A 3-d spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields

A three-dimensional spectral-element method (SEM) based on Gauss-Lobatto-Legendre polynomials is proposed to solve vector electromagnetic-wave equations. To suppress spurious solutions, mixed-order curl conforming vector basis functions are used in the SEM. The advantages of this method include its high-order accuracy and its diagonal mass matrix due to the use of orthogonal Legendre polynomials. Thus, the proposed method leads to a regular eigenvalue problem rather than a generalized eigenvalue problem, greatly reducing the computer memory requirement and CPU time in comparison with the conventional high-order finite-element method (FEM). Numerical examples of eigenvalue problems verify the spectral accuracy with the interpolation orders and show that the SEM is superior to the FEM for the class of problems considered. A waveguide model is analyzed with mixed boundary conditions and its results are in excellent agreement with reference values. All numerical results show that the SEM is an efficient alternative to the FEM for electromagnetic fields.