Cross-Validation of numerical schemes for extended hydrodynamical models of semiconductors

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2000
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Anile, Angelo Marcello
Romano, Vittorio
Russo, Giovanni
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Mathematical Models and Methods in Applied Sciences ; 10 (2000), 06. - S. 833-861. - ISSN 0218-2025. - eISSN 1793-6314
Zusammenfassung
The numerical integration of the hydrodynamical model of semiconductors based on extended thermodynamics has been tackled. On account of the mathematical complexity of the system, no theoretical conditions of convergence are available for the existing schemes. Therefore in order to obtain numerical solution it was almost mandatory to resort to a cross-validation comparing the results given by two different methods. The kinetic scheme and the finite difference method represented by a suitable modification of the Nessyahu–Tadmor scheme furnish numerical results for the ballistic diode problem in good agreement even for non-smooth solutions.
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510 Mathematik
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ISO 690ANILE, Angelo Marcello, Michael JUNK, Vittorio ROMANO, Giovanni RUSSO, 2000. Cross-Validation of numerical schemes for extended hydrodynamical models of semiconductors. In: Mathematical Models and Methods in Applied Sciences. 10(06), pp. 833-861. ISSN 0218-2025. eISSN 1793-6314. Available under: doi: 10.1142/S0218202500000434
BibTex
@article{Anile2000Cross-25475,
  year={2000},
  doi={10.1142/S0218202500000434},
  title={Cross-Validation of numerical schemes for extended hydrodynamical models of semiconductors},
  number={06},
  volume={10},
  issn={0218-2025},
  journal={Mathematical Models and Methods in Applied Sciences},
  pages={833--861},
  author={Anile, Angelo Marcello and Junk, Michael and Romano, Vittorio and Russo, Giovanni}
}
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    <dcterms:abstract xml:lang="eng">The numerical integration of the hydrodynamical model of semiconductors based on extended thermodynamics has been tackled. On account of the mathematical complexity of the system, no theoretical conditions of convergence are available for the existing schemes. Therefore in order to obtain numerical solution it was almost mandatory to resort to a cross-validation comparing the results given by two different methods. The kinetic scheme and the finite difference method represented by a suitable modification of the Nessyahu–Tadmor scheme furnish numerical results for the ballistic diode problem in good agreement even for non-smooth solutions.</dcterms:abstract>
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