First-Order Singular Basis Functions for Corner Diffraction Analysis Using the Method of Moments

IEEE Trans. Antennas Propagat.

Petrini

2020

Electromagnetic scattering from targets such as thin conducting plates induce singular currents and charges at sharp edges and sharp tips. In this paper, a hierarchical family of divergence-conforming singular basis functions are presented for modeling the singularities associated with current and charge density at tips. These new basis functions are used to increment existing edge-singular bases so that on cells that contain a singular tip where two singular edges join together, the final base combines a hierarchical polynomial representation with linearly independent singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest and for the specific angle at the tip. Several variations on the tip functions are proposed.

Section: Numerical Resultsmentioning

confidence: 99%

“…However, most MoM approaches for the EFIE are based on divergence-conforming basis functions, and Andersson's functions for the square plate are only approximately so. A second attempt at the corner problem was proposed by Ozturk et al [24], who employed triangular cells, but included only one exponent at the tip.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Divergence Conforming Bases for Tip Singularities in Quadrilateral Cells

Graglia

IEEE Trans. Antennas Propagat.

Petrini

2020

“…For cells containing a tip, the representation will employ a mixture of polynomial functions and terms from (6)- (8), in order to include both edge and tip singularities in combination with polynomial terms. A representation that included the dominant tip exponent was proposed in [19]. High order expansions are expected to include multiple tip exponents.…”

Section: Extensions To 3d Problemsmentioning

confidence: 99%

Progress in controlled accuracy numerical solutions of integral equations

2014 International Conference on Electromagnetics in Advanced Applications (ICEAA)

Bibby

2014

This presentation will review the state of progress in high accuracy computations such as the method-of-moments solution of integral equations of electromagnetics.The fundamental question to be addressed is: "What is needed in order to obtain solutions of general problems to 'dialable' accuracy?" In other words, what technological advances are required before we can routinely specify, in advance, that we would like a result that is accurate to N decimal places, and reliably obtain such a result? Specific contributions of the authors toward this goal will be highlighted and ongoing efforts will be detailed.

“…For low-order numerical techniques, substitutive bases (specially constructed singular functions that replace the original basis functions on a 1:1 ratio) can be effective. Substitutive vector bases for edge singularities on triangular cells were proposed by Brown and Wilton [6], Graglia and Lombardi [7], and Ozturk et al [8], while bases for quadrilateral cells were proposed by Andersson [9] and Graglia and Lombardi [7]. Conversely, an additive representation is obtained by augmenting the regular polynomial vector bases with additional independent degrees of freedom (DoFs) to model the singular field behavior [10].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Divergence Conforming Bases for Edge Singularities in Quadrilateral Cells

Graglia

IEEE Trans. Antennas Propagat.

Petrini

2018

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.Index Terms-Basis functions, hierarchical basis functions, method of moments (MoM), singular basis functions, wedges.