is to be solved over a region R where is a positive function of the rectangular coordinates x, y, and may also depend A finite-difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two-dimen-on or its derivatives, and S is a given function of x, y. sional Poisson equation ١ и (١) ϩ S ϭ 0, where is a function of The boundary conditions are taken to be of the form a ϩ or its derivatives, S is a function of position, and or its normal b Ѩ/Ѩn ϭ c, where Ѩ/Ѩn is the normal derivative and a, derivative is specified on the boundary. The finite-difference equab, c are constants that may take on different values over tions are solved by successive overrelaxation. The triangle mesh, different portions of the boundary. The dependent variable which is constructed numerically by solving Laplace's equation, is easily adapted to nonrectangular boundaries and interfaces. Exam-is assumed to be continuous over R, and the quantities ples of numerical results are given for the magnetostatic problem
, S are assumed to be continuous over subregions of R, with iron, and other possible applications are mentioned. ᮊ 1967 so that there may be interfaces at which and S are discon-Academic Press tinuous; at such interfaces, (Ѩ/Ѩn) is assumed to be continuous.
The basic assumptions of the finite-difference method