Abstract
Singular divergence-conforming bases have been proposed for the solution of integral equations although they have seen only occasional use in practical applications. The existing singular bases are not hierarchical, which prevents their use in adaptive $ {p}$ -refinement applications. In this paper, a new family of singular hierarchical basis functions is proposed for quadrilateral cells. These functions model the singularities associated with current and charge density at edges and are more convenient for modeling such singularities than triangular bases of the same kind. The basis functions are of the additive kind and combine a hierarchical polynomial representation on quadrilaterals with linearly independent singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest. Moreover, the added singular basis functions are computed on the fly. On the basis of various reported numerical results, this paper also illustrates the difficulties, the advantages, the accuracy, and the cost of using such bases in the method of moment solutions of integral equations.
Highlights
T HE electromagnetic modeling of complex 3-D structures requires numerical techniques
Sectors having aperture angle higher than 180◦ are termed “reentrant”; these are out of the scope of this article and ought to be numerically modeled in a manner different from the one reported in this article. Previous work on this topic was published by Andersson, who carried out a method of moments (MoM) analysis of the rectangular plate by developing special basis functions that provide the leading order current and charge singularities on rectangular cells within the electric field integral equation (EFIE) [5]
These new functions form a hierarchical set whose lowest-order members are motivated by the Andersson bases; members of the set may be added to the edge-singular bases of [3] in cells connected to tips to more properly model the current and charge density singularities
Summary
T HE electromagnetic modeling of complex 3-D structures requires numerical techniques. Sectors having aperture angle higher than 180◦ are termed “reentrant”; these are out of the scope of this article and ought to be numerically modeled in a manner different from the one reported in this article Previous work on this topic was published by Andersson, who carried out a method of moments (MoM) analysis of the rectangular plate by developing special basis functions that provide the leading order current and charge singularities on rectangular cells within the electric field integral equation (EFIE) [5]. In the following, improved divergence-conforming basis functions are proposed for modeling tip singularities of salient sectors of arbitrary aperture angle These new functions form a hierarchical set whose lowest-order members are motivated by the Andersson bases; members of the set may be added to the edge-singular bases of [3] in cells connected to tips to more properly model the current and charge density singularities.
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