Efficient Evaluation of the Finite Part of Pole-Free Sommerfeld Integrals in Half-Space Problems with Predefined Accuracy

Basta, Nikola; Kolundžija, Branko M.

doi:10.1109/tap.2019.2916573

Cited by 2 publications

(2 citation statements)

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“…obtained by MRW [31][32][33] or by DE [34,35] quadrature rules are used as comparison patterns. However, the performance of these two types of quadrature rules have never been compared to each other in an MoM context.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Both MRW [21,25,28] and DE [27,29,30] quadrature rules have been successfully used for the determination of integrals with singularities that arise in the application of the MoM for multilayer problems. In more recent works, results obtained by MRW [31][32][33] or by DE [34,35] quadrature rules are used as comparison patterns. However, the performance of these two types of quadrature rules have never been compared to each other in an MoM context.…”

Section: Description Of the Problemmentioning

confidence: 99%

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Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures

et al. 2020

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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.

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