Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures
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 surfa...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
|
| Series: | Electronics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2079-9292/9/12/2043 |
| _version_ | 1797545946023723008 |
|---|---|
| author | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra Lorena Lozano |
| author_facet | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra Lorena Lozano |
| author_sort | Rafael Florencio |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T14:23:11Z |
| format | Article |
| id | doaj.art-3ea6f1bc59684d0ea37455e80d106259 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T14:23:11Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-3ea6f1bc59684d0ea37455e80d1062592023-11-20T23:13:28ZengMDPI AGElectronics2079-92922020-12-01912204310.3390/electronics9122043Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer StructuresRafael Florencio0Álvaro Somolinos1Iván González2Felipe Cátedra3Lorena Lozano4Department of Physics and Mathematics, University of Alcalá, 28805 Alcalá de Henares, SpainDepartment of Computer Science, University of Alcalá, 28805 Alcalá de Henares, SpainDepartment of Computer Science, University of Alcalá, 28805 Alcalá de Henares, SpainDepartment of Computer Science, University of Alcalá, 28805 Alcalá de Henares, SpainDepartment of Computer Science, University of Alcalá, 28805 Alcalá de Henares, SpainA 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.https://www.mdpi.com/2079-9292/9/12/2043integral equationsmoment methodsmultilayered mediaperiodic structuresreflectarrays |
| spellingShingle | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra Lorena Lozano Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures Electronics integral equations moment methods multilayered media periodic structures reflectarrays |
| title | Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures |
| title_full | Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures |
| title_fullStr | Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures |
| title_full_unstemmed | Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures |
| title_short | Comparison between Specialized Quadrature Rules for Method of Moments with NURBS Modelling Applied to Periodic Multilayer Structures |
| title_sort | comparison between specialized quadrature rules for method of moments with nurbs modelling applied to periodic multilayer structures |
| topic | integral equations moment methods multilayered media periodic structures reflectarrays |
| url | https://www.mdpi.com/2079-9292/9/12/2043 |
| work_keys_str_mv | AT rafaelflorencio comparisonbetweenspecializedquadraturerulesformethodofmomentswithnurbsmodellingappliedtoperiodicmultilayerstructures AT alvarosomolinos comparisonbetweenspecializedquadraturerulesformethodofmomentswithnurbsmodellingappliedtoperiodicmultilayerstructures AT ivangonzalez comparisonbetweenspecializedquadraturerulesformethodofmomentswithnurbsmodellingappliedtoperiodicmultilayerstructures AT felipecatedra comparisonbetweenspecializedquadraturerulesformethodofmomentswithnurbsmodellingappliedtoperiodicmultilayerstructures AT lorenalozano comparisonbetweenspecializedquadraturerulesformethodofmomentswithnurbsmodellingappliedtoperiodicmultilayerstructures |