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

Rafael Florencio,Álvaro Somolinos,Iván González,Felipe Cátedra

doi:10.3390/electronics9020234

Rafael Florencio, Álvaro Somolinos + Show 2 more

Open Access

https://doi.org/10.3390/electronics9020234

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Journal: Electronics	Publication Date: Jan 31, 2020
Citations: 3	License type: CC BY 4.0

Affiliation: University of Alcalá

Abstract

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.

Highlights

In the design and analysis of electromagnetic devices likes frequency selective surfaces (FSSs) [1], reflectarrays/transmitarrays [2], leaky wave antennas [3] and metasurfaces antennas [4], efficient electromagnetic analysis tools of multilayer periodic structures are required
We show that this new approach leads to discrete cyclic convolutions which were be efficiently computed for a very dense equi-spaced mesh by means of an Fast Fourier Transform (FFT) procedure
Figure structure which is considered in this work

Summary

Introduction

In the design and analysis of electromagnetic devices likes frequency selective surfaces (FSSs) [1], reflectarrays/transmitarrays [2], leaky wave antennas [3] and metasurfaces antennas [4], efficient electromagnetic analysis tools of multilayer periodic structures are required. Generalized subsectional rooftop BFs are defined on a pair of adjacent Bézier patches in [19] to approximate the surface density currents induced on metallic surfaces Despite all these improvements, the direct computation of MM matrix entries leads to computational complexity of CPU time consumption as a function of the number of BFs Nb which is roughly O(Nb 2 ) [23,24]. Since the Green’s functions and generalized rooftops involved in the discrete convolutions are not strictly periodic functions, an EPP which contains the original problem is proposed [26] We show that this new approach leads to discrete cyclic convolutions which were be efficiently computed for a very dense equi-spaced mesh by means of an FFT procedure.

Description of the Problem

Efficient Computation of MM Matrix Entries Using Pulses Expansions of BFs

Results

Square

Two Concentric Split Rings

Conclusions