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  • 1990-1994  (4)
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  • 1
    Electronic Resource
    Electronic Resource
    Multi-grid solution of two coupled Stefan equations arising in induction heating of large steel slabs (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 779-801 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Induction heating of large steel slabs can be described by a coupled system of non-linear evolution equations of Stefan type represnting the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi-grid algorithms are given which, combined with a nested iteration type continuation strategy to proceed in time, result in computationally highly efficient schemes for the numerical simulation of the induction heating process.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300414
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Adaptive multivlevel methods in three space dimensions (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3187-3203 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the approximate solution of self-adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361808
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Self-adaptive finite-element simulation of bipolar, strongly reverse-biased pn-junctions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 243-250 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The potential distribution of bipolar, strongly reverse-biased pn-junctions can be described by a double obstacle problem for the Laplacian. The problem is solved by a self-adaptive finite-element method involving automatic termination criteria for the iterative solver, local error estimation and local mesh refinement. Special attention is paid to the efficient resolution of the geometries typically arising in semiconductor device simulation. The algorithm is applied to a reverse-biased pn-junction with multistep field plate and stop electrode to illustrate its efficiency and reliability.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090308
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  • 4
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    Monotone multigrid methods for elliptic variational inequalities I (1994)
    Springer
    Details
    Publication Date: 1994-12-01
    Print ISSN: 0029-599X
    Electronic ISSN: 0945-3245
    Topics: Mathematics
    Published by Springer
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