A novel method of applying finite element method to open region problems: Electrostatic case

Finite Element/Finite Difference Techniques for solution of differential form of Maxwell's equation are well known. However, when applied to open region problems, the termination of the mesh at the finite distance from the object generally poses problems. In this work, while utilizing the finite element technique to open region problems, the mesh is terminated close to the object using a truncation condition based on MEI (Measured Equation Invariance) concept. The MEI concept is based on the integral equation solution approach using Green's functions which automatically enforce the radiation condition. Utilizing this novel approach leads to an increased computational efficiency of the finite element method. The major advantages of the present scheme are significant reduction in the number of unknowns yet retaining the sparsity of the generating matrix. Typical numerical results are presented for the solution of Laplace's Equation to illustrate the accuracy of the technique.