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Manuscript Title: Solution of Poisson's equation in cylindrical coordinates.
Authors: M.H. Hughes
Program title: DELSQRZ
Catalogue identifier: ABUC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)157
Programming language: Fortran.
Computer: ICL KDF9.
Operating system: EGDON 3.
RAM: 5K words
Word size: 48
Keywords: Plasma physics, Stability, Poisson, Fast fourier transform, Cylindrical, Collisionless plasma.
Classification: 19.3, 19.6.

Subprograms used:
Cat Id Title Reference
ABUA_v1_0 FOUR67 CPC 2(1971)127

Nature of problem:
The DELSQRZ package obtains a rapid solution of Poisson's equation in the (r,z) plane subject to the following boundary conditions: (1) the potentials on the axis and at some radius r=r0 are always given; (2) either (i) the potential is given on the z-boundaries, or (ii) periodic z-geometry.

Solution method:
Poisson's equation is replaced by a 5-point finite difference approximation and the resulting equations are solved by a method based on FOURIER analysis. The FOUR67 package is used for this.

The (r,z) plane is divided into a uniform rectangular mesh of dimensions NR and NZ (not necessarily equal). To simplify the Fourier analysis NZ is restricted to be a power of two.

Unusual features:
The program is written in ASA FORTRAN apart from the use of symbolic dimensions, which on certain computer systems must be replaced by actual numerical values. The PRELUDE section should then be removed.

Running time:
On the Culham KDF9 loading and compilation takes 250 s. The running time depends on the mesh size and on the z-boundary conditions. Typically, on a 64X64 mesh the times are 20 s when the potential is given on the z-boundaries, and 15 s when the z-geometry is periodic.