Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

Details Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

2011-02-10

arxiv.org/abs/1102.2033v1

Mathematics

Numerical Analysis

20 pages, 5 figures

Scientific paper

In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates $(r,\theta,z)$ with free-space radiation conditions. By combining integral equation methods in the radial variable $r$ with Fourier methods in $\theta$ 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.

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