Strong FEM solution for the square coaxial line

Abstract

In this paper the strong FEM formulation based on hierarchical basis functions of higher order and Galerkin method is proposed. This physically means that the boundary conditions -continuity of the electric potential V and of the normal component of vector D, on element boundaries are exactly satisfied. As a benchmark example, a coaxial transmission line of the square cross section is analyzed.

Strong and weak FEM formulations of higher order for quasi‐static analysis of shielded planar transmission lines

“…For homogeneous elements (i.e., for constant e inside each element), strong 2D basis functions can be constructed in analogy with 2D weak basis functions, namely by generalization of 1D strong hierarchical basis functions of the form presented in [3]. The resulting functions [5] are given by Eq. (4) and where l represents x and y dimensions of the element ( l x and l y in Fig.…”

“…We have previously shown [5] that both presented FEM formulations, applied to a benchmark problem of a square coaxial line, result in high accuracy and a uniform convergence and that the weak formulation of the order n = n = 3 is somewhat more accurate (for the same number of unknowns) than the other strong and weak formulations considered. Our next task is to apply the presented strong and weak FEM formulations on more realistic shielded planar transmission lines.…”