Condition numbers for higher order vector FEM matrices

Higher order vector basis functions have been widely recognized in the computational electromagnetics community and, furthermore, have been combined with FEM or MOM for solving various electromagnetic problems. Although the higher order approaches have the distinct advantages of higher accuracy and faster convergence, some recognized inherent deficiencies of leading to larger condition numbers of FEM matrices have limited them in the use of iterative methods. A rectangular resonator cavity is considered and the eigenvalue matrix equation is obtained by FEM where the higher order hexahedral vector basis functions are employed to expand the unknown field. The condition numbers of two stiffness matrices resulting from the eigenvalue equation are analyzed with respect to different higher order bases. The results provide deep a insight into higher order approaches.