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Manuscript Title: POT4A: a program for the direct solution of Poisson's equation in complex geometries.
Authors: S.J. Beard, R.W. Hockney
Program title: POT4A
Catalogue identifier: ACDB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 36(1985)25
Programming language: Fortran.
Computer: RAL IBM 360/195.
Operating system: OS-MVT.
RAM: 324K words
Word size: 32
Keywords: General purpose, Differential equation, Poisson's equation, Direct methods, Analysis fourier, Cyclic reduction, Irregular regions, Two-dimensional, Isolated system, Electrodes, Dielectric interfaces, Capacity matrix, Electromagnetic.
Classification: 4.3, 10.

Subprograms used:
Cat Id Title Reference
ABUF_v1_0 OLYMPUS CPC 7(1974)245
ABUF_v2_0 OLYMPUS FOR IBM 370/165 CPC 9(1975)51
ABUF_v3_0 OLYMPUS FOR CDC 6500 CPC 10(1975)167
ABUA_v1_0 FOUR 67 CPC 2(1971)127

Nature of problem:
The program solves Poisson's equation in a rectangular region. Electrodes and dielectric interfaces can be included anywhere in the region. An electrode is defined as a line segment along which the potential is held at a given value. A dielectric interface is defined as a line across which the normal component of the electric displacement is held constant. The boundary conditions on the edge of the rectangle can be given value, zero normal gradient or periodic in the x-direction. In the y-direction, in addition to these conditions, a mixed boundary condition of the form a thetha + b delta thetha/delta y = c(x) and an open boundary condition, where delta thetha/delta y > 0 as abs(y) > infinity are included. The program was developed to solve problems in electrostatics but can also be applied in other fields.

Solution method:
The program solves a five-point finite difference form of Poisson's equation using Hockney's Fourier Analysis-Cyclic Reduction Algorithm, with one level of odd-even reduction. The effects of electrodes and changes in dielectric constant are calculated using a numerical capacity matrix technique.

Restrictions:
The problem must be embedded in a rectangular region. The number of electrode and interface line segments is limited to 150. The dielectrics are assumed to have the polarisation proportional to the electric field, so that the field, E, and the displacement D are related by D = Epsilon E (where Epsilon is the permittivity of the material).

Unusual features:
The program is written in standard FORTRAN using the OLYMPUS conventions for structure, layout, notation and documentation. The program requires a function which generates uniformly distributed random numbers in the range 0 to 1.

Running time:
The c.p.u. time, T (in seconds), for the solution on a rectangular mesh NX*NY is, to within 10%, T = k1NXNY + k2 (where k1 = 25 mu sec/(mesh point) and k2 = 7 ms. In general if electrodes or dielectric interfaces are included the time is doubled. The initialisation stage take's a negligible time if no electrodes or interfaces are present. When electrodes and interfaces are used the initialisation time is approximately nT (where n is the number of electrode and interface line segments used).