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Manuscript Title: A program package for the Dirichlet problem with axially symmetric boundary conditions.
Authors: J.B. Campbell
Program title: DIRPAK
Catalogue identifier: ABSB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 9(1975)283
Programming language: Fortran.
Computer: IBM 360/67.
Operating system: TSS/360.
RAM: 35K words
Word size: 32
Peripherals: magnetic tape.
Keywords: General purpose, Differential equations, Laplace, Dirichlet problem, Capacitance, Axisymmetric, Finite difference.
Classification: 4.3.

Nature of problem:
In this communication, I describe accurate finite difference techniques for the solution of the Dirichlet problem in cylindrical coordinates with axially symmetric boundary conditions. The program package can be used for the calculation of the capacitance of ring capacitors.

Solution method:
Laplace's equation in cylindrical coordinates is replaced by a nine- point, finite difference approximation. At mesh points close to the boundary of the region, a nine-point, irregular difference approximation is used. The package allows for solution of the difference equations by sucessive overrelaxation (SOR) or by symmetric successive overrelaxation with semi-iterative refinement (SSOR-SI). The gradient of the potential is also approximated by nine-point differences. The total charge on a surface is obtained by integration, using Simpson's quadrature rule.

The region where the Dirichlet problem is being solved cannot contain the axis of symmetry. The capacitor can consist of no more than siz rings.

Running time:
A boundary value problem was solved in an irregular region with 204 mesh points. The difference equations were solved by SOR iteration with a relaxation factor omega = 1.7. The maximum residual of the difference equations was reduced to 10**-8. The computing time for this example was approximately 12 s and the solution was accurate to 6 digits.