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Manuscript Title: Computing a Laplacian field component from boundary observations only.
Authors: M.J. O'Connell
Program title: MAGNETSUITE
Catalogue identifier: ABCM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 11(1976)221
Programming language: Fortran.
Computer: IBM 360/195.
Operating system: IBM OS/HASP.
RAM: 40K words
Word size: 32
Peripherals: magnetic tape, disc.
Keywords: Electrostatics, Experimental analysis, Magnet, Potential, Field component, Boundary observation, Laplace.
Classification: 10.

Nature of problem:
Many physics experiments require a knowledge of magnetic field component at a grid of points within the aperture of a magnet. These are to be computed from evenly spaced observations of magnetic field made on the boundary of a hypothetical rectangular box surrounding the volume being considered.

Solution method:
The magnetic field component in vacuum is fully determined by its boundary values, by Maxwell's equations. Consequently it has zero laplacian and has its largest absolute value on the boundary. If it is modelled by a function which itself has a zero laplacian then the errors of representation are largest at the absolute value on the boundary. If these errors are acceptable, the computed values at internal points are even more so. The mathematical model is a sum of products of trigometrical and hyperbolic functions.

The periodicity of the trigometrical functions precludes extrapolation beyond the confines of the box. This is not a handicap in practice.

Unusual features:
The program suite comprises a preliminary program to read data, an analysis program to generate coefficients from the observations and a synthesis program to evaluate the field from the coefficients. To simplify changing the system from one application to another there are also two editing programs which set array dimensions and other data in the analysis and synthesis programs.

Running time:
30 s on IBM 360/195.