Abstract
Recent approaches to model corner singularities in electromagnetic analysis require a treatment substantially different from that of edge singularities. In this article, new algorithms are proposed for handling the combination of corner singularities and Green’s function singularities on quadrilateral cells in method-of-moments procedures.
Highlights
T HE Method of Moments (MoM) and the finite element method (FEM) often use vector basis functions defined on subdomains of simple shape [1]
The mapping formulas from parent to child coordinates are usually of the polynomial type so that it is simple to turn a parent into child coordinates
When the structures to be modeled contain edges or corners, it is possible to augment the set of bounded basis functions with an appropriate set of unbounded or singular basis functions that incorporate the singular behavior of the fields in the neighborhood of the edges [1], [2] and corners [3]
Summary
T HE Method of Moments (MoM) and the finite element method (FEM) often use vector basis functions defined on subdomains of simple shape [1] It is common practice for these functions to be defined in a parent ξ -space and mapped by coordinate transformations onto the 3-D x-y-z child-space of the observer [1]. When the structures to be modeled contain edges or corners, it is possible to augment the set of bounded basis functions (normally vector polynomials) with an appropriate set of unbounded or singular basis functions that incorporate the singular behavior of the fields in the neighborhood of the edges [1], [2] and corners [3] In these cases, a second nonlinear mapping from the parent to a grandparent ζ -space becomes necessary to perform the required numerical integrals [2].
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