Application of Physical Spline Finite Element Method (Psfem) to Fullwave Analysis of Waveguides

Abstract

Abstract-In this paper, the physical spline finite element method (PSFEM) is applied to the fullwave analysis of inhomogeneous waveguides. Combining (rectangular) edge element and the PSFEM, the cubic spline interpolation is successfully applied to the wave equation. For waveguide problems, the resulting nonlinear eigenvalue problem is solved by a simple iteration method in which the initial estimate is taken as the linear Lagrange interpolation, and then the solutions are improved by a few iterations. The bandwidth of the resultant matrix from the PSFEM is the same as that of linear Lagrange interpolation and is sparse. As a result, sparse matrix solver can be used. Three typical examples are demonstrated and compared with the analytical solutions and with the linear Lagrange interpolation results. It is observed that the present method converges much faster than the Lagrange interpolation method.

A Single-Feed Cylindrical Superquadric Dielectric Resonator Antenna for Circular Polarization

“…In particular, the three-dimensional (3D) FEM allows for the rigorous analysis of a broad range of practical structures [16][17][18][19][20]. The routine use of the FEM in design problems can, however, become cumbersome due to the vast computational resources often required.…”

Dielectric Resonator Antenna Mounted on a Circular Cylindrical Ground Plane

“…The results are compared with that calculated by the finite integration technique (FIT). The finite element method is one of the most popular numerical techniques to solve a wide range of problems in applied science and engineering [9,10]. In FEM, the region under consideration is discretized by finite elements, a variation of the unknown is assumed within each element, and the element response matrices are then found.…”

Mixed Finite Element Method for 2d Vector Maxwell's Eigenvalue Problem in Anisotropic Media

“…Because the nodal basis functions do not have this property, making use of nodal based finite element method to solve vector Maxwell's eigenvalue problem with inhomogeneous medium will lead to the presence of nonphysical nonzero eigenvalues. In 1980s, Nédélec [10,11] proposed the edge elements, which can preserve this actual physical property of electric field E. Therefore edge elements are very well suited for approximating electric field E. The review of edge element method has been given in [12]. For the Maxwell's eigenvalue problem in isotropic media, with the edge element method there are no spurious modes with nonzero eigenvalues, but the number of spurious modes with nonphysical zero eigenvalue is equal to the number of interior nodes inside the computational domain [13,14].…”