UTILIZATION OF INTEGRAL EQUATIONS FOR SOLVING 3-DIMENSIONAL TIME-INVARIANT CONSERVATIVE FIELDS

This paper develops and demonstrates a method of obtaining computer solutions to three-dimensional boundary-value problems involving time-invariant, conservative fields in isotropic, linear, and piecewise-homogeneous media. The technique is applicable to the Dirichlet, Neumann, and mixed boundary types of problems. The method is based on a surface integral form of Poisson's equation and results in a set of integral equations. These equations are then approximated by a set of linear algebraic equations which are solved by a digital computer. Numerical approximation of a two-dimensional integral equation effectively reduces the three-dimensional problem to a two-dimensional problem. © 1969.