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Manuscript Title: DELSQPHI, a two-dimensional Poisson-solver program.
Authors: J.P. Christiansen, R.W. Hockney
Program title: DELSQPHI
Catalogue identifier: ABUB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)139
Programming language: Fortran.
Computer: ICL KDF9.
Operating system: EGDON 3.
RAM: 6K words
Word size: 48
Keywords: Plasma physics, Two-dimensional, Poisson, Fast fourier transform, Collisionless plasma, Stability, Recursive cyclic Reduction.
Classification: 19.3, 19.6.

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

Nature of problem:
Plasma simulations, fluid flow problems and many related computations require a fast method of solving Poisson's equation on a discrete mesh. DELSQPHI has been written for this purpose.

Solution method:
The solution of Poisson's equation is obtained using a 5-point finite difference approximation. The method of solution is "direct", i.e. it does not involve any iterative procedures. A reduction of the matrix equations eliminates the unknown quantites on alternate lines, (odd lines") and a fast FOURIER transform technique is used to decouple the remaining equations. The FOUR67 package is used for this. The fourier components of the potential are found by a method called recursive cyclic reduction. The inverse Fourier transform yields the solution on even lines and the use of the 5-point approximation completes the solution for the odd lines. For storage economy the calculated potential overwrites the charge distribution which was previously supplied as input.

Restrictions:
DELSQPHI will accept any real charge distribution specified in floating point form on a rectangular mesh of dimensions NX and NY. The maximum size of the mesh is determined by the size of the core store of the computer employed.

Running time:
The execution times depend on the mesh dimensions and on the set of boundary conditions chosen. On the ICL KDF9 at Culham Laboratory the solution is obtained over a 64X64 mesh in 13 s when the electric field field is zero on the (x,y) boundaries, and in 10 s when the potential is periodic in (x,y). Compilation and loading on the KDF9 take about 250 s. 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.