A prism finite element time domain method with automatic mesh generation for solving microwave cavities

We describe the application of a finite element time domain approach for modeling EM problems whose geometries are two-dimensional in nature and can be meshed by using prism elements. The use of prism elements significantly reduces the number of unknowns. The proposed method uses edge elements on a prism element to model the spatial variation of the fields and employs finite differences in time to solve the time varying Maxwell's equations. To validate and investigate the accuracy of the algorithm, we first applied the method to study the resonant frequencies of various microwave cavities. Furthermore, one of the most difficult problems associated with finite element modeling is the discretization of the problem domain. We discretize the cross section by triangles, and extend them to form the prism mesh for the computation. Delaunay triangulation techniques have been chosen to automatically discretize any two dimensional cross section into triangles. One of the properties of Delaunay triangulation is that the circumcircle of a Delaunay triangle may not contain another Delaunay vertex in its interior. Hence, in the event that the fourth point of the quadrilateral is located within the circle, the diagonal is swapped. This circle-swapping technique forms the heart of our two-dimensional mesh generation.