EFFICIENT SINGULAR ELEMENT FOR FINITE-ELEMENT ANALYSIS OF QUASI-TEM TRANSMISSION-LINES AND WAVE-GUIDES WITH SHARP METAL EDGES

The FEM presents a slow rate of convergence when it is used in the ana lysis of quasi-TEM transmission lines or homogeneous waveguides with f ield singularities. In order to improve this drawback, mesh techniques or vector elements that cope with the singularities can be used. A di fferent solution is to employ scalar singular elements although, most of those that have been used are only compatible with first-order ordi nary elements or can only be used with field singularities of order O( r-1/2) and O(r-1/3). In this paper, we present an improvement on the r ate of convergence of FEM by employing a scalar singular element, whic h can be utilized for any order of singularity, is compatible with qua dratic or higher order standard elements and is also easy to implement in standard finite element codes. Several transmission lines and wave guides with sharp metal edges have been analysed with a reduced number of degrees of freedom that compares well with other FEM approaches. W e also show that electromagnetic fields computed using the proposed si ngular element have very good agreement with the ones theoretically ex pected from the singular edge condition.