Numerical Solution of Boundary Condition to Poisson's Equation and Its Incorporation into the Program Poisson

1 October 1985

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Nuclear Science

Vol. 32 (5) , 3722-3724
https://doi.org/10.1109/TNS.1985.4334481

Abstract

Two dimensional cartesian and axially-symmetric problems in electrostatics or magnetostatics frequently are solved numerically by means of relaxation techniques -- employing, for example, the program POISSON. In many such problems the "sources" (charges or currents, and regions of permeable material) lie exclusively within a finite closed boundary curve and the relaxation process in principle then could be confined to the region interior to such a boundary -- provided a suitable boundary condition is imposed onto the solution at the boundary. This paper discusses and illustrates the use of a boundary condition of such a nature in order thereby to avoid the inaccuracies and more extensive meshes present when alternatively a simple Dirichlet or Neumann boundary condition is specified on a somewhat more remote outer boundary.

Keywords

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