Higher-order hybrid method for curl-conforming elements on tetrahedrons and bricks

We present a brick-tetrahedron hybrid finite-element method with higher-order basis functions for solving electromagnetic field problems. For the brick-shaped elements, we use mass lumping for interpolatory basis-functions of incomplete order, which yields a diagonal mass-matrix. Hierarchical basis functions of incomplete and/or complete order are used for the tetrahedral elements. We enforce tangential continuity at the brick-tetrahedron interface in the weak sense. Our hybrid method correctly reproduces the lowest eigenvalues with correct multiplicity for a closed cavity-resonator. For tests in a rectangular waveguide, we demonstrate that the hybrid interface yields a low reflection coefficient.