A dual vector spectral element method for waveguide analysis

A dual vector spectral element method is proposed for waveguide analysis. An electromagnetic waveguide problem is cast from the Lagrangian system with single variable (electric or magnetic field), into the Hamiltonian system with dual variables (both electric and magnetic fields). Higher order curl-conforming and divergence-conforming vector basis functions based on the Gauss-Lobatto-Legendre polynomials are employed to construct the dual vector spectral element method for solving eigenvalue problems of an electromagnetic waveguide. Numerical results demonstrate that the dual vector spectral element method is free of spurious modes, and it can achieve spectral accuracy with the increase of interpolation degrees of basis functions.