Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator

Authors:
Andras Pataki;Leslie Greengard
Affiliations:
Courant Institute, New York University, 251 Mercer Street, NY 10012, United States;Courant Institute, New York University, 251 Mercer Street, NY 10012, United States
Venue:
Journal of Computational Physics
Year:
2011

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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,@q,z) with free-space radiation conditions. By combining integral equation methods in the radial variable r with Fourier methods in @q 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.