The Advantages of Triangular and Tetrahedral Edge Elements for Electromagnetic Modeling with the Finite-Element Method

In this paper, we examine the numerical dispersion properties of the tetrahedral edge element in comparison to other edge and nodal elements. For all nodal elements as well as hexahedral edge elements, the phase error is always either positive or negative for waves propagating at any incidence angle, which means that the error accumulates as the wave propagates from element to element. This effect can produce large errors for electrically large geometries. On the other hand, the tetrahedral edge elements can produce either a negative or positive phase error, depending on the direction of propagation through the element. For an unstructured mesh, phase cancellation occurs since the orientation of the tetrahedral elements are arbitrary. Because of the cancellation, the numerical dispersion error is very low for meshes composed of well-shaped tetrahedral edge elements. Numerical results are presented to demonstrate this point.