This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
In order to reduce the mismatch error, a direct current （DC） calibration method is introduced when the modulated microwave signal is measured. The microwave power is input to the left section of the power sensor, an...In order to reduce the mismatch error, a direct current （DC） calibration method is introduced when the modulated microwave signal is measured. The microwave power is input to the left section of the power sensor, and the DC power is input to the right of the power sensor. Due to the existence of parasitic loss and electromagnetic coupling, the microwave power results in a mismatch error. However, the DC power does not have the mismatch error. So the DC power applied in the right section can calibrate the mismatch error of the microwave power in the left section. The calibration factor is measured at different modulation rates and modulation depths.The measurement results show that the carrier frequency is the major factor influencing the measurement results. After calibration, the carrier frequency and the modulation rate have little effect on the output voltage. The frequency response becomes relatively flat in the frequency range up to 20 GHz, and the sensitivity on average is enhanced by about 0.12 mV/dBm. Therefore, the DC calibration method has a certain reference value for the terminal-type microwave power sensor.展开更多
波达方向(Direction of Arrival,DOA)估计是阵列观测数据研究领域的一个基本问题.对于观测数据服从复椭球对称分布的应用场景,现有的方法多采用l1-范数惩罚项来实现信号波达方向的稀疏估计,其中的l1-范数惩罚项仅考虑信号的稀疏性而没...波达方向(Direction of Arrival,DOA)估计是阵列观测数据研究领域的一个基本问题.对于观测数据服从复椭球对称分布的应用场景,现有的方法多采用l1-范数惩罚项来实现信号波达方向的稀疏估计,其中的l1-范数惩罚项仅考虑信号的稀疏性而没有考虑信号的多样性,从而造成这些估计方法一般将弱信号(具有较低功率的信号)略去,可能无法准确地估计弱信号的波达方向.为解决这个问题,本文通过引入一个组合范数惩罚项构建了一个新的估计(模型)方法,其中的组合范数惩罚项是l1-范数惩罚项与l2-范数平方惩罚项的线性组合,其组合系数(惩罚参数)互不相关,l2-范数平方惩罚项则可以保留弱信号的多样性.然后,本文基于Majorization-Minimization(MM)算法设计了模型的求解算法,并证明该方法是收敛的.数值实验表明,相较于那些基于l1-惩罚项的估计方法,本方法具有更高的精度.展开更多
In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and...In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the [13] broad class of commutative search directions for cone of semidefinite matrices, extended by [18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.展开更多
Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step si...Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.展开更多
A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SI...A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SIADMM is proved to be O(1/√k).Two kinds of elliptic equation constrained optimization problems,the un-constrained cases as well as the box-constrained cases of the distributed control and the Robin boundary control,are analyzed theoretically and solved numerically.First,the existence and uniqueness of the solutions to these problems are proved.Second,these continuous optimization problems are transformed into discrete optimization problems by thefinite element method,and then the discrete optimization problems are solved by the proposed SIADMM.Numerical experiments with different problems are investigated to demonstrate the efficiency of the SIADMM.And the numerical per-formance of the SIADMM is better than the performance of the ADMM.Moreover,the numerical results show that the convergence rate of the SIADMM tends to be faster than O(1/√k)in calculation process.展开更多
远距离海上风电越来越多地选择柔性直流经海缆送出的方式。采用电缆的柔性直流(voltage source converter based high voltage direct current,VSC-HVDC)输电系统,其故障特性比传统架空线直流输电系统更加复杂。文中基于对称单极拓扑的...远距离海上风电越来越多地选择柔性直流经海缆送出的方式。采用电缆的柔性直流(voltage source converter based high voltage direct current,VSC-HVDC)输电系统,其故障特性比传统架空线直流输电系统更加复杂。文中基于对称单极拓扑的双端VSC-HVDC海上风电送出工程,简化了电缆和VSC-HVDC输电系统的数学模型,分析换流变阀侧交流系统单相接地和直流电缆线路单极接地等典型故障下的故障特性,运用叠加原理对故障机理进行解释;根据不同故障类型的故障源等效出不同的故障回路,得到了长距离电缆显著的电容效应对VSC-HVDC系统故障特征的复杂影响;利用实时数字仿真平台,搭建远海风电送出系统硬件在环仿真模型,验证了故障机理解析分析的正确性。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金The National Natural Science Foundation of China(No.60976094)the National High Technology Research and Development Program of China(863 Program)(No.2007AA04Z328)
文摘In order to reduce the mismatch error, a direct current （DC） calibration method is introduced when the modulated microwave signal is measured. The microwave power is input to the left section of the power sensor, and the DC power is input to the right of the power sensor. Due to the existence of parasitic loss and electromagnetic coupling, the microwave power results in a mismatch error. However, the DC power does not have the mismatch error. So the DC power applied in the right section can calibrate the mismatch error of the microwave power in the left section. The calibration factor is measured at different modulation rates and modulation depths.The measurement results show that the carrier frequency is the major factor influencing the measurement results. After calibration, the carrier frequency and the modulation rate have little effect on the output voltage. The frequency response becomes relatively flat in the frequency range up to 20 GHz, and the sensitivity on average is enhanced by about 0.12 mV/dBm. Therefore, the DC calibration method has a certain reference value for the terminal-type microwave power sensor.
文摘波达方向(Direction of Arrival,DOA)估计是阵列观测数据研究领域的一个基本问题.对于观测数据服从复椭球对称分布的应用场景,现有的方法多采用l1-范数惩罚项来实现信号波达方向的稀疏估计,其中的l1-范数惩罚项仅考虑信号的稀疏性而没有考虑信号的多样性,从而造成这些估计方法一般将弱信号(具有较低功率的信号)略去,可能无法准确地估计弱信号的波达方向.为解决这个问题,本文通过引入一个组合范数惩罚项构建了一个新的估计(模型)方法,其中的组合范数惩罚项是l1-范数惩罚项与l2-范数平方惩罚项的线性组合,其组合系数(惩罚参数)互不相关,l2-范数平方惩罚项则可以保留弱信号的多样性.然后,本文基于Majorization-Minimization(MM)算法设计了模型的求解算法,并证明该方法是收敛的.数值实验表明,相较于那些基于l1-惩罚项的估计方法,本方法具有更高的精度.
基金Shahrekord University for financial supportpartially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran
文摘In this paper, we present a neighborhood following primal-dual interior-point algorithm for solving symmetric cone convex quadratic programming problems, where the objective function is a convex quadratic function and the feasible set is the intersection of an affine subspace and a symmetric cone attached to a Euclidean Jordan algebra. The algorithm is based on the [13] broad class of commutative search directions for cone of semidefinite matrices, extended by [18] to arbitrary symmetric cones. Despite the fact that the neighborhood is wider, which allows the iterates move towards optimality with longer steps, the complexity iteration bound remains as the same result of Schmieta and Alizadeh for symmetric cone optimization problems.
基金This research was supported by National Natural Science Foundation of China Grant 11771078Natural Science Foundation of Jiangsu Province Grant BK20181258+1 种基金Project of 333 of Jiangsu Province Grant BRA2018351Postgraduate Research&Practice Innovation Program of Jiangsu Province Grant KYCX18_0200.
文摘Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.12171052,11871115 and 11671052)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2021320).The authors sincerely thank Prof.Haiming Song and Doctor Xin Gao for their valuable discussions.The authors also thank all of the editors and reviewers for their very important suggestions.
文摘A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SIADMM is proved to be O(1/√k).Two kinds of elliptic equation constrained optimization problems,the un-constrained cases as well as the box-constrained cases of the distributed control and the Robin boundary control,are analyzed theoretically and solved numerically.First,the existence and uniqueness of the solutions to these problems are proved.Second,these continuous optimization problems are transformed into discrete optimization problems by thefinite element method,and then the discrete optimization problems are solved by the proposed SIADMM.Numerical experiments with different problems are investigated to demonstrate the efficiency of the SIADMM.And the numerical per-formance of the SIADMM is better than the performance of the ADMM.Moreover,the numerical results show that the convergence rate of the SIADMM tends to be faster than O(1/√k)in calculation process.
文摘远距离海上风电越来越多地选择柔性直流经海缆送出的方式。采用电缆的柔性直流(voltage source converter based high voltage direct current,VSC-HVDC)输电系统,其故障特性比传统架空线直流输电系统更加复杂。文中基于对称单极拓扑的双端VSC-HVDC海上风电送出工程,简化了电缆和VSC-HVDC输电系统的数学模型,分析换流变阀侧交流系统单相接地和直流电缆线路单极接地等典型故障下的故障特性,运用叠加原理对故障机理进行解释;根据不同故障类型的故障源等效出不同的故障回路,得到了长距离电缆显著的电容效应对VSC-HVDC系统故障特征的复杂影响;利用实时数字仿真平台,搭建远海风电送出系统硬件在环仿真模型,验证了故障机理解析分析的正确性。
