Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures
Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) mod...
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| Format: | Article |
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MDPI AG
2020-11-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/11/1938 |
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| author | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra |
| author_facet | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra |
| author_sort | Rafael Florencio |
| collection | DOAJ |
| description | Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner. |
| first_indexed | 2024-03-10T14:47:07Z |
| format | Article |
| id | doaj.art-c442cd3c24954058b76c76ebce132d5b |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T14:47:07Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-c442cd3c24954058b76c76ebce132d5b2023-11-20T21:19:06ZengMDPI AGElectronics2079-92922020-11-01911193810.3390/electronics9111938Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer StructuresRafael Florencio0Álvaro Somolinos1Iván González2Felipe Cátedra3Department 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, SpainFast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner.https://www.mdpi.com/2079-9292/9/11/1938integral equationsmoment methodsmultilayered mediaiterative methodsreflectarrays |
| spellingShingle | Rafael Florencio Álvaro Somolinos Iván González Felipe Cátedra Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures Electronics integral equations moment methods multilayered media iterative methods reflectarrays |
| title | Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures |
| title_full | Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures |
| title_fullStr | Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures |
| title_full_unstemmed | Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures |
| title_short | Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures |
| title_sort | fast preconditioner computation for bicgstab fft method of moments with nurbs in large multilayer structures |
| topic | integral equations moment methods multilayered media iterative methods reflectarrays |
| url | https://www.mdpi.com/2079-9292/9/11/1938 |
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