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Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator
In this paper, we describe a new class of fast solvers for separable elliptic
partial differential equations in cylindrical coordinates with
free-space radiation conditions. By combining integral equation methods in the
radial variable with Fourier methods in and , 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
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.Comment: 20 pages, 5 figure
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