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Fast conservative and entropic numerical methods for the Boson Boltzmann equation

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Summary.

In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the entropy inequality and generalized Bose-Einstein distributions as steady states. These properties are essential in order to develop schemes that are able to capture the energy concentration behavior of bosons. In addition we develop fast algorithms for the numerical evaluation of the resulting quadrature formulas which allow the final schemes to be computed only in O(N2 log 2N) operations instead of O(N3).

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Authors and Affiliations

  1. Institute of Mathematics, University of Vienna, Boltzmanngasse 9 A, 1090, Vienna, Austria

    Peter A Markowich

  2. Department of Mathematics, University of Ferrara, Via Machiavelli 35, 44100, Ferrara, Italy

    Lorenzo Pareschi

Authors
  1. Peter A Markowich
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  2. Lorenzo Pareschi
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Correspondence to Lorenzo Pareschi.

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Mathematics Subject Classification (2000):82C10, 76P05, 65D32, 65T50

This work was supported by the WITTGENSTEIN AWARD 2000 of Peter Markowich, financed by the Austrian Research Fund FWF and by the European network HYKE, funded by the EC as contract HPRN-CT-2002-00282.

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Markowich, P., Pareschi, L. Fast conservative and entropic numerical methods for the Boson Boltzmann equation. Numer. Math. 99, 509–532 (2005). https://doi.org/10.1007/s00211-004-0570-5

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  • DOI: https://doi.org/10.1007/s00211-004-0570-5

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