scholarly journals BICGSTAB-FFT Method of Moments with NURBS for Analysis of Planar Generic Layouts Embedded in Large Multilayer Structures

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1476 ◽  
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Multilayer Structure ◽  
Fourier Transforms ◽  
Periodic Problem ◽  
Basis Functions ◽  
Multilayer Structures ◽  
Method Of Moment ◽  
Efficient Computation ◽  
Normalized Error ◽  
Nurbs Surfaces

BICGSTAB-FFT method of moment (MM) scheme is proposed to analyze several levels of planar generic layouts embedded in large multilayer structures when the layout geometries are modeled by NURBS surfaces. In this scheme, efficient computation of normalized error defined in iterative bi-conjugate gradient stabilized (BICGSTAB) method for large multilayer structure analysis problems is implemented. The efficient computation is based on pulse expansion with dense equi-spaced mesh of generalized rooftop basis functions (BFs) defined on NURBS surfaces and equivalent periodic problem (EPP) in order to apply fast Fourier transforms (FFT). Moreover, efficient computation of Green’s functions for multilayer structure is implemented for near and far field regions. Experimental and numerical validations of whole printed reflect array antennas of electrical size between 8 and 16 times the vacuum wavelengths are shown. In these validations, CPU time consumptions of the proposed method are obtained with results between few minutes and half an hour using a conventional laptop.

scholarly journals Method of Moments Based on Equivalent Periodic Problem and FFT with NURBS Surfaces for Analysis of Multilayer Periodic Structures

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 234 ◽  
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Original Problem ◽  
Periodic Structures ◽  
Periodic Problem ◽  
Nurbs Surface ◽  
Direct Computation ◽  
Cpu Time ◽  
Phase Errors ◽  
Nurbs Surfaces ◽  
Time Savings

In this paper, an efficient technique of computation of method of moments (MM) matrix entries for multilayer periodic structures with NURBS surface and Bézier patches modelling is proposed. An approximation in terms of constant pulses of generalized rooftop basis functions (BFs) defined on Bézier patches is proposed. This approximation leads discrete convolutions instead of usual continuous convolution between Green’s functions and BFs obtained by the direct mixed potential integral equation (MPIE) approach. An equivalent periodic problem (EPP) which contains the original problem is proposed to transform the discrete convolutions in discrete cyclic convolutions. The resultant discrete cyclic convolutions are computed by efficiently using the Fast Fourier Transform (FFT) procedure. The performance of the proposed method and direct computation of the MM entries are compared for phases of reflection coefficient. The proposed method is between 9 and 50 times faster than the direct computation for phase errors less than 1 deg. The proposed method exhibits a behaviour of CPU time consumption of O(NbLog10Nb) as the number Nb of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(Nb2) provided by the direct computation of the MM matrix entries.

scholarly journals Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1938
Author(s):  
Rafael Florencio ◽  
Álvaro Somolinos ◽  
Iván González ◽  
Felipe Cátedra
Keyword(s):  
Near Field ◽  
Periodic Problem ◽  
Coefficient Matrix ◽  
Multilayer Structures ◽  
Method Of Moment ◽  
Approximate Inverse ◽  
Matrix Vector Multiplication ◽  
Sparse Approximate Inverse ◽  
Matrix Vector ◽  
Discrete Functions

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.

scholarly journals Closed-Form Expressions for Numerical Evaluation of Self-Impedance Terms Involved on Wire Antenna Analysis by the Method of Moments

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1316
Author(s):  
Carlos-Ivan Paez-Rueda ◽  
Arturo Fajardo ◽  
Manuel Pérez ◽  
Gabriel Perilla
Keyword(s):  
Numerical Integration ◽  
Method Of Moments ◽  
Computing Time ◽  
Basis Functions ◽  
Wire Antenna ◽  
Complex Geometries ◽  
Point Matching ◽  
Piecewise Constant ◽  
Matching Procedure ◽  
Time Required

This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the solution of wire antennas with complex geometries. The new expressions have complexity O(1) with well-defined theoretical bound errors. They were compared with an adaptive numerical integration. We obtain an accuracy between 7 and 16 digits depending on the chosen basis function and segmentation used. Besides, the computing time involved in the calculation of the self-impedance terms was evaluated and compared with the time required by the adaptative quadrature integration solution of the same problem. Expressions have a run-time bounded between 50 and 200 times faster than an adaptive numerical integration assuming full computation of all constant of the expressions.

scholarly journals Self- and Dopant Diffusion in Extrinsic Boron Doped Isotopically Controlled Silicon Multilayer Structures

2002 ◽  
Vol 719 ◽  
Author(s):  
Ian D. Sharp ◽  
Hartmut A. Bracht ◽  
Hughes H. Silvestri ◽  
Samuel P. Nicols ◽  
Jeffrey W. Beeman ◽  
...  
Keyword(s):  
Multilayer Structure ◽  
Secondary Ion Mass Spectrometry ◽  
Diffusion Processes ◽  
Quantitative Description ◽  
Multilayer Structures ◽  
Dopant Diffusion ◽  
Enhanced Diffusion ◽  
Self Diffusion ◽  
Boron Doped ◽  
P Type

AbstractIsotopically controlled silicon multilayer structures were used to measure the enhancement of self- and dopant diffusion in extrinsic boron doped silicon. 30Si was used as a tracer through a multilayer structure of alternating natural Si and enriched 28Si layers. Low energy, high resolution secondary ion mass spectrometry (SIMS) allowed for simultaneous measurement of self- and dopant diffusion profiles of samples annealed at temperatures between 850°C and 1100°C. A specially designed ion-implanted amorphous Si surface layer was used as a dopant source to suppress excess defects in the multilayer structure, thereby eliminating transient enhanced diffusion (TED) behavior. Self- and dopant diffusion coefficients, diffusion mechanisms, and native defect charge states were determined from computer-aided modeling, based on differential equations describing the diffusion processes. We present a quantitative description of B diffusion enhanced self-diffusion in silicon and conclude that the diffusion of both B and Si is mainly mediated by neutral and singly positively charged self-interstitials under p-type doping. No significant contribution of vacancies to either B or Si diffusion is observed.

scholarly journals Method of Moments Simulation of Modulated Metasurface Antennas With a Set of Orthogonal Entire-Domain Basis Functions

2019 ◽  
Vol 67 (2) ◽  
pp. 1119-1130 ◽  
Author(s):  
Modeste Bodehou ◽  
David Gonzalez-Ovejero ◽  
Christophe Craeye ◽  
Isabelle Huynen
Keyword(s):  
Method Of Moments ◽  
Basis Functions ◽  
Entire Domain

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

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