A Domain Decomposition Scheme With Curvilinear Discretizations for Solving Large and Complex PEC Scattering Problems

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

“…Metallic surface is discretized by f SH n (r), as defined over single triangular elements near the cutting contours. Because f SH n (r) cannot ensure the continuity of J S (r) across the cutting contours, an additional continuity term [9] is introduced to enforce this continuity in this DG-VSIE. The electric potential generated by error electric charges can be expressed as…”

“…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 [6] and [7], by introducing half RWG basis functions, the SIE allows nonconformal discretization in the cutting contours. However, half RWG basis functions cannot ensure the continuity of surface current across the cutting contours; therefore, an additional internal penalty term [7,9] depending on the line integral over interactions of nonmatching meshes is introduced to enforce this continuity. To improve the capability of modeling complex electrically large objects, the conventional D-formulation VIE (DVIE) [10], Eformulation VIE (EVIE) [11], and VSIE with nonconformal discretization [12,13] have been developed for dielectric objects and composite objects.…”

“…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.…”

“…Different from the previous work, our DG-VSIE applies DG-JVIE and DG-SIE respectively to the dielectric part and metallic part, through which the conformal as well as nonconformal meshes can be used for volume and surface discretization. For this proposed DG-VSIE method, several remarks should be given as follows: 1) by introducing half CRWG bases and half CSWG bases in this VSIE, fewer unknowns than the conventional VSIE with CRWG and CSWG bases defined in conformal elements can be obtained; 2) the hyper-singularity problems are avoided by the use of the vector and scaler potentials rather than the dyadic Green's function; 3) a new continuity term [9] is adopted in DG-SIE to enforce the continuity of surface current across the cutting contours, which avoids the introduction of a stabilization term relying on the line integral over interactions of nonmatching meshes; 4) in comparison with the conventional VSIE method, the proposed DG-VSIE shows advantages in alleviating the difficulty of mesh generation and enhancing the accuracy of geometrical modeling. Moreover, fewer unknowns and less simulation time can be obtained by this DG-VISE than that of using nonconformal VSIE with the constant piecewise basis functions [12].…”