New basis functions for the electromagnetic solution of arbitrarily‐shaped, three dimensional conducting bodies using method of moments

Abstract

In this work, we present a new set of basis functions, defined over a pair of planar triangular patches, for the solution of electromagnetic scattering and radiation problems associated with arbitrarily-shaped surfaces using the method of moments solution procedure. The basis functions are constant over the function subdomain and resemble pulse functions for one and two dimensional problems. Further, another set of basis functions, point-wise orthogonal to the first set, is also defined over the same function space. The primary objective of developing these basis functions is to utilize them for the electromagnetic solution involving conducting, dielectric, and composite bodies. However, in the present work, only the conducting body solution is presented and compared with other data.

An alternate set of basis functions for the electromagnetic solution of arbitrarily shaped, three‐dimensional, closed, conducting bodies using method of moments

“…In this section, we present numerical results for a PEC sphere (diameter ϭ 0.15 ) and a cube (length ϭ 0.15 ), and we compare the results with the solution obtained using the procedure presented in [1]. Also, for the case of the sphere, the results are compared with the exact solution.…”

“…The new basis functions are pulse basis functions defined over a pair of triangular patches and tangential to the common edge. The present set of basis functions along with the functions defined in our previous work [1] should prove helpful in obtaining a stable and well-conditioned solution to the material body problem. At present, the work is in progress to apply these two sets of basis functions to material bodies, and the results will be reported in the near future.…”

“…Note that the basis functions defined in (7,8) are actually pulse functions, pointwise orthogonal to each other, defined over the region S n . The electromagnetic solution procedure using the basis functions f n is described in [1], and in this work we present a similar solution using the basis functions g n .…”

“…It may also be noted here that the basis functions g n are less versatile than the basis functions f n . Unlike the basis functions f n , which are applicable to both open and closed bodies as demonstrated in [1], the basis functions g n are applicable to closed bodies only. The main reason for this restriction is that the functions g n are defined parallel to the edges of the planar triangular patches and represent the tangential component of the current.…”

“…In a recent article, we have introduced a new set of pulse-type basis functions, each defined over a pair of planar triangular patches, to calculate the electromagnetic scattering/radiation associated with three-dimensional, arbitrarily shaped conducting bodies [1]. The primary motivation for this work is to develop an efficient and well-conditioned method of moments (MoM) [2] solution for dielectric material bodies via a surface integral equation (SIE) approach [3].…”