Nonconformal Discretization of Electric Current Volume Integral Equation With Higher Order Hierarchical Vector Basis Functions

Discontinuous Galerkin Vsie Method for Electromagnetic Scattering From Composite Metallic and Dielectric Structures

“…In the geometrical modeling, the dielectric volume and metallic surface are respectively discretized into the curved quadratic tetrahedral and triangular elements, whose flexibility makes our VSIE more powerful and attractive. According to [18], a curved quadratic tetrahedral element in physical space (x, y, z) can be described by a second-order transformation from the reference tetrahedron in normalized parentcoordinates (ξ 1 , ξ 2 , ξ 3 , ξ 4 ). The associated shape function is…”

“…where V (ξ 1 , ξ 2 , ξ 3 ) is the Jacobian factor over a tetrahedron [18]. To model discontinuous currents across the interface between two different media in JVIE, monopolar CSWG basis functions f V H n (r) defined over a single tetrahedral element can be utilized, because J V (r) has no continuity across material interfaces.…”

“…To alleviate the above problems, integral equation methods, e.g., SIE [6][7][8][9], VIE [10][11][12][13][14][15][16]19], VSIE [17,18], with nonconformal discretization have been extensively studied. In [6] and [7], by introducing half RWG basis functions, the SIE allows nonconformal discretization in the cutting contours.…”

“…In recent years, the J-formulation VIE (JVIE) in terms of equivalent polarization currents J has been proposed for the scattering simulation of anisotropic materials [15], bi-anisotropic materials [16], multilayered materials [17], and highly inhomogeneous materials [18], where the accuracy, flexibility, and efficiency of the JVIE were well demonstrated. It is then preferred over the DVIE and EVIE [15,19,20] due to its robustness.…”

“…Given the superiority of JVIE and a wider application range in VSIE, to extend this JVIE to VSIE is of great importance for the CMD structures' EM property analysis. Although the SIE and JVIE are respectively introduced in [8,9] and [18] to support nonconformal discretization, its combination version, i.e., coupling the SIE with J-formulation JVIE, has not been used to construct any form of VSIE with nonconformal discretization yet. To the best of our knowledge, this is the first time that the coupling is applied into the VSIE to simulate CMD structures.…”