Fast conservative and entropic numerical methods for the Boson Boltzmann equation

Peter Markowich, Lorenzo Pareschi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

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 log2 N) operations instead of O(N3).

Original languageEnglish (US)
Pages (from-to)509-532
Number of pages24
JournalNumerische Mathematik
Volume99
Issue number3
DOIs
StatePublished - Jan 1 2005

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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