive refinement forms the foundation for the fast iterative solution of the resulting linear systems by a multigrid method. The guiding principle underlying the design of both the error estimators and the multigrid method is the separate treatment of the kernel of the curl--operator and its orthogonal complement. Only on the latter we have proper ellipticity of the problem. Yet, exploiting the existence of computationally available discrete potentials for edge element spaces, we can switch to an elliptic problem in potential space to deal with nullspace of curl. Thus both cases become amenable to strategies of error estimation and multigrid solution developed for second order elliptic problems. The efficacy of the approach is confirmed by numerical experiments which cover several model problems and an application to waveguide simulation.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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