Singular vector expansion functions for finite methods

This paper describes the fundamental properties of new singular vector bases that incorporate the edge conditions in curved triangular elements. The bases are fully compatible with the interpolatory or hierarchical high-order regular vector bases used in adjacent elements. Several numerical results confirm the faster convergence of these bases on wedge problems and the capability to model regular fields when the singularity is not excite

Evaluation of hierarchical vector basis functions for quadrilateral cells

New hierarchical vector basis functions for quadrilateral cells are introduced, and the matrix condition numbers associated with their use are compared to those of existing vector basis families to assess the relative linear independence of the functions. Scale factors are employed to improve the condition numbers. In addition, the proper use of subsets of these families to transition from one order to another (as needed for adaptive -refinement) without exciting spurious modes is considere

Singular Higher-Order Complete Vector Bases for Finite Methods

This paper presents new singular curl- and divergence- conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems

Diffraction by an imperfect half plane in a bianisotropic medium

A general theory to study the electromagnetic diffraction by imperfect half planes immersed in linear homogeneous bianisotropic media is presented. The problem is formulated in terms of Wiener-Hopf equations by deriving explicit spectral domain expressions for the characteristic impedances of bianisotropic media, which allow one to exploit their analytical properties. In the simpler case of perfect electric conducting and perfect magnetic conducting half planes, the Wiener-Hopf equations involve matrices of order 2, which can be factorized in closed form if the constitutive tensors of the bianisotropic material are of special form. Four of these special cases are discussed in detail. In order to deal with the more general problem, a technique to numerically factorize the Wiener-Hopf matrix kernels is presented. Our numerical approach is discussed on one example, by considering the previously unsolved problem of a perfect electric conducting half plane in a gyrotropic medium. The reported numerical results show that the diffracted field contribution is obtained by use of the saddle point integration method

Curl-conforming hierarchical vector bases for triangles and tetrahedra

A new family of hierarchical vector bases is proposed for triangles and tetrahedra. These functions span the curl-conforming reduced-gradient spaces of Nédélec. The bases are constructed from orthogonal scalar polynomials to enhance their linear independence, which is a simpler process than an orthogonalization applied to the final vector functions. Specific functions are tabulated to order 6.5. Preliminary results confirm that the new bases produce reasonably well-conditioned matrice

Cylindrical Resonator Sectorally Filled With DNG Metamaterial and Excited by a Line Source

A circular cylindrical resonator with metallic walls is analyzed in the phasor domain. The resonator contains a wedge of double-negative (DNG) metamaterial that is anti-isorefractive to the double-positive (DPS) material filling the remaining volume of the resonator, and whose edge is located on the resonator axis. The resonance conditions are established. The problem of an electric line source parallel to the axis and located anywhere inside the DPS region is solved exactly. Numerical results are presented and discusse