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arXiv · 1102.2033

Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

Andras Pataki·Leslie Greengard
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Abstract

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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Andras Pataki, Leslie Greengard. 2011-02-10. Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator. https://doi.org/10.1016/j.jcp.2011.07.005

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