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Vol. 123, 281-293, 2022
download: 207
NavIC Multipath Signal Analysis for Soil Moisture Sensitivity in the Perspective of a Winter Wheat Crop
Vivek Chamoli , Rishi Prakash and Anurag Vidyarthi
The retrieval of soil moisture in presence of vegetation has received relatively less attention than bare land when observations are made with Global Navigation Satellite System (GNSS). In plane bare land, the reflected GNSS signal is affected by the land characteristics which is dielectric constant of soil. However, in vegetated land, the reflected signal is affected by dielectric constant of soil as well as the characteristics of vegetation which makes the retrieval of soil moisture a cumbersome task in presence of vegetation. Monitoring soil moisture in vegetated land is important for soil health and its suitability for agriculture purposes. Therefore, analysis of soil moisture in presence of vegetation has been studied in this manuscript by utilising the Navigation with Indian Constellation (NavIC) which is a very new entry in GNSS domain by Indian Space Research Organization (ISRO). NavIC receiver setup was installed in a wheat agriculture land situated in Dehradun, India. The wheat crop was sown in the month of November, and it was harvested in the month of April. In situ measurement of soil moisture, crop height, humidity, soil temperature and air temperature were made. Fixed frequency method and Lomb–Scargle Periodogram (LSP) method have been analysed to determine the sensitivity of soil moisture in presence of vegetation. 15° to 30° elevation angle was utilised in the study. The sensitivity analysis was carried out by categorizing the crop based on crop height. Three crop categories have been considered which are 0 to 20 cm, 20 to 80 cm, and greater than 80 cm. The correlation coefficient in the first stage of crop growth using the fixed frequency method was 0.76, which decreased to 0.42 in second stage of crop growth and finally to 0.35 in final stage of crop growth. The correlation coefficient using LSP method was -0.68, -0.65, and -0.50 for the first, second, and third stages of crop growth, respectively. It was observed that for lower crop height (< 20 cm) fixed frequency method is more useful than LSP method. However, for higher crop height (> 20 cm) LSP method is better suited.
Vol. 123, 263-279, 2022
download: 215
A Wideband Polarization Conversion Coding Metasurface for Monostatic Radar Cross Section Reduction of High Altitude Aerospace Platforms
E. V. Bhavya , Balamati Choudhury and Raveendranath Nair
A novel wideband cross-polarized coding metasurface has been presented in this paper towards reduction of monostatic radar cross section (RCS). A broadband reflective cross-polarization converter for linearly polarized (LP) electromagnetic waves covering both X and Ku bands has been designed for this purpose. The proposed unit cell is ultrathin (λ/15.7) and demonstrates a polarization conversion bandwidth of 10.84 GHz from 7.96 GHz to 18.8 GHz for a linearly polarized normal incidence wave which helps in reduction of radar cross section. In order to have a better understanding of cross polarization conversion (CPC), the physical mechanism of the structure has been investigated and elucidated in detail, along with the surface current distribution. The proposed structure has been studied for both transverse electric (TE) and transverse magnetic (TM) polarizations. For 1 bit coding, the suggested unit cell is utilized as the `0' bit, while the 90˚ rotated version of the unit cell is used as the `1' bit. A 4 × 4 matrix is built, and 16 configurations are explored. These combinations are known as the 2 × 2 metasurface sub-blocks, and they are used to build 200 × 200 components with size of 180 mm × 180 mm. The RCS simulation studies have been carried out from 2 to 30 GHz, and the proposed design shows a 10 dB RCS reduction from 10 GHz to 20 GHz. The scattering pattern of the suggested metasurface is comprehensively analyzed at 10 GHz, 15 GHz, and 18 GHz and demonstrates diffuse scattering in the other direction, minimizing the forward scattering RCS. The designed structure of 2.4 mm thickness has been fabricated and measured in the X and Ku bands. The measured results are in good agreement with simulated ones. In order to show the efficiency of the proposed coding metasurface, monostatic RCS estimation of the wing and body sections of high altitude aerospace paltforms (HAPS) has been simulated, and a 14.32 dB reduction has been observed over the body cross section.
Vol. 123, 253-262, 2022
download: 186
A Ku-Band Low-Profile Dual Circularly Polarized Antenna Based on QMSIW
Jingchun Zhai , Wen Wang , Cheng Chang , Yiqing Liu , Luzhen Wang and Zhuopeng Wang
In this paper, a low-profile dual circularly polarized (CP) antenna for Ku band satellite communication is proposed. A quarter-mode SIW (QMSIW) is designed as a circular polarization unit, which realizes circular polarization by using high-order mode TE130, and a pair of units are combined to form the antenna proposed in this paper. Feeding different units can realize left-handed circular polarization and right-handed circular polarization, respectively. The antenna impedance bandwidth is 5.66 GHz (15.16 GHz-20.82 GHz); the circular polarization bandwidth (CPBW) is 540 MHz (15.64 GHz-16.18 GHz); and the gain in the passband is 5.1 dBi, with a minimum axial ratio (AR) of 1 dB. The thickness of the antenna is only 1.5 mm, which has obvious low-profile characteristics.
A Ku-band Low-profile Dual Circularly Polarized Antenna Based On QMSIW
Vol. 123, 237-251, 2022
download: 224
Design of Ultra-Wideband MIMO Antenna with Dual Band Elimination Characteristics and Low Mutual Coupling
Ravindra Subhash Bakale , Anil Nandgaonkar , Shankar B. Deosarkar and Mahesh Munde
The paper proposes the design of an ultra-wideband MIMO antenna with low mutual coupling and dual-band elimination characteristics. The proposed structure consists of a microstrip-fed monopole antenna with a stub to enhance the isolation for ultra-wideband applications. The dual rejection bands corresponding to WiMAX and WLAN frequencies are designed using electromagnetic band-gap structures of mushroom-type and placed close to the microstrip transmission line of the designed antenna. The isolation enhancement of |S21| > 20 dB is achieved over the impedance bandwidth by adding two counter-facing F-pattern stubs to the ground. The impedance bandwidth of 9 GHz (2.65-11.65 GHz) for VSWR < 2.13 with the notch bands of 3.6-4.2 GHz and 5.15-5.87 GHz is obtained. The diversity gain, correlation coefficient, radiation pattern, TARC, and peak gain are also studied in the paper. The simulated and measured results are in close agreement with each other. Therefore, the proposed structure is a potential candidate for wireless communication.
Vol. 123, 227-236, 2022
download: 205
Development of a Low Profile Wideband SIW Cavity-Backed I-Shaped Slot Antenna
Anil Kumar Katta and Praveen Babu Choppala
In this paper, a bandwidth improvement technique in substrate integrated waveguide (SIW) slotted antennas is presented. Here, wideband is achieved by using a single cavity mode (TE210) instead of multiple cavity modes, which is the most distinct approach as compared to other SIW based antennas. When the rectangle slot is loaded at bottom surface of the cavity, the TE210 cavity mode of the antenna is perturbed. As a result, two independent modes namely odd TE210 and even TE210 are successfully generated and merged in close proximity. Consequently, an impedance bandwidth of 12.8% is obtained. When a vertical slit is added at each end of the rectangle slot to make as an I-shaped slot, the impedance bandwidth is increased from 12.8% to 13.94%. The fabricated antenna shows the measured impedance bandwidth of 14.4% andexhibits a gain of 5 dBi to 7 dBi throughout the operating band. The proposed design still retains many features such as light weight, easy fabrication, and easy integration.
Development of a Low Profile Wideband SIW Cavity-backed I-shaped Slot Antenna
Vol. 123, 213-226, 2022
download: 209
A Compact UWB DRA MIMO Antenna Realizing Band Notch Characteristics and Fractal Inspired Isolation Mechanism
Anindita Bhattacharjee , Anirban Karmakar and Anuradha Saha
In this communication, a new compact UWB dual port multiple-input multiple-output (MIMO) antenna is presented for wireless application. The design utilizes the property of dielectric resonator to achieve a bandwidth that ranges from 3.1 GHz to 18.5 GHz. The design has a compact size of 19×30×0.8 mm3. It consists of two rectangular shape monopole antenna elements with rectangular dielectric resonators sharing a similar ground plane. On the ground plane, a modified Hilbert curve with a meander line parasitic element was introduced to improve isolation between radiating elements which reduces mutual coupling issues. A band notch is achieved at WLAN band (5.09-5.8 GHz) by etching a pair of L-shape slots on each radiator. The gain of the antenna drops significantly at the centre of the notch band which indicates good interference suppression. Results show that the designed antenna provides a wide impedance bandwidth (below -10 dB) throughout the operating band of 3.1-18.5 GHz (142.6%). The antenna also produces nearly -20 dB isolation for the entire operating band. Results show that the simulated characteristics are in good agreement with the measured counterpart.
Vol. 123, 197-212, 2022
download: 353
A Foam-Based Compact Flexible Wideband Antenna for Healthcare Applications
Kailash Vaijinath Karad and Vaibhav S. Hendre
In recent times, the study of flexible wireless devices has attracted ample attention in the fields of biomedicine and healthcare. Biomedical systems are becoming more popular and employed to find harmful elements within human bodies. A portable biomedical device makes use of a contacting or non-contacting way to find tumours inside the human body. In view of this, a compact two-slot hexagonal shape flexible wideband microstrip antenna for healthcare application is presented. The proposed antenna is designed using a low-cost, light-weight, and broadly accessible flexible foam material. The slots incorporated into the geometry have enriched the percentage bandwidth of 106.67% with a total gain of 4.67 dBi. The flexible wideband antenna of dimension 28×26×2 mm3 is fabricated using copper foil. The designed and fabricated antenna operates over the frequency of 2.94 to 9.66 GHz resulting in three different resonating frequencies; 3.8 GHz, 6.7 GHz, and 9.1 GHz. The flexible antenna is tested under different bending conditions and obtains good performance to substantiate flexibility. The Specific Absorption Rate (SAR) analysis is also performed over a three-layer tissue equivalent body model and observes a maximum SAR value of 1.9 W/Kg less than the safety limit of 2 W/Kg for 10 gm of tissue. A good agreement is observed between the simulated and measured results of the proposed antenna for free space and human proximity.
Vol. 123, 181-196, 2022
download: 250
Statistical Analysis of Diffraction Loss in Outdoor Urban Microcells for 5G/6G Millimeter Wave Communications
Abdelbasset Bedda Zekri and Riadh Ajgou
Millimeter-wave (mmWave) frequencies are considered as candidate bands for 5G/6G mobile networks. Diffraction models are significant for predicting non-line-of-sight (NLOS) wireless channels while it is shown that the line of sight (LOS) path is usually blocked by buildings in urban area environments. A lot of investigations on the diffraction loss have been performed, and most of them just considered a one obscuring object and a short propagation distance. In this paper, we conduct a statistical analysis of the diffraction loss in the outdoor NLOS in Urban Micro Cell, considering a transmitter (TX) and a receiver (RX) which are located at an aggregation point on the roof of a building. We have focused on analyzing the diffraction loss suffered by mmWave signals when they hit one or two obscuring points located over rooftop of the buildings. The objects have different heights located at various distances between TX and RX. We have considered the bands: 28 GHz, 38 GHz, 60 GHz, 73 GHz and 100 GHz. The analysis is based on the diffraction model named the Knife Edge Diffraction (KED). We have strictly followed the ITU Recommendations ITU-R P.526-15 (10/2019). In this work, we use two schemes that characterize the KED model, namely Single KED (SKED) and Double Isolated KED (DIKED). Different scenarios are performed by varying different parameters of the channel between TX and RX. The results show that the diffraction loss is inversely proportional to the distance between the obscuring object and the transmitter, the wavelength, and the distance between the TX and RX.
Vol. 123, 167-179, 2022
download: 224
Design and Analysis of a Novel Mechanical Variable Flux Interior Permanent Magnet Synchronous Motor
Jianwei Liang , Dabin Liu , Yun Gao , Hongwei Yuan and Xiping Liu
In this paper, a novel mechanical variable flux interior permanent magnet synchronous motor (MVF-IPMSM) is proposed. Based on the basic topology and operating principle of MVF-IPMSM, the effect of the special PMs structure in the new rotor topology on the air gap magnetic field and the design of the mechanical magnetic adjustment device of the proposed motor are analyzed, in which the finite element analysis (FEA) method is adopted. The electromagnetic characteristics of the MVF-IPMSM are analyzed including internal magnetic field distribution, air gap flux density, and torque characteristics. Furthermore, the ability of magnetic field regulation is also analyzed which can be reflected by the torque-speed and power-speed envelopes. Finally, a prototype is manufactured and tested. The measured results are compared with the FEA results, and the prototype experiments verify the effectiveness and feasibility of the design of the proposed MVF-IPMSM.
Design and Analysis of a Novel Mechanical Variable Flux Interior Permanent Magnet Synchronous Motor
Vol. 123, 151-166, 2022
download: 329
A Charged Particle Model Based on Weber Electrodynamics for Electron Beam Trajectories in Coil and Solenoid Elements
Christof Baumgärtel and Simon Maher
To aid with the design, evaluation, and optimisation of charged particle instrumentation, computer modelling is often used. It is therefore of interest to obtain accurate predictions for trajectories of charged species with the help of simulation. Particularly for solenoids and coils, which are often used for guiding, deflecting or focusing particle beams, knowledge of the magnetic field is required, especially in the fringing field regions. A novel model, which is based on a direct-line-of-action force between interacting charges, is described in this paper which accurately predicts the deflection of an electron beam trajectory traversing through a coil and the fringe field region. The model is further compared with a standard field model and a commercially available software package. Additionally, a relatively straightforward experiment has been designed and implemented to verify the simulation results, where it is found that the presented direct-action model is equally as accurate as field-based simulations compared with the experimental results. Furthermore, the magnetic field of a solenoid is visualised and analysed in terms of its radial, axial, and total field strength and compared to a force map obtained from the direct-interaction model. This representation allows for further comparison of the field and force interaction models and it is found that they are qualitatively the same.
A Charged Particle Model based on Weber Electrodynamics for Electron Beam Trajectories in Coil and Solenoid Elements
Vol. 123, 135-150, 2022
download: 174
Fast Predictive Switching Table-Based Model Predictive Torque Control for PMSM
Cheng Zhang , Zichen Xiong , Yang Zhang , Hao Xie and Pengcheng Zhang
To reduce the calculation time of traditional model predictive torque control (MPTC), lower torque ripple, and improve the dynamic characteristics of predictive control, a model predictive torque control strategy applied in permanent magnet synchronous motor (PMSM) based on fast predictive switching table is proposed. This paper presents the 12-sector division method first. Then, based on sector division MPTC, a fast predictive switching table is proposed to reduce the 14 candidate voltage vectors of the sector division MPTC to 5. In addition, the the Proportional Integral (PI)-based adjustable weight coefficient is designed, so that the two physical quantities in the cost function have different weights under different working conditions, which improves the dynamic response of the system. As the experiment shows, PMSM uses the control strategy of this paper to output smaller torque steady-state fluctuation and faster dynamic response.
Vol. 123, 117-133, 2022
download: 229
Improved Higher-Order Sliding Mode Controller for Model Predictive Current Control of PMSM
Qianghui Xiao , Zihao Liu , Yang Zhang , Zhe Li , Bing Luo and Tingting Wang
To improve the control accuracy of the model prediction current (MPC) loop of a permanent magnet synchronous motor (PMSM), a new high-order super-twisting sliding-mode controller combined with a sliding-mode disturbance observer is proposed as a speed control strategy. Firstly, the linear term is added to the scaling term based on the original algorithm, which enhances robustness while weakening jitter. In addition, load perturbations and parameter uptake in the system are considered. The perturbation observation error is introduced into the switching gain function, and an improved sliding-mode disturbance observer is designed as feedforward compensation. The disturbance immunity of the system is effectively enhanced. Simulated and experimental results verify the correctness and effectiveness of this control strategy.
Vol. 123, 101-116, 2022
download: 226
Analysis on the Spatial Impedance of the Wireless Power Transfer System in the Near Field
Jianwei Kang , Jie Lu , Deyu Zeng and Xiangyang Shi
In this paper, the spatial impedance of the wireless power transfer (WPT) system is analyzed, and a resistance tunnel is found. First, the definitions of the spatial impedance in the near field are discussed, and one definition is chosen. By using this definition, the concept of the resistance and the reactance are extended from a scaler form into a vector form. Under this definition and this concept, the spatial impedance is analyzed, and a resistance tunnel is found. The tunnel possesses an obvious direction which is from the receive coil to the transmit coil, and possesses a concave phenomenon on the resistance's magnitude curves. The reason for the forming of the tunnel is also analyzed by discussing the x- and z-components of the resistance. Second, the influences on the resistance tunnel by four factors are discussed. Only the current phase difference determines the existence of the resistance tunnel. The other factors only influence the magnitude and the distribution of the resistance. The correctness of the theoretical calculation is verified by implementing an electromagnetic simulation via FEM. Since the WPT system is one of the typical coupling systems in the near field, one can infer that the resistance tunnel not only exists in the WPT system, but also exists in other coupling coil systems in the near field.
Vol. 123, 91-99, 2022
download: 299
Four-Element Compact and Dual-Band MIMO Antenna with Self-Decoupled Mechanism for 5G Applications
Abhilash Achariparambil , Paulbert Thomas , Karamkulambel Kunjappan Indhu , Kinatingal Neema , Ramakrishnan Anil Kumar and Chandroth K. Aanandan
This paper describes the concept and implementation of a compact dual-band microstrip slot antenna and its four-unit multiple-input–multiple-output (MIMO) implementation for sub-6 GHz utilizations. The proposed structure comprises a 50 ohm microstrip monopole on the top side with a defective ground structure (DGS) having semicircular and rectangular slots. This quad-element MIMO antenna has a size of 60 × 60 × 1.6 mm3. The proposed antenna provides wide impedance bandwidths of 23.7% (2.42 GHz to 3.07 GHz) for the first band and 42.2% (4.14 GHz to 6.37 GHz) for the second band with a mutual coupling value less than -34 dB for the two bands. The antenna also provides a low envelope correlation coefficient, good antenna gain, and acceptable radiation efficiency across the frequency ranges.
Vol. 123, 75-89, 2022
download: 184
A Fault-Tolerant Control Strategy for d -PMSG Wind Power Generation System
Bing Luo , Sicheng Peng , Yang Zhang , Zihao Liu and Bo Huang
Aiming at the problem of motor speed decrease in direct-drive permanent magnet synchronous generator (D-PMSG) wind power generation system after permanent magnet (PM) demagnetization faults, a demagnetization fault-tolerant control strategy in D-PMSG wind power generation system is proposed. Firstly, the D-PMSG mathematical model is described in normal and demagnetization. Secondly, an extended Kalman filter (EKF) observer is designed to observe the PM flux online. Then, flux linkage parameters are introduced into the two-vector model predictive fault-tolerant control so that the increase of stator current is controlled within the limit range. Meanwhile, the motor speed can follow the change of the given speed. In addition, the improved Luenberger mechanical torque observer is designed in the speed outer ring to deal with the vibration caused by unstable wind speed. Finally, compared with the dual-closed-loop Proportional Integral (PI) control, the experimental results show that the demagnetization fault-tolerant control strategy has smaller speed overshoot and smaller speed fluctuation when the mechanical torque changes. The method can maintain the speed balance when the PM demagnetization faults occur and have stronger fault tolerance and anti-interference ability.
Vol. 123, 61-73, 2022
download: 205
Mutual Impedance Computation of a Waveguide Slot-Fed Arbitrary Patch Using Combined Conventional Moment Method and Equivalent Electric and Magnetic Dipole Method
Mehri Hosseini , Keyvan Forooraghi and Ali Abdolali
This paper proposes computing the mutual impedance of a multi-layer patch fed by a slotted waveguide using the combined equivalent electric and magnetic dipole-moment method and conventional moment method (EDM-MOM) as an efficient technique. The slot, PEC, and dielectric regions are substituted with equivalent currents. The unknown currents are expanded using the Rao-Wilton-Glisson and Schaubert-Wilton-Glisson basis functions. The matrix equations are then extracted from the boundary conditions. Using the EDM, each RWG or SWG of the PEC and dielectric is equivalent to an infinitesimal electric dipole, and that of the slot is equivalent to a magnetic dipole. The element matrix related to the waveguide excitation is calculated using the conventional moment method due to simple integration and accuracy. Further, the superposition of the mutual coupling between each equivalent electric or magnetic dipole in the first element and each dipole in the second element is used to obtain the mutual impedance of the two elements of the waveguide slot-fed patch array. The proposed method shows good agreement with CST software simulation results.
Mutual Impedance Computation of a Waveguide Slot-fed Arbitrary Patch Using Combined Conventional Moment Method and Equivalent Electric and Magnetic Dipole Method
Vol. 123, 45-59, 2022
download: 248
Comprehensive Assessment of Power Transfer Capability of Electromagnetically Coupled Wireless Power Transfer Systems
Suraj Kumar Panigrahi , Sivnarayan Bhuyan , Sushree Sangita Biswal , Durga Prasanna Kar , Renu Sharma and Satyanarayan Bhuyan
Magnetic coupling based Wireless Power Transfer (WPT) systems for charging no doubt have emerged as an eye catching alternative charging methodology in recent years. However, a rigorous assessment between magnetic coupling based traditional WPT system and magnetic resonant coupling based WPT system is essential in order to characterize and decide the best suited technology corresponding to their applicability. The effectiveness of both the technologies and their power transfer characteristics have been demonstrated in perception of consumed input power, delivered load power for different coupling coefficient over varying operating frequency and electric load condition. The theoretical and analytical study supported with the simulation and bench set up experiments have been carried out in order to disclose the viability of both the technologies in the device charging. In addition, an inclusive correlation between the performance parameters of the WPT systems is established through the analysis, and justification regarding the RIC-WPT system as an alternative viable solution in the charging field has been outlined.
Vol. 123, 27-43, 2022
download: 281
Third Order U-Shaped Quasi-Reflectionless Bandpass Filter
Bahaa Hamzah Alkhuwaildi and Nasr Alkhafaji
A filter with good impedance matching for both in-band and a wide range of out-of-band is reported in this paper. Thus, the proposed filter offers low reflection for a wide range of frequencies, and it can be called as quasi-reflectionless filter. Also, the proposed filter improves the passband flatness significantly. The quasi-reflectionless filter consists of n-pole conventional U-shaped bandpass filters with absorptive stubs (ABSs) placed at the input and output ports. Each part in the whole filter is individually investigated. The U-shaped resonator is studied first, and then the ABSs are analyzed mathematically and simulated to optimize the attenuation rejection. Several parameters that have an influence on the overall performance are investigated. Different n-pole filters are simulated to simply enhance the out-of-band rejection without affecting the passband response. The filter response is furthermore improved by introducing two transmission zeros using the cross-coupling between the two ABSs. To validate the proposed idea, the 3-pole U-shaped quasi-reflectionless BPF is fabricated on an FR4 substrate at the operating frequency of 3.5 GHz. The filter has measured responses very close to the simulated ones.
Third Order U-Shaped Quasi-Reflectionless Bandpass Filter
Vol. 123, 17-26, 2022
download: 187
Array Pattern Restoration Under Defective Elements
Jafar Ramadhan Mohammed and Ahmed Jameel Abdulqader
The defective array elements which are unavoidable due to the long full-time antenna system operation directly affect its radiation pattern, sidelobe level (SLL), directivity, and the system performance. Therefore, reducing these undesirable effects is a main interest in designing such arrays in practice. In this paper, a partially compensating method based on the genetic optimization algorithm (GA) is proposed to mainly reduce those undesirable effects of the defected elements. Unlike the existing fully compensating methods where all of their active elements were optimized to compensate for the effects of the defected elements, the proposed method optimizes the excitation weights of some optimally selected active-elements. Thus, the whole array elements do not need to be redesigned again as in the case of the fully compensating methods. This greatly simplifies the design implementation of these arrays. Moreover, a very large defective percentage ranging from 5% up to 50% has been considered to demonstrate the effectiveness of the proposed method. Furthermore, the drawback effects of the randomly failing elements at the array center have been highlighted, and some suggestions have been provided.
Vol. 123, 1-16, 2022
download: 315
A Normal-Vector-Field-Based Preconditioner for a Spatial Spectral Domain-Integral Equation Method for Multi-Layered Electromagnetic Scattering Problems
Ligang Sun , Roeland Johannes Dilz and Martijn Constant van Beurden
A normal-vector-field-based block diagonal-preconditioner for the spatial spectral integral method is proposed for an electromagnetic scattering problem with multi-layered medium. This preconditioner has a block-diagonal matrix structure for both 2D TM polarization and 3D cases. Spectral analysis shows that the preconditioned system has a more clustered eigenvalue distribution, compared to the unpreconditioned system. For the cases with high contrast or negative permittivity, numerical experiments illustrate that the preconditioned system requires fewer iterations than the unpreconditioned system. The total computation time is reduced accordingly while the accuracy based on the normal-vector field formulation of the solution is preserved.
A Normal-vector-field-based Preconditioner for a Spatial Spectral Domain-integral Equation Method for Multi-Layered Electromagnetic Scattering Problems