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Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs.

Please always quote using this URN: urn:nbn:de:0297-zib-160
  • Induction heating of large steel slabs can be described by a coupled system of nonlinear evolution equations of Stefan type representing 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. {\bf Keywords:} induction heating, system of two coupled Stefan equations, multi-grid algorithms. {\bf Subject Classification:} AMS(MOS): 35K60, 35R35, 65H10, 65N05, 65N20, 78A25, 78A55.

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Metadaten
Author:Ronald H. W. Hoppe, Ralf Kornhuber
Document Type:ZIB-Report
Tag:induction heating; multi-grid algorithms; system of two coupled Stefan equations
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K60 Nonlinear initial value problems for linear parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R35 Free boundary problems
65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H05 Single equations
65-XX NUMERICAL ANALYSIS / 65Hxx Nonlinear algebraic or transcendental equations / 65H10 Systems of equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Axx General / 78A25 Electromagnetic theory, general
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80) / 78Axx General / 78A55 Technical applications
Date of first Publication:1988/11/15
Series (Serial Number):ZIB-Report (SC-88-08)
ZIB-Reportnumber:SC-88-08
Published in:Appeared in: J. for Num. Methods in Engineering 30, pp. 779-801 (1990)
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