Search results

A hybrid formulation is proposed that incorporates finite element substructuring and Galerkin boundary elements in the numerical solution of Poisson's or Laplace's equation with open boundaries. Substructuring the problem can dramatically decreases the size of matrix to be solved. It is shown that the boundary integration that results from application of Green's first theorem to the weighted residual statement can be used to advantage by imposing potential and flux continuity through the contour which separates the interior and exterior regions. In fact, the boundary integration is of exactly the same form as that found in Galerkin boundary elements.

We present two models of the electric field for a canonical problem in electric discharge machining. In particular, an analytical solution based on optimal parameter estimation is discussed, followed by a comparison with numerical solutions based on finite elements and Galerkin boundary elements. The problem is interesting because the structure of the field near the sharp asperity is a critical parameter in realistic models of the electric discharge machining process.