Electromagnetic Waves, Materials, and Computation with MATLAB®

381

17

Advanced Topics on Finite-Element Method

*

17.1 Node- and Edge-Based FEM

Let us consider the example of a ridged waveguide. Point A is on a sharp conducting cor-

ner of 90° internal angle. A eld point in the waveguide can be described by the cylindrical

co-ordinates shown in Figure 17.1.

In the neighborhood of a point such as A, it can be shown that the longitudinal compo-

nents E

z

and H

z

vary as ρ

1/3

and the transverse components E

ρ

, E

ϕ

, H

ρ

, and H

ϕ

have singu-

larities at the point A (see Appendix 17A) and vary as ρ

−2/3

. If the point A is on an edge, the

transverse components of E or H at A becomes innite. If we expand longitudinal compo-