A new spectral matching algorithm is proposed by us- ing nonsubsampled contourlet transform and scale-invariant fea- ture transform. The nonsubsampled contourlet transform is used to decompose an image into a low freq...A new spectral matching algorithm is proposed by us- ing nonsubsampled contourlet transform and scale-invariant fea- ture transform. The nonsubsampled contourlet transform is used to decompose an image into a low frequency image and several high frequency images, and the scale-invariant feature transform is employed to extract feature points from the low frequency im- age. A proximity matrix is constructed for the feature points of two related images. By singular value decomposition of the proximity matrix, a matching matrix （or matching result） reflecting the match- ing degree among feature points is obtained. Experimental results indicate that the proposed algorithm can reduce time complexity and possess a higher accuracy.展开更多
To quickly identify the mineral pigments in the Dunhuang murals,a spectral matching algorithm(SMA)based on four methods was combined with laser-induced breakdown spectroscopy(LIBS)for the first time.The optimal range ...To quickly identify the mineral pigments in the Dunhuang murals,a spectral matching algorithm(SMA)based on four methods was combined with laser-induced breakdown spectroscopy(LIBS)for the first time.The optimal range of LIBS spectrum for mineral pigments was determined using the similarity value between two different types of samples of the same pigment.A mineral pigment LIBS database was established by comparing the spectral similarities of tablets and simulated samples,and this database was successfully used to identify unknown pigments on tablet,simulated,and real mural debris samples.The results show that the SMA method coupled with the LIBS technique has great potential for identifying mineral pigments.展开更多
In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model....In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model. The conductivity and relative permittivity logging curves are obtained from the data of borehole radar for well logging. Since the relative permittivity logging curve is not affected by salinity of formation water, borehole radar for well logging has obvious advantages as compared with conventional electrical logging. The borehole radar for well logging is a one-transmitter and two-receiver logging tool. The conductivity and relative permittivity logging curves are obtained successfully by measuring the amplitude radio and the time difference of pulse waveform from two receivers. The calculated conductivity and relative permittivity logging curves are close to the true value of surrounding formation, which tests the usability and reliability of borehole radar for well logging. The numerical modeling of borehole radar for well logging laid the important foundation for researching its logging tool.展开更多
Cyclic spectral correlation above the bifrequency plane for the received signal was calculated by the strip spectral correlation algorithm （SSCA）and then was normalized. The result was expressed by matrix. The sum o...Cyclic spectral correlation above the bifrequency plane for the received signal was calculated by the strip spectral correlation algorithm （SSCA）and then was normalized. The result was expressed by matrix. The sum of error-square was computed between corresponding elements for the theoretical sampling matrix of all kinds of modulated signals and calculated matrix. The modulation type was recognized by exploiting the minimum value of the sum of error-square. No extracted characteristic parameter and prior information are needed for identifying the modulation type compared to the conventional methods. In addition, the new method extends the recognition scope and has high recognition probability at low SNR. The simulation results obtained by means of Monter-Carlo method proved the presented algorithm.展开更多
There exist a considerable variety of factors affecting the spectral emissivity of an object. The authors have designed an improved combined neural network emissivity model, which can identify the continuous spectral ...There exist a considerable variety of factors affecting the spectral emissivity of an object. The authors have designed an improved combined neural network emissivity model, which can identify the continuous spectral emissivity and true temperature of any object only based on the measured brightness temperature data. In order to improve the accuracy of approximate calculations, the local minimum problem in the algorithm must be solved. Therefore, the authors design an optimal algorithm, i.e. a hybrid chaotic optimal algorithm, in which the chaos is used to roughly seek for the parameters involved in the model, and then a second seek for them is performed using the steepest descent. The modelling of emissivity settles the problems in assumptive models in multi-spectral theory.展开更多
Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal...Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.展开更多
In this paper, we explore a novel ensemble method for spectral clustering. In contrast to the traditional clustering ensemble methods that combine all the obtained clustering results, we propose the adaptive spectral ...In this paper, we explore a novel ensemble method for spectral clustering. In contrast to the traditional clustering ensemble methods that combine all the obtained clustering results, we propose the adaptive spectral clustering ensemble method to achieve a better clustering solution. This method can adaptively assess the number of the component members, which is not owned by many other algorithms. The component clusterings of the ensemble system are generated by spectral clustering （SC） which bears some good characteristics to engender the diverse committees. The selection process works by evaluating the generated component spectral clustering through resampling technique and population-based incremental learning algorithm （PBIL）. Experimental results on UCI datasets demonstrate that the proposed algorithm can achieve better results compared with traditional clustering ensemble methods, especially when the number of component clusterings is large.展开更多
To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root...To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.展开更多
This paper proposes a novel phishing web image segmentation algorithm which based on improving spectral clustering.Firstly,we construct a set of points which are composed of spatial location pixels and gray levels fro...This paper proposes a novel phishing web image segmentation algorithm which based on improving spectral clustering.Firstly,we construct a set of points which are composed of spatial location pixels and gray levels from a given image.Secondly,the data is clustered in spectral space of the similar matrix of the set points,in order to avoid the drawbacks of K-means algorithm in the conventional spectral clustering method that is sensitive to initial clustering centroids and convergence to local optimal solution,we introduce the clone operator,Cauthy mutation to enlarge the scale of clustering centers,quantum-inspired evolutionary algorithm to find the global optimal clustering centroids.Compared with phishing web image segmentation based on K-means,experimental results show that the segmentation performance of our method gains much improvement.Moreover,our method can convergence to global optimal solution and is better in accuracy of phishing web segmentation.展开更多
We developed a scheme based on wood surface novel wood recognition spectral features that aimed to solve three problems. First was elimination of noise in some bands of wood spectral reflection curves. Second was imp...We developed a scheme based on wood surface novel wood recognition spectral features that aimed to solve three problems. First was elimination of noise in some bands of wood spectral reflection curves. Second was improvement of wood feature selection based on analysis of wood spectral data. The wood spectral band is 350-2500 nm, a 2150D vector with a spectral sampling interval of 1 nm. We developed a feature selection proce- dure and a filtering procedure by solving the eigenvalues of the dispersion matrix. Third, we optimized the design for the indoor radian＇s mounting height. We used a genetic algorithm to solve the optimal radian＇s height so that the spectral reflection curves had the best classification infor- mation for wood species. Experiments on fivecommon wood species in northeast China showed overall recogni- tion accuracy 〉95 % at optimal recognition velocity.展开更多
Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral...Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral analysis（SPECAN） algorithm is proposed and applied in the BiSAR system.The modifications include Doppler centroid compensation,range curve correction and azimuth processing method.The modified SPECAN algorithm solves the imaging problem under the condition of huge range migration,long synthetic aperture time and phase-coded signal.The proposed algorithm is verified by experiment results.展开更多
Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive p...Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive projected Landweber （APL） super-resolution algorithm using a spectral correction procedure, which attempts to combine the strong points of all of the projected Landweber （PL） iteration and the adaptive relaxation parameter adjustment and the spectral correction method, is proposed. In the algorithm, the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component. Then, the algorithm updates the relaxation parameter adaptively at each iteration. A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer. From experiments, it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error （MSE）. These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.展开更多
A global spectral atmospheric model has been vectorized and multitasked on the YH-2 supercomputer. The model is used for the operational system of medium--range numerical weather prediction in National Meteorological ...A global spectral atmospheric model has been vectorized and multitasked on the YH-2 supercomputer. The model is used for the operational system of medium--range numerical weather prediction in National Meteorological Center(NMC), China. In this paper the vectorization algorithms of the spectral-grid transformation and multitasking schemes of the model are discussed in detail. The results show that high speed-up for tile model can be obtained.展开更多
The harmonic and interharmonic analysis recommendations are contained in the latest IEC standards on power quality. Measurement and analysis experiences have shown that great difficulties arise in the interharmonic de...The harmonic and interharmonic analysis recommendations are contained in the latest IEC standards on power quality. Measurement and analysis experiences have shown that great difficulties arise in the interharmonic detection and measurement with acceptable levels of accuracy. In order to improve the resolution of spectrum analysis, the traditional method (e.g. discrete Fourier transform) is to take more sampling cycles, e.g. 10 sampling cycles corresponding to the spectrum interval of 5 Hz while the fundamental frequency is 50 Hz. However, this method is not suitable to the interharmonic measurement, because the frequencies of interharmonic components are non-integer multiples of the fundamental frequency, which makes the measurement additionally difficult. In this paper, the tunable resolution multiple signal classification (TRMUSIC) algorithm is presented, which the spectrum can be tuned to exhibit high resolution in targeted regions. Some simulation examples show that the resolution for two adjacent frequency components is usually sufficient to measure interharmonics in power systems with acceptable computation time. The proposed method is also suited to analyze interharmonics when there exists an undesirable asynchronous deviation and additive white noise.展开更多
Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a four...Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm（ETDRK4） to solve the modified diffusion equation（MDE） which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms, we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE, resulting in a boost of the overall computation efficiency, while it shares the same spatial accuracy with other algorithms. In addition, to demonstrate the power of our ETDRK4 algorithm, we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase, the lamellar phase and the cylindrical phase.展开更多
基金supported by the National Natural Science Foundation of China (6117212711071002)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (20113401110006)the Innovative Research Team of 211 Project in Anhui University (KJTD007A)
文摘A new spectral matching algorithm is proposed by us- ing nonsubsampled contourlet transform and scale-invariant fea- ture transform. The nonsubsampled contourlet transform is used to decompose an image into a low frequency image and several high frequency images, and the scale-invariant feature transform is employed to extract feature points from the low frequency im- age. A proximity matrix is constructed for the feature points of two related images. By singular value decomposition of the proximity matrix, a matching matrix （or matching result） reflecting the match- ing degree among feature points is obtained. Experimental results indicate that the proposed algorithm can reduce time complexity and possess a higher accuracy.
基金supported by the National Key Research and Development Program of China(No.2019YFC1520701)National Natural Science Foundation of China(Nos.61965015,61741513)+2 种基金the 2020 Industry Support Plan Project in University of Gansu Province(No.2020C-17)the Young Teachers Scientific Research Ability Promotion Plan of Northwest Normal University Province(No.NWNW-LKQN2019-1)the Funds for Innovative Fundamental Research Group Project of Gansu Province(No.21JR7RA131)。
文摘To quickly identify the mineral pigments in the Dunhuang murals,a spectral matching algorithm(SMA)based on four methods was combined with laser-induced breakdown spectroscopy(LIBS)for the first time.The optimal range of LIBS spectrum for mineral pigments was determined using the similarity value between two different types of samples of the same pigment.A mineral pigment LIBS database was established by comparing the spectral similarities of tablets and simulated samples,and this database was successfully used to identify unknown pigments on tablet,simulated,and real mural debris samples.The results show that the SMA method coupled with the LIBS technique has great potential for identifying mineral pigments.
基金supported by the Open Fund of Key Laboratory of Geo-detection (China University of Geosciences,Beijing),Ministry of Education (No. GDL0805)
文摘In this article, numerical modeling of borehole radar for well logging in time domain is developed using pseudo-spectral time domain algorithm in axisymmetric cylindrical coordinate for proximate true formation model. The conductivity and relative permittivity logging curves are obtained from the data of borehole radar for well logging. Since the relative permittivity logging curve is not affected by salinity of formation water, borehole radar for well logging has obvious advantages as compared with conventional electrical logging. The borehole radar for well logging is a one-transmitter and two-receiver logging tool. The conductivity and relative permittivity logging curves are obtained successfully by measuring the amplitude radio and the time difference of pulse waveform from two receivers. The calculated conductivity and relative permittivity logging curves are close to the true value of surrounding formation, which tests the usability and reliability of borehole radar for well logging. The numerical modeling of borehole radar for well logging laid the important foundation for researching its logging tool.
文摘Cyclic spectral correlation above the bifrequency plane for the received signal was calculated by the strip spectral correlation algorithm （SSCA）and then was normalized. The result was expressed by matrix. The sum of error-square was computed between corresponding elements for the theoretical sampling matrix of all kinds of modulated signals and calculated matrix. The modulation type was recognized by exploiting the minimum value of the sum of error-square. No extracted characteristic parameter and prior information are needed for identifying the modulation type compared to the conventional methods. In addition, the new method extends the recognition scope and has high recognition probability at low SNR. The simulation results obtained by means of Monter-Carlo method proved the presented algorithm.
文摘There exist a considerable variety of factors affecting the spectral emissivity of an object. The authors have designed an improved combined neural network emissivity model, which can identify the continuous spectral emissivity and true temperature of any object only based on the measured brightness temperature data. In order to improve the accuracy of approximate calculations, the local minimum problem in the algorithm must be solved. Therefore, the authors design an optimal algorithm, i.e. a hybrid chaotic optimal algorithm, in which the chaos is used to roughly seek for the parameters involved in the model, and then a second seek for them is performed using the steepest descent. The modelling of emissivity settles the problems in assumptive models in multi-spectral theory.
文摘Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.
基金Supported by the National Natural Science Foundation of China (60661003)the Research Project Department of Education of Jiangxi Province (GJJ10566)
文摘In this paper, we explore a novel ensemble method for spectral clustering. In contrast to the traditional clustering ensemble methods that combine all the obtained clustering results, we propose the adaptive spectral clustering ensemble method to achieve a better clustering solution. This method can adaptively assess the number of the component members, which is not owned by many other algorithms. The component clusterings of the ensemble system are generated by spectral clustering （SC） which bears some good characteristics to engender the diverse committees. The selection process works by evaluating the generated component spectral clustering through resampling technique and population-based incremental learning algorithm （PBIL）. Experimental results on UCI datasets demonstrate that the proposed algorithm can achieve better results compared with traditional clustering ensemble methods, especially when the number of component clusterings is large.
基金Shandong University of Science and Technology Research Fund(No.2010KYTD101)
文摘To avoid drawbacks of classic discrete Fourier transform(DFT)method,modern spectral estimation theory was introduced into harmonics and inter-harmonics analysis in electric power system.Idea of the subspace-based root-min-norm algorithm was described,but it is susceptive to noises with unstable performance in different SNRs.So the modified root-min-norm algorithm based on cross-spectral estimation was proposed,utilizing cross-correlation matrix and independence of different Gaussian noise series.Lots of simulation experiments were carried out to test performance of the algorithm in different conditions,and its statistical characteristics was presented.Simulation results show that the modified algorithm can efficiently suppress influence of the noises,and has high frequency resolution,high precision and high stability,and it is much superior to the classic DFT method.
文摘针对工作在毫米波频段下的去蜂窝大规模多输入多输出(cell-free massive multiple-input multipleoutput,CF-mMIMO)系统中混合预编码设计面临的链路开销大与数值不稳定等问题,提出了一种适配分布式架构的基于列正交约束的正交匹配追踪(orthogonal matching pursuit,OMP)算法。在模拟预编码阶段,采用基于旋转不变性技术的信号参数最小二乘估计(least squares estimation of signal parameters via rotational invariance technique,LS-ESPRIT)算法,基于接收信号直接估计信号到达角,并重构波束码本,有效压缩了反馈开销;在数字预编码阶段,引入列正交约束并推导了最优因子,重构了优化目标函数,规避了病态矩阵求逆问题,提升了预编码矩阵的数值稳定性与匹配精度。仿真结果表明,该算法在不同接入点分布结构与系统参数设置下均能保持稳定且明显的频谱效率性能提升,验证了其在CF-mMIMO系统中的鲁棒性与优越性。
基金Supported by the Fundamental Research Funds for the Central Universities in North China Electric Power University(11MG13)the Natural Science Foundation of Hebei Province(F2011502038)
文摘This paper proposes a novel phishing web image segmentation algorithm which based on improving spectral clustering.Firstly,we construct a set of points which are composed of spatial location pixels and gray levels from a given image.Secondly,the data is clustered in spectral space of the similar matrix of the set points,in order to avoid the drawbacks of K-means algorithm in the conventional spectral clustering method that is sensitive to initial clustering centroids and convergence to local optimal solution,we introduce the clone operator,Cauthy mutation to enlarge the scale of clustering centers,quantum-inspired evolutionary algorithm to find the global optimal clustering centroids.Compared with phishing web image segmentation based on K-means,experimental results show that the segmentation performance of our method gains much improvement.Moreover,our method can convergence to global optimal solution and is better in accuracy of phishing web segmentation.
基金financially supported by the Fund of Forestry 948 Project (No. 2011-4-04)the Fundamental Research Funds for the Central Universities (No. 2572014EB05-01)
文摘We developed a scheme based on wood surface novel wood recognition spectral features that aimed to solve three problems. First was elimination of noise in some bands of wood spectral reflection curves. Second was improvement of wood feature selection based on analysis of wood spectral data. The wood spectral band is 350-2500 nm, a 2150D vector with a spectral sampling interval of 1 nm. We developed a feature selection proce- dure and a filtering procedure by solving the eigenvalues of the dispersion matrix. Third, we optimized the design for the indoor radian＇s mounting height. We used a genetic algorithm to solve the optimal radian＇s height so that the spectral reflection curves had the best classification infor- mation for wood species. Experiments on fivecommon wood species in northeast China showed overall recogni- tion accuracy 〉95 % at optimal recognition velocity.
基金Sponsored by the National Natural Science Foundation of China(60890071-1160890071-0760890073)
文摘Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral analysis（SPECAN） algorithm is proposed and applied in the BiSAR system.The modifications include Doppler centroid compensation,range curve correction and azimuth processing method.The modified SPECAN algorithm solves the imaging problem under the condition of huge range migration,long synthetic aperture time and phase-coded signal.The proposed algorithm is verified by experiment results.
基金the National Natural Science Foundation of China (60632020).
文摘Passive millimeter wave （PMMW） images inherently have the problem of poor resolution owing to limited aperture dimension. Thus, efficient post-processing is necessary to achieve resolution improvement. An adaptive projected Landweber （APL） super-resolution algorithm using a spectral correction procedure, which attempts to combine the strong points of all of the projected Landweber （PL） iteration and the adaptive relaxation parameter adjustment and the spectral correction method, is proposed. In the algorithm, the PL iterations are implemented as the main image restoration scheme and a spectral correction method is included in which the calculated spectrum within the passband is replaced by the known low frequency component. Then, the algorithm updates the relaxation parameter adaptively at each iteration. A qualitative evaluation of this algorithm is performed with simulated data as well as actual radiometer image captured by 91.5 GHz mechanically scanned radiometer. From experiments, it is found that the super-resolution algorithm obtains better results and enhances the resolution and has lower mean square error （MSE）. These constraints and adaptive character and spectral correction procedures speed up the convergence of the Landweber algorithm and reduce the ringing effects that are caused by regularizing the image restoration problem.
文摘A global spectral atmospheric model has been vectorized and multitasked on the YH-2 supercomputer. The model is used for the operational system of medium--range numerical weather prediction in National Meteorological Center(NMC), China. In this paper the vectorization algorithms of the spectral-grid transformation and multitasking schemes of the model are discussed in detail. The results show that high speed-up for tile model can be obtained.
文摘The harmonic and interharmonic analysis recommendations are contained in the latest IEC standards on power quality. Measurement and analysis experiences have shown that great difficulties arise in the interharmonic detection and measurement with acceptable levels of accuracy. In order to improve the resolution of spectrum analysis, the traditional method (e.g. discrete Fourier transform) is to take more sampling cycles, e.g. 10 sampling cycles corresponding to the spectrum interval of 5 Hz while the fundamental frequency is 50 Hz. However, this method is not suitable to the interharmonic measurement, because the frequencies of interharmonic components are non-integer multiples of the fundamental frequency, which makes the measurement additionally difficult. In this paper, the tunable resolution multiple signal classification (TRMUSIC) algorithm is presented, which the spectrum can be tuned to exhibit high resolution in targeted regions. Some simulation examples show that the resolution for two adjacent frequency components is usually sufficient to measure interharmonics in power systems with acceptable computation time. The proposed method is also suited to analyze interharmonics when there exists an undesirable asynchronous deviation and additive white noise.
基金financially supported by the China Scholarship Council (No. 201406105018)the National Natural Science Foundation of China (No. 21004013)the National Basic Research Program of China (No. 2011CB605701)
文摘Self-consistent field theory（SCFT）, as a state-of-the-art technique for studying the self-assembly of block copolymers, is attracting continuous efforts to improve its accuracy and efficiency. Here we present a fourth-order exponential time differencing Runge-Kutta algorithm（ETDRK4） to solve the modified diffusion equation（MDE） which is the most time-consuming part of a SCFT calculation. By making a careful comparison with currently most efficient and popular algorithms, we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE, resulting in a boost of the overall computation efficiency, while it shares the same spatial accuracy with other algorithms. In addition, to demonstrate the power of our ETDRK4 algorithm, we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase, the lamellar phase and the cylindrical phase.
