Implementation for higher order curvilinear vector FEM

To overcome the shortcoming of typical rectilinear higher order vector elements which cannot exactly model curved boundaries, an efficient higher order geometrical mapping technology based on tetrahedral hierarchical vector elements is studied. The implementation process for 3D higher order curvilinear vector elements is researched, and some key issues are discussed. The results of a numerical experiment that investigates the resonant problem of a spherical cavity, compare the performance of different rectilinear and curvilinear vector elements systematically (such as calculated accuracy, condition numbers), which are also applied to the eigen-solution of inhomogeneously-filled cavities. Numerical results demonstrate that for the same computational efficiency, curvilinear elements can provide more accurate results than rectilinear elements when higher order elements are used to such problems.