Programs in Physics & Physical Chemistry
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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.|
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.
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.
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.
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.
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