Irregular vector triangles and tetrahedra for finite-element analysis in electromagnetics

The potential advantages and related costs of developing irregular triangles and tetrahedra for vector field modeling applications in the finite-element analysis of electromagnetic systems are investigated. The "irregular-cut" formulations for scalar field modeling are generalized to derive analogous "edge element" definitions. The formulations are developed independent of the choice of vector basis; then implemented and tested using both the classical mixed-order bases, and the hierarchal grad-curl basis. The results illustrate that the flexibility and efficiency of purely localized h-refinements offered by irregular scalar elements translate into similar benefits, at comparable costs, for vector elements.