Abstract
A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.
Highlights
IntroductionLeakywave antennas [4,5,6] are analyzed many times assuming a periodic environment
Many electrical devices built using planar multilayer structures such as frequency selective surfaces (FSS) [1], reflectarray/transmitarray [2,3] antennas, phased array antennas, and metasurface (MTS)leakywave antennas [4,5,6] are analyzed many times assuming a periodic environment
The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and Non Uniform Rational B-Splines (NURBS) modelling
Summary
Leakywave antennas [4,5,6] are analyzed many times assuming a periodic environment This assumption is known as local periodicity assumption and it was experimentally validated in the literature, and was enabled for accurate design of many antennas [3]. Electronics 2020, 9, 2043 used in the design of a reflectarray, the scattering problem of a plane wave obliquely incident on a periodic multilayered structure has to be analyzed a huge number of times. A mesh of NURBS surfaces of an arbitrary layout is accurate for constructing and storing the surface of layout, more suitable surface meshing for numerical computation of parameters associated with the surface is preferred (curvature, derivatives, integrations, etc) Bézier patches provide these desired properties with parametric surfaces defined by Bernstein polynomials [9]. In this context, generalized subsectional rooftops functions are usually defined between pairs of adjacent Bézier patches to approximate the surface current densities induced on the layout [7]
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