hp-Adaptation for the FEM Analysis of Waveguides
Thesis (MScEng (Electrical and Electronic Engineering))--Stellenbosch University, 2008.
The nite element method (FEM) is a powerful tool for the computational analysis of a wide range of electromagnetic problems. As the complexity of the problems is increased so are the demands in terms of the computational resources required to obtain a su ciently accurate solution. In an attempt to obtain a desired accuracy at a lower computational cost adaptive and higher order methods are often employed. These methods generally entail re ning the solution only in the areas where greater complexity is required, thus decreasing the total computational demand. The adaptive nite element method is implemented and used to analyse the transverse electric cuto eigenmodes of 2D waveguiding structures. The higher order hierarchical vector basis functions that form part of this implementation are automatically generated to very high orders, with the results presented in excellent agreement to analytical ones where applicable. Accuracy to the order of numeric precision is attained. Using these adaptive methods, it is also possible to achieve improved cost e ciency of the error metrics considered with respect to storage requirements and computational cost.