In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure betwe...In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.展开更多
Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight s...Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.展开更多
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
The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engin...The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.展开更多
This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the meth...This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.展开更多
Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-A...Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.展开更多
The contact point configuration should be carefully chosen to ensure a stable capture,especially for the non-cooperative target capture mission using multi-armed spacecraft.In this work scenario,the contact points on ...The contact point configuration should be carefully chosen to ensure a stable capture,especially for the non-cooperative target capture mission using multi-armed spacecraft.In this work scenario,the contact points on the base and on the arms are distributed on the opposite side of the target.Otherwise,large forces will be needed.To cope with this problem,an uneven-oriented distribution union criterion is proposed.The union criterion contains a virtual symmetrical criterion and a geometry criterion.The virtual symmetrical contact point criterion is derived from the proof of the force closure principle using computational geometry to ensure a stable grasp,and the geometry criterion is calculated by the volume of the minimum polyhedron formed by the contact points to get a wide-range distribution.To further accelerate the optimization rate and enhance the global search ability,a line array modeling method and a continuous-discrete global search algorithm are proposed.The line array modeling method reduces the workload of calculating the descent direction and the gradient available,while the continuous-discrete global search algorithm reducing the optimization dimension.Then a highly efficient grasping is achieved and the corresponding contact point is calculated.Finally,an exhaustive verification is conducted to numerically analyze the disturbance resistance ability,and simulation results demonstrate the effectiveness of the proposed algorithms.展开更多
We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical sim...We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation.Furthermore,they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.展开更多
The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of ...The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.展开更多
To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However,...To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However, no systematic algorithm yet exists to evaluate the consistency of the current distribution of short-circuit tests. A methodology is proposed in this paper to address this problem. Based on Kirchhoff’s current law and the generalized method of symmetrical components, the current deviations of the AT feeding systems are analysed and then normalized with the short-circuit current as they vary greatly with systems and short-circuit sites. It is also found that the short-circuit current varies with the calculation methods, and its unbiased standard deviation also reflects the consistency of the short-circuit test. The mean and maximum of the current deviations, as well as the unbiased standard deviation of the short-circuit current, show the consistency of the short-circuit test from different aspects,although the last two items are highly relevant. Therefore, a unified evaluation index is defined as the sum of the three items, and then applied in two case studies to test its performance. The results show that, the proposed index canclearly distinguish the consistency of the short-circuit tests and may be used to sort the short-circuit tests for fault location systems. Besides, some short-circuit tests may have very poor consistency indices, and thus are not applicable to the tuning of fault location systems. In the authors’ opinion, the determination of the threshold of the proposed index needs further investigation.展开更多
In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with...In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.展开更多
The multi-frequency and multi-dimensional adapted Runge-Kutta^NystrSm （ARKN） integrators, and multi-frequency and multi-dimensional extended Runge-Kutta-NystrSm （ERKN） integrators have been developed to efficientl...The multi-frequency and multi-dimensional adapted Runge-Kutta^NystrSm （ARKN） integrators, and multi-frequency and multi-dimensional extended Runge-Kutta-NystrSm （ERKN） integrators have been developed to efficiently solve multi-frequency oscillatory Hamiltonian systems. The aim of this paper is to analyze and derive high-order sym- plectic and symmetric composition methods based on the ARKN integrators and ERKN integrators. We first consider the symplecticity conditions for the multi-frequency and multi-dimensional ARKN integrators. We then analyze the symplecticity of the adjoint in- tegrators of the multi-frequency and multi^dimensional symplectic ARKN integrators and ERKN integrators, respectively. On the basis of the theoretical analysis and by using the idea of composition methods, we derive and propose four new high-order symplectic and symmetric methods for the multi-frequency oscillatory Hamiltonian systems. The numer- ical results accompanied in this paper quantitatively show the advantage and efficiency of the proposed high-order symplectic and symmetric methods.展开更多
In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we f...In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use.展开更多
Symmetrical components method is employed in analysis of the characteristic motor faults.Motor protection method is put forward based on detecting positive sequence,negative sequence and zero sequence current.And prob...Symmetrical components method is employed in analysis of the characteristic motor faults.Motor protection method is put forward based on detecting positive sequence,negative sequence and zero sequence current.And problems of lack of motor overload capacity in existing mining motor protection system,impact of dynamic current on stage and definite-time delay operation and inaccuracy of criterion phase failure protection are analyzed.The unbalanced faults protection and inverse-time overload protection,which can make protection time change with the current movement,are proposed.The above problems can be solved,and the reliability and intelligent of coal shearer are improved.展开更多
The paper reports quality analysis and evaluation at 6 - 10/0.4 kV low-voltage distribution grids in Uzbekistan. Power quality frequently does not correspond to the rated value which is largely due to unbalanced phase...The paper reports quality analysis and evaluation at 6 - 10/0.4 kV low-voltage distribution grids in Uzbekistan. Power quality frequently does not correspond to the rated value which is largely due to unbalanced phase loading in grids and which also results in increased power loss. The study of the asymmetrical operating modes of the rural distribution networks of 0.4 kV was conducted in three steps: measurement, calculations and analysis of relevant data;providing practical guidelines and finally, implementing instruments to normalize grid operation. Measuring was conducted using certified instrumentation analyzer “MALIKA” designed by authors. The study and analysis of additional power losses as the function of indicators of asymmetrical features of voltage and current in operating 0.4 kV grids reveals that, quality of electric power at grids under investigation, merely does not meet the requirements of the Interstate Standard.展开更多
In this paper, the numerical solutions of the nonlinear Hadamard fractional diffusion-wave model with the initial singularity are investigated. Firstly, the model is transformed into coupled equations by virtue of a s...In this paper, the numerical solutions of the nonlinear Hadamard fractional diffusion-wave model with the initial singularity are investigated. Firstly, the model is transformed into coupled equations by virtue of a symmetric fractional-order reduction method. Then the L_(log,2-1σ) formula on nonuniform grids is applied to approach to the time fractional derivative. In addition, the discrete fractional Grönwall inequality is used to analyze the optimal convergence of the constructed numerical scheme by the energy method. The accuracy of the theoretical analysis will be demonstrated by means of a numerical experiment at the end.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
基金Supported by the Natural Science Foundation of Hubei Province(2008CDZD47)
文摘In this paper, we present a large-update primal-dual interior-point method for symmetric cone optimization（SCO） based on a new kernel function, which determines both search directions and the proximity measure between the iterate and the center path. The kernel function is neither a self-regular function nor the usual logarithmic kernel function. Besides, by using Euclidean Jordan algebraic techniques, we achieve the favorable iteration complexity O（ √r（1/2）（log r）^2 log（r/ ε））, which is as good as the convex quadratic semi-definite optimization analogue.
基金supported by the National Natural Science Foundation of China(Grants Nos.51978150 and 52050410334)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grants No.SJCX23_0069)the Fundamental Research Funds for the Central Universities.
文摘Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.
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support of the National Natural Science Foundation of China(12072011).
文摘The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures,because only boundary and crack-surface elements are needed.However,for engineering structures subjected to body forces such as rotational inertia and gravitational loads,additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain.In this study,weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed.By using divergence theorem or alternatively the radial integration method,the domain integral terms caused by body forces are transformed into boundary integrals.And due to the weak singularity of the formulated boundary integral equations,a simple Gauss-Legendre quadrature with a few integral points is sufficient for numerically evaluating the SGBEM equations.Some numerical examples are presented to verify this approach and results are compared with benchmark solutions.
文摘This paper mainly proposes a new C-XSC （C- for eXtended Scientific Computing） software for the symmetric single step method and relaxation method for computing an enclosure for the solution set and compares the methods with others＇ and then makes some modifications and finally, examples illustrating the applicability of the proposed methods are given.
文摘Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.
基金supported by the National Natural Science Foundation of China(Nos.62003115,11972130)Shenzhen Natural Science Fund(the Stable Support Plan Program GXWD20201230155427003-20200821170719001).
文摘The contact point configuration should be carefully chosen to ensure a stable capture,especially for the non-cooperative target capture mission using multi-armed spacecraft.In this work scenario,the contact points on the base and on the arms are distributed on the opposite side of the target.Otherwise,large forces will be needed.To cope with this problem,an uneven-oriented distribution union criterion is proposed.The union criterion contains a virtual symmetrical criterion and a geometry criterion.The virtual symmetrical contact point criterion is derived from the proof of the force closure principle using computational geometry to ensure a stable grasp,and the geometry criterion is calculated by the volume of the minimum polyhedron formed by the contact points to get a wide-range distribution.To further accelerate the optimization rate and enhance the global search ability,a line array modeling method and a continuous-discrete global search algorithm are proposed.The line array modeling method reduces the workload of calculating the descent direction and the gradient available,while the continuous-discrete global search algorithm reducing the optimization dimension.Then a highly efficient grasping is achieved and the corresponding contact point is calculated.Finally,an exhaustive verification is conducted to numerically analyze the disturbance resistance ability,and simulation results demonstrate the effectiveness of the proposed algorithms.
基金supported by the ITER-China Program(Grant No.2014GB124005)the National Natural Science Foundation of China(Grant Nos.11371357 and 11505186).
文摘We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system.The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation.Furthermore,they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.
基金supported by the National Natural Science Foundation of China (51176003)
文摘The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.
文摘To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However, no systematic algorithm yet exists to evaluate the consistency of the current distribution of short-circuit tests. A methodology is proposed in this paper to address this problem. Based on Kirchhoff’s current law and the generalized method of symmetrical components, the current deviations of the AT feeding systems are analysed and then normalized with the short-circuit current as they vary greatly with systems and short-circuit sites. It is also found that the short-circuit current varies with the calculation methods, and its unbiased standard deviation also reflects the consistency of the short-circuit test. The mean and maximum of the current deviations, as well as the unbiased standard deviation of the short-circuit current, show the consistency of the short-circuit test from different aspects,although the last two items are highly relevant. Therefore, a unified evaluation index is defined as the sum of the three items, and then applied in two case studies to test its performance. The results show that, the proposed index canclearly distinguish the consistency of the short-circuit tests and may be used to sort the short-circuit tests for fault location systems. Besides, some short-circuit tests may have very poor consistency indices, and thus are not applicable to the tuning of fault location systems. In the authors’ opinion, the determination of the threshold of the proposed index needs further investigation.
基金supported by the National Natural Science Foundation of China (Grant No.50808066)
文摘In this study, for the purpose of improving the efficiency and accuracy of numerical simulation of massive concrete, the symmetric successive over relaxation-preconditioned conjugate gradient method （SSOR-PCGM） with an improved iteration format was derived and applied to solution of large sparse symmetric positive definite linear equations in the computational process of the finite element analysis. A three-dimensional simulation program for massive concrete was developed based on SSOR-PCGM with an improved iteration format. Then, the programs based on the direct method and SSOR-PCGM with an improved iteration format were used for computation of the Guandi roller compacted concrete （RCC） gravity dam and an elastic cube under free expansion. The comparison and analysis of the computational results show that SSOR-PCGM with the improved iteration format occupies much less physical memory and can solve larger-scale problems with much less computing time and flexible control of accuracy.
文摘The multi-frequency and multi-dimensional adapted Runge-Kutta^NystrSm （ARKN） integrators, and multi-frequency and multi-dimensional extended Runge-Kutta-NystrSm （ERKN） integrators have been developed to efficiently solve multi-frequency oscillatory Hamiltonian systems. The aim of this paper is to analyze and derive high-order sym- plectic and symmetric composition methods based on the ARKN integrators and ERKN integrators. We first consider the symplecticity conditions for the multi-frequency and multi-dimensional ARKN integrators. We then analyze the symplecticity of the adjoint in- tegrators of the multi-frequency and multi^dimensional symplectic ARKN integrators and ERKN integrators, respectively. On the basis of the theoretical analysis and by using the idea of composition methods, we derive and propose four new high-order symplectic and symmetric methods for the multi-frequency oscillatory Hamiltonian systems. The numer- ical results accompanied in this paper quantitatively show the advantage and efficiency of the proposed high-order symplectic and symmetric methods.
文摘In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use.
文摘Symmetrical components method is employed in analysis of the characteristic motor faults.Motor protection method is put forward based on detecting positive sequence,negative sequence and zero sequence current.And problems of lack of motor overload capacity in existing mining motor protection system,impact of dynamic current on stage and definite-time delay operation and inaccuracy of criterion phase failure protection are analyzed.The unbalanced faults protection and inverse-time overload protection,which can make protection time change with the current movement,are proposed.The above problems can be solved,and the reliability and intelligent of coal shearer are improved.
文摘The paper reports quality analysis and evaluation at 6 - 10/0.4 kV low-voltage distribution grids in Uzbekistan. Power quality frequently does not correspond to the rated value which is largely due to unbalanced phase loading in grids and which also results in increased power loss. The study of the asymmetrical operating modes of the rural distribution networks of 0.4 kV was conducted in three steps: measurement, calculations and analysis of relevant data;providing practical guidelines and finally, implementing instruments to normalize grid operation. Measuring was conducted using certified instrumentation analyzer “MALIKA” designed by authors. The study and analysis of additional power losses as the function of indicators of asymmetrical features of voltage and current in operating 0.4 kV grids reveals that, quality of electric power at grids under investigation, merely does not meet the requirements of the Interstate Standard.
基金supported by the National Natural Science Foundation of China(No.11701103)the Natural Science Foundation of Guangdong Province of China(Nos.2022A1515012147,2023A1515011504)University of Macao(File Nos.MYRG2020-00035-FST,MYRG2018-00047-FST).
文摘In this paper, the numerical solutions of the nonlinear Hadamard fractional diffusion-wave model with the initial singularity are investigated. Firstly, the model is transformed into coupled equations by virtue of a symmetric fractional-order reduction method. Then the L_(log,2-1σ) formula on nonuniform grids is applied to approach to the time fractional derivative. In addition, the discrete fractional Grönwall inequality is used to analyze the optimal convergence of the constructed numerical scheme by the energy method. The accuracy of the theoretical analysis will be demonstrated by means of a numerical experiment at the end.
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.
