A fast, higher order three-dimensional finite-element analysis of microwave waveguide devices

A fast, higher order three-dimensional finite-element method is presented for the efficient and accurate analysis of microwave waveguide devices. Two solution algorithms are designed. The first one uses mixed-order triangular prism elements in conjunction with a special frontal solver. It has a very low memory requirement, and is extremely fast for waveguide devices with one dimension longer than the other two. However, the solution must be repeated at each frequency. The second solution algorithm employs higher order tetrahedral elements, which are particularly suitable for modeling complex devices, in conjunction with the multifrontal solver. This algorithm has the major advantage that it can be combined with the asymptotic waveform evaluation and complex frequency-hopping techniques to perform fast frequency-sweep calculations to obtain the response of a device over a wide band. Numerical results are presented to demonstrate the performance of both solution algorithms and their higher order convergence. It is shown that, using the first solution algorithm, the solution accuracy increases with the order of elements for a fixed number of unknowns, while the computing time and memory requirements remain basically unchanged. With the second solution algorithm, the solution accuracy improves even faster with the increase in the order of elements for a fixed number of unknowns, and very surprisingly, the computing time and memory requirements actually decrease sometimes.