Highorder triangular finite elements for electromagnetic waves in anisotropic media
Abstract
Specialized functionals are introduced for traveling and circulating electromagnetic waves in planar and axisymmetric twodimensional geometries, without recourse to complex arithmetic. The singularities in the functional for axisymmetric geometries are eliminated by a transformation of the field components. The transformed fields are approximated by highorder interpolation polynomials over triangular regions in the xy and rz coordinate planes. A matrix expression assembled from constant element matrices and geometric factors relating to triangle shape, size, and position is obtained which is the discretized equivalent of the original functional. The necessary element matrices have been computed to sixthorder polynomial approximation. The procedure for assembling a global problem is stated. Finally, a matrix equation is generated by minimizing the discretized functional.
 Publication:

IEEE Transactions on Microwave Theory Techniques
 Pub Date:
 May 1977
 DOI:
 10.1109/TMTT.1977.1129103
 Bibcode:
 1977ITMTT..25..353K
 Keywords:

 Anisotropic Media;
 Electromagnetic Wave Transmission;
 Finite Element Method;
 Functional Analysis;
 Traveling Waves;
 Interpolation;
 Matrices (Mathematics);
 Polynomials;
 Singularity (Mathematics);
 Triangles;
 Variational Principles;
 Communications and Radar