Triangular prisms for edge-based vector finite element analysis of conformal antennas

This paper deals with the derivation of the edge-based shape functions for the distorted triangular prism and their applications for the analysis of doubly curved conformal antennas in the context of the finite element method (FEM). Although the tetrahedron is often the element of choice for volume tessellation, mesh generation using tetrahedra is cumbersome and the central processing unit (CPU) intensive. On the other hand, the distorted triangular prism allows for meshes which are unstructured in two dimensions and structured in the third dimension. This leads to substantial simplifications in the meshing algorithm, and many conformal printed antenna and microwave circuit geometries can be easily tessellated using such a mesh. The new edge-based shape functions are first validated by computing the eigenvalues of three different cavities (rectangular, cylindrical, and pie-shell). We then proceed with their application to computing the input impedance of conformal patch antennas on planar, spherical, conical, and other doubly curved (ogival) platforms, where the FEM mesh is terminated using an artificial absorber applied conformal to the platform. Use of artificial absorbers for mesh termination avoids introduction of Green's functions and, in contrast to absorbing boundary conditions, a knowledge of the principal radii of curvature of the closure's boundary is not required.