Surface based differential forms

Higher-order basis functions have been constructed for surface-based differential forms that are used in engineering simulations. These surface-based forms have been designed to complement the volume-based forms present in EMSolve , a finite element code. The basis functions are constructed on a reference element and transformed, as necessary, for each element in space. Lagrange polynomials are used to create the basis functions. This approach is a necessary step in creating a hybrid finite-element/integral-equation time-domain code for electromagnetic analysis.