Mesh termination schemes for the finite element method in electromagnetics
Thesis (MScEng (Electrical and Electronic Engineering))--Stellenbosch University, 2007.
The finite element method is a very efficient numerical tool to solve geometrically complex problems in electromagnetics. Traditionally the method is applied to bounded domain problems, but it can also be forged to solve unbounded domain problems using one of various mesh termination schemes. A scalar finite element solution to a typical unbounded two-dimensional problem is presented and the need for a proper mesh termination scheme is motivated. Different such schemes, specifically absorbing boundary conditions, the finite element boundary integral method and infinite elements, are formulated and implemented. These schemes are directly compared using different criteria, especially solution accuracy and computational efficiency. A vector finite element solution in three dimensions is also discussed and a new type of infinite element compatible with tetrahedral vector finite elements is presented. The performance of this infinite element is compared to that of a first order absorbing boundary condition.