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  • 2000-2004  (2)
  • 1990-1994  (2)
  • 2000  (2)
  • 1991  (2)
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  • 2000-2004  (2)
  • 1990-1994  (2)
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  • 1
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    Two-Dimensional Adaptive Simulation of Dopant Diffusion in Silicon (2000)
    Details
    Publication Date: 2014-02-26
    Description: One important step in the fabrication of silicon-based integrated circuits is the creation of semiconducting areas by diffusion of dopant impurities into silicon. Complex models have been developed to investigate the redistribution of dopants and point defects. In general, numerical analysis of the resulting PDEs is the central tool to assess the modelling process. We present an adaptive approach which is able to judge the quality of the numerical approximation and which provides an automatic mesh improvement. Using linearly implicit methods in time and multilevel finite elements in space, we are able to integrate efficiently the arising reaction-drift-diffusion equations with high accuracy. Two different diffusion processes of practical interest are simulated.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 2
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    An Adaptive Discontinuous Finite Element Method for the Transport Equation. (1991)
    Details
    Publication Date: 2014-02-26
    Description: In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and can be easily extended to nonlinear problems. Two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary variing flow directions. Numerical results are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators. {\bf Key words:} neutron transport equation, discontinuous finite element, adaptive grid refinement. {\bf Subject classifications:} AMS(MOS) 65N30, 65M15.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 3
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    Adaptive Linearly Implicit Methods for Heat and Mass Transfer Problems (2000)
    Details
    Publication Date: 2019-05-10
    Description: Dynamical process simulation of complex real-life problems often requires the use of modern algorithms, which automatically adapt both the time and space discretization in order to get error-controlled approximations of the solution. In this paper, a combination of linearly implicit time integrators of Rosenbrock type and adaptive multilevel finite elements based on a posteriori error estimates is presented. This approach has proven to work quite satisfactorily for a wide range of challenging practical problems. We show the performance of our adaptive method for two applications that arise in the study of flame balls and brine transport in porous media.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 4
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    An Adaptive Finite Element Method for Convection-Diffusion Problems by Interpolation Techniques. (1991)
    Details
    Publication Date: 2014-02-26
    Description: For adaptive solution of convection- difussion problems with the streamline-diffusion finite element method, an error estimator based on interpolation techniques is developed. It can be shown that for correctness of this error estimator a restriction of the maximum angle is to be sufficient. Compared to usual methods, the adaptive process leads to more accurate solutions at much less computational cost. Numerical tests are enclosed. {\bf Keywords: } Adaptive finite elements, convection- diffusion equation, internal and boundary layers, streamline-diffusion. {\bf Subject Classifications:} AMS(MOS): 65N15, 65N30
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
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