The dyadic Green’s function in multi-layer structures for Maxwell equations is a key component for the integral equation method,but time consuming to calculate.A novel algorithm,the Fast Interpolation and Filtering A...The dyadic Green’s function in multi-layer structures for Maxwell equations is a key component for the integral equation method,but time consuming to calculate.A novel algorithm,the Fast Interpolation and Filtering Algorithm(FIFA),for the calculation of the dyadic Green’s function in multi-layer structures is proposed in this paper.We discuss in specific details,ready for use in practical calculations of scattering in layer media,how to apply FIFA to calculate various components of the dyadic Green’s function.The algorithm is based on two techniques:interpolation of Green’s function both in the spectral domain and spatial domain,and low pass filter window based acceleration.Compared to the popular Complex Image Method(CIM),FIFA provides the same speed and overcomes several difficulties associated with CIM while being more general and robust.Specifically,there are no limitations on the frequency range,the number of layers in the structure and the type of Green’s functions to be calculated,and moreover,no need to extract surface wave poles from the spectral form of the Green’s function.Numerical results are given to demonstrate the efficiency and robustness of the proposed method.展开更多
The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the refle...The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.展开更多
In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usa...In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usage of linear interpolation principle.The original problem is projected onto the reduced basis space by linear interpolation projection,and subsequently an associated interpolation matrix is generated.To ensure the largest nonsingularity,the interpolation matrix needs to go through a timenode choosing process,which is developed by applying the angle of vector spaces.As a part of this technique,error estimation is recommended for achieving the computational error bound.To ensure the successful performance of this technique,the offline-online computational procedures are conducted in practical engineering.Two numerical examples demonstrate the accuracy and efficiency of the presented method.展开更多
In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and freq...In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and frequencies,as well as the mutual interferences among SsO modes with close frequencies,the accurate parameter estimation of SsO has become a particularly challenging topic.To solve this issue,this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision.First,by aiming at the sidelobe characteristics of the window function as evaluation criteria,a combined cosine function is optimized using a genetic algorithm(GA).Furthermore,the obtained window function is self-convolved to extend its excellent characteristics,which have better performance in reducing mutual interference from other SSO modes.Subsequently,a new form of interpolated all-phase fast Fourier transform(IpApFFT)using the optimized window function is proposed to estimate the parameters of SsO.This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience.The performance of the pro-posed method is demonstrated under various conditions,com-pared with other estimation methods.Simulation results validate the effectiveness and superiority of the proposed method.展开更多
文摘The dyadic Green’s function in multi-layer structures for Maxwell equations is a key component for the integral equation method,but time consuming to calculate.A novel algorithm,the Fast Interpolation and Filtering Algorithm(FIFA),for the calculation of the dyadic Green’s function in multi-layer structures is proposed in this paper.We discuss in specific details,ready for use in practical calculations of scattering in layer media,how to apply FIFA to calculate various components of the dyadic Green’s function.The algorithm is based on two techniques:interpolation of Green’s function both in the spectral domain and spatial domain,and low pass filter window based acceleration.Compared to the popular Complex Image Method(CIM),FIFA provides the same speed and overcomes several difficulties associated with CIM while being more general and robust.Specifically,there are no limitations on the frequency range,the number of layers in the structure and the type of Green’s functions to be calculated,and moreover,no need to extract surface wave poles from the spectral form of the Green’s function.Numerical results are given to demonstrate the efficiency and robustness of the proposed method.
基金Supported by the National Natural Science Foundation of China under Grant No 11604115the Educational Commission of Jiangsu Province of China under Grant No 17KJA460004the Huaian Science and Technology Funds under Grant No HAC201701
文摘The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.
基金supported by the National Natural Science Foundation of China (10802028)the Major State Basic Research Development Program of China (2010CB832705)the National Science Fund for Distinguished Young Scholars (10725208)
文摘In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usage of linear interpolation principle.The original problem is projected onto the reduced basis space by linear interpolation projection,and subsequently an associated interpolation matrix is generated.To ensure the largest nonsingularity,the interpolation matrix needs to go through a timenode choosing process,which is developed by applying the angle of vector spaces.As a part of this technique,error estimation is recommended for achieving the computational error bound.To ensure the successful performance of this technique,the offline-online computational procedures are conducted in practical engineering.Two numerical examples demonstrate the accuracy and efficiency of the presented method.
基金supported in part by Science and Technology Project of State Grid Corporation of China(No.5108-202299269A-1-0-ZB).
文摘In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and frequencies,as well as the mutual interferences among SsO modes with close frequencies,the accurate parameter estimation of SsO has become a particularly challenging topic.To solve this issue,this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision.First,by aiming at the sidelobe characteristics of the window function as evaluation criteria,a combined cosine function is optimized using a genetic algorithm(GA).Furthermore,the obtained window function is self-convolved to extend its excellent characteristics,which have better performance in reducing mutual interference from other SSO modes.Subsequently,a new form of interpolated all-phase fast Fourier transform(IpApFFT)using the optimized window function is proposed to estimate the parameters of SsO.This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience.The performance of the pro-posed method is demonstrated under various conditions,com-pared with other estimation methods.Simulation results validate the effectiveness and superiority of the proposed method.
