A hybrid method for terminating the finite‐element mesh (electrostatic case)

The finite‐element or finite‐difference techniques are well known for the solution of Maxwell's equation in differential form. But terminating the mesh accurately at a finite distance from the body in the case of an open problem is a major challenge. Though there have been several techniques presented [1, 2], this new approach allows for the terminating surface to encapsulate the body very tightly. In this proposed method, the finite‐element technique is used for open‐region problems, whereas an integral equation solution approach using the Green's function is applied to enforce the radiation condition. At each iteration cycle, field sources within the domain are evaluated and their potential at the terminating surface is calculated. The proposed method leads to increased computational efficiency of the finite‐element method. It can be generalized for the case of inhomogeneous and nonlinear media, for static and dynamic fields. Typical numerical results are presented for the solution of the Laplace equation to illustrate the accuracy of the technique. © 1995 John Wiley & Sons. Inc.