Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

Andras Pataki, Leslie Greengard

Research output: Contribution to journalArticlepeer-review


In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates (r, θ, z) with free-space radiation conditions. By combining integral equation methods in the radial variable r with Fourier methods in θ and z, we show that high-order accuracy can be achieved in both the governing potential and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. We show how these solvers can be applied to the evaluation of the Coulomb collision operator in kinetic models of ionized gases.

Original languageEnglish (US)
Pages (from-to)7840-7852
Number of pages13
JournalJournal of Computational Physics
Issue number21
StatePublished - Sep 1 2011


  • Biharmonic equation
  • Collision operator
  • Fast solvers
  • Plasma physics
  • Poisson equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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