Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

Tonatiuh Sánchez-Vizuet, Antoine J. Cerfon

Research output: Contribution to journalArticlepeer-review


We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.

Original languageEnglish (US)
Article number025018
JournalPlasma Physics and Controlled Fusion
Issue number2
StatePublished - Feb 2018


  • Fokker-Planck collisions
  • kinetic calculations
  • orthogonal polynomials
  • pseudo spectral methods

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Condensed Matter Physics


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