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  • 1
    Digitale Medien
    Digitale Medien
    Monotone multigrid methods for elliptic variational inequalities II (1996)
    Springer
    Numerische Mathematik 72 (1996), S. 481-499 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 65N30, 65N55, 35J85
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. We derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements. The coarse grid corrections are computed from certain obstacle problems. The actual constraints are fixed by the preceding nonlinear fine grid smoothing. This new approach allows the implementation as a classical V-cycle and preserves the usual multigrid efficiency. We give $1-O(j^{-3})$ estimates for the asymptotic convergence rates. The numerical results indicate a significant improvement as compared with previous multigrid approaches.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050178
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 16 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620300414
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 16 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620361808
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: 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.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640090308
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  • 5
    Buch
    Buch
    Domain decomposition methods in science and engineering /; 40 (2005)
    Berlin [u.a.] :Springer,
    Details
    Titel: Domain decomposition methods in science and engineering /; 40
    Beteiligte Person(en): Kornhuber, Ralf
    Verlag: Berlin [u.a.] :Springer,
    Erscheinungsjahr: 2005
    Seiten: XVIII, 684 S. : , Ill., graph. Darst.
    Serie: Lecture notes in computational science and engineering 40
    ISBN: 3-540-22523-4
    Materialart: Buch
    Sprache: Englisch
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  • 6
    Buch
    Buch
    Adaptive monotone multigrid methods for nonlinear variational problems (1997)
    Stuttgart :Teubner,
    Details
    Titel: Adaptive monotone multigrid methods for nonlinear variational problems
    Autor: Kornhuber, Ralf
    Verlag: Stuttgart :Teubner,
    Erscheinungsjahr: 1997
    Seiten: 157 S.
    Serie: Advances in Numerical Mathematics
    Materialart: Buch
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  • 7
    Buch
    Buch
    Adaptive monotone multigrid methods for nonlinear variational problems. Berlin, Freie Univ., Habilitationschrift, o. J.
    Details
    Titel: Adaptive monotone multigrid methods for nonlinear variational problems. Berlin, Freie Univ., Habilitationschrift, o. J.
    Autor: Kornhuber, Ralf
    Seiten: 93 S.
    Materialart: Buch
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  • 8
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    Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs. (1988)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: 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.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
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    Self Adaptive Computation of the Breakdown Voltage of Planar pn-Junctions with Multistep Field Plates. (1991)
    Details
    Publikationsdatum: 2014-02-26
    Beschreibung: The breakdown voltage highly depends on the electric field in the depletion area whose computation is the most time consuming part of the simulation. We present a self adaptive Finite Element Method which reduces dramatically the required computation time compared to usual Finite Difference Methods. A numerical example illustrates the efficiency and reliability of the algorithm.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 10
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    Adaptive Multilevel-Methods for Obstacle Problems in Three Space Dimensions. (1993)
    Details
    Publikationsdatum: 2020-10-02
    Beschreibung: We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub--problems are solved iteratively by preconditioned cg--iterations. We propose a variant of the BPX preconditioner and prove an $O(j)$ estimate for the resulting condition number. To allow for local mesh refinement we derive semi--local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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