Semi-analytical form of full-wave self-interaction integrals over rectangles

On the rectangular mesh and the decomposition of a Green’s-function-based quadruple integral into elementary integrals

“…However, the most recent S-PEEC method usually adopts a rectangular and orthogonal mesh, which calls for a different type of analysis. Only recently, the work in [30] showed how to decouple a double-surface integral used in the S-PEEC method but only in the 2D scenario, namely for the selfinteraction integrals. In this work, we extend and generalize the work to 3D, namely for mutual-interaction integrals.…”

“…The problem of evaluating the Green's function integrals in triangular patches is also addressed in [28], where the authors exploit a polar-coordinate transformation and a mixed analytic and numerical quadrature that mitigates the singularity and increases the accuracy of the integral computation. For the S-PEEC method with rectangular mesh, some first attempts in this direction have been made in [29,30]. In [29], the Taylor expansion of the exponential term in the Green's function allows a complete analytic formulation of both the self-interaction and the mutual-interaction integrals.…”

“…However, the accuracy depends on the Taylor expansion order, and the method suffers when used for lossy materials in the low-frequency range. The paper [30] proposes a novel semi-analytical approach for the self-interaction integrals over rectangles. The technique is based on the mathematical manipulation of the integral that is firstly converted into a two-dimensional (2D) integral, then into a one-dimensional integral by transformation into polar coordinates.…”

“…In this work, we follow a similar approach as in [30] but extending it to the mutual-interaction integrals used in the S-PEEC method. In fact, in [30] only the local behavior of the integrals has been considered, i.e., all calculations were done for the 2D case.…”

“…In this work, we follow a similar approach as in [30] but extending it to the mutual-interaction integrals used in the S-PEEC method. In fact, in [30] only the local behavior of the integrals has been considered, i.e., all calculations were done for the 2D case. In the present paper, we generalize these results to the 3D case and consider different spatial configurations and aspect ratios.…”