According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, ...According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm.展开更多
In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed...In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.展开更多
In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element m...In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.展开更多
We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,thi...We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.展开更多
Because the magnetic signal information of pipeline defects obtained by magnetic flux leakage detection contains interference signals, it is difficult to accurately extract the features. Therefore, a novel pipeline de...Because the magnetic signal information of pipeline defects obtained by magnetic flux leakage detection contains interference signals, it is difficult to accurately extract the features. Therefore, a novel pipeline defect feature extraction method based on VMD-OSVD (variational modal decomposition - optimal singular value decomposition) is proposed to promote the signal to noise ratio (SNR) and reduce aliasing in the frequency domain. By using the VMD method, the sampled magnetic signal is decomposed, and the optimal variational mode is selected according to the rate of relative change (VMK) of Shannon entropy (SE) to reconstruct the signal. After that, SVD algorithm is used to filter the reconstructed signal again, in which the H-matrix is optimized with the phase-space matrix to enhance SNR and decrease the frequency domain aliasing. The results show that the method has excellent denoising ability for defect magnetic signals, and SNR is increased by 21.01%, 24.04%, 0.96%, 32.14%, and 20.91%, respectively. The improved method has the best denoising effect on transverse mechanical scratches, but a poor denoising effect on spiral welding position. In the frequency domain, the characteristics of different defects are varied, and their corresponding frequency responses are spiral weld corrosion > transverse mechanical cracking > girth weld > deep hole > normal pipe. The high-frequency band is the spiral weld corrosion with f1 = 153.37 Hz. The low-frequency band is normal with f2 = 1 Hz. In general, the VMD-OSVD method is able to improve the SNR of the signal and characterize different pipe defects. And it has a certain guiding significance to the application of pipeline inspection in the field of safety in the future.展开更多
文摘According to the sequential BFGS method, in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact. We assume that we have p + q processors, which are divided-into two groups, the first group has p processors, the second group has q processors, the two groups are asynchronous. parallel, If we assume the objective function is twice continuously differentiable and uniformly convex, we prove the iteration converge globally to the solution, and under some additional conditions we show the method is superlinearly convergent. Finally, we show the numerical results of this algorithm.
文摘In this paper, we consider the mixed Navier-Stokes/Darcy model with BeaversJoseph interface conditions. Based on two-grid discretizations, a local and parallel finite element algorithm for this mixed model is proposed and analyzed. Optimal errors are obtained and numerical experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithm.
基金Subsidized by NSFC (11701343)partially supported by NSFC (11571274,11401466)
文摘In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.
基金Supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2012030)
文摘We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.
基金sponsored by the National Key Research and Development Program of China(No.2018YFF0215003)State Key Laboratory of Process Automation in Mining&Metallurgy and Beijing Key Laboratory of Process Automation in Mining&Metallurgy(No.BGRIMM-KZSKL-2021-04)Tribology Science Fund of State Key Laboratory of Tribology(No.SKLTKF20B15).
文摘Because the magnetic signal information of pipeline defects obtained by magnetic flux leakage detection contains interference signals, it is difficult to accurately extract the features. Therefore, a novel pipeline defect feature extraction method based on VMD-OSVD (variational modal decomposition - optimal singular value decomposition) is proposed to promote the signal to noise ratio (SNR) and reduce aliasing in the frequency domain. By using the VMD method, the sampled magnetic signal is decomposed, and the optimal variational mode is selected according to the rate of relative change (VMK) of Shannon entropy (SE) to reconstruct the signal. After that, SVD algorithm is used to filter the reconstructed signal again, in which the H-matrix is optimized with the phase-space matrix to enhance SNR and decrease the frequency domain aliasing. The results show that the method has excellent denoising ability for defect magnetic signals, and SNR is increased by 21.01%, 24.04%, 0.96%, 32.14%, and 20.91%, respectively. The improved method has the best denoising effect on transverse mechanical scratches, but a poor denoising effect on spiral welding position. In the frequency domain, the characteristics of different defects are varied, and their corresponding frequency responses are spiral weld corrosion > transverse mechanical cracking > girth weld > deep hole > normal pipe. The high-frequency band is the spiral weld corrosion with f1 = 153.37 Hz. The low-frequency band is normal with f2 = 1 Hz. In general, the VMD-OSVD method is able to improve the SNR of the signal and characterize different pipe defects. And it has a certain guiding significance to the application of pipeline inspection in the field of safety in the future.
