约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模...约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模型的最大分划,并采用一种松弛技术,提出一个具有高度并行结构的最大分划松弛ADMM算法,分析了算法的计算复杂度,讨论了算法的收敛性,并给出了算法的参数设置方法.实验表明,最大分划松弛ADMM比非松弛的最大分划ADMM收敛快很多;与现有算法相比,提高了计算效率.GPU加速实验中获得的大加速比,表明了所提算法的高度并行性和可扩展性,在图像处理、计算机视觉、模式识别及机器学习等领域有广阔的应用前景.展开更多
In this paper,numerical analyses of fluid flow around the ship hulls such as Series 60,the Kriso Container Ship(KCS),and catamaran advancing in calm water,are presented.A commercial computational fluid dynamic(CFD)cod...In this paper,numerical analyses of fluid flow around the ship hulls such as Series 60,the Kriso Container Ship(KCS),and catamaran advancing in calm water,are presented.A commercial computational fluid dynamic(CFD)code,STAR-CCM+is used to analyze total resistance,sinkage,trim,wave profile,and wave pattern for a range of Froude numbers.The governing RANS equations of fluid flow are discretized using the finite volume method(FVM),and the pressure-velocity coupling equations are solved using the SIMPLE(semi-implicit method for pressure linked equations)algorithm.Volume of fluid(VOF)method is employed to capture the interface between air and water phases.A fine discretization is performed in between these two phases to get a higher mesh resolution.The fluid-structure interaction(FSI)is modeled with the dynamic fluid-body interaction(DFBI)module within the STAR-CCM+.The numerical results are verified using the results available in the literatures.Grid convergence studies are also carried out to determine the dependence of results on the grid quality.In comparison to previous findings,the current CFD analysis shows the satisfactory results.展开更多
Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed bas...Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.展开更多
In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed al...In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order oracles.To encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search condition.Otherwise,a small step size will be taken to help induce desired good properties.Then we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain conditions.We also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen output.Furthermore,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high probability.At last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.展开更多
In this paper, we present a modified projection method for the linear feasibility problems （LFP）. Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of th...In this paper, we present a modified projection method for the linear feasibility problems （LFP）. Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.展开更多
文摘约束二维有限脉冲响应(Finite Impulse Response,FIR)滤波器,现有设计算法计算复杂度高.针对二维FIR滤波器的约束最小二乘设计,本文应用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM),研究其并行优化方法.通过模型的最大分划,并采用一种松弛技术,提出一个具有高度并行结构的最大分划松弛ADMM算法,分析了算法的计算复杂度,讨论了算法的收敛性,并给出了算法的参数设置方法.实验表明,最大分划松弛ADMM比非松弛的最大分划ADMM收敛快很多;与现有算法相比,提高了计算效率.GPU加速实验中获得的大加速比,表明了所提算法的高度并行性和可扩展性,在图像处理、计算机视觉、模式识别及机器学习等领域有广阔的应用前景.
文摘In this paper,numerical analyses of fluid flow around the ship hulls such as Series 60,the Kriso Container Ship(KCS),and catamaran advancing in calm water,are presented.A commercial computational fluid dynamic(CFD)code,STAR-CCM+is used to analyze total resistance,sinkage,trim,wave profile,and wave pattern for a range of Froude numbers.The governing RANS equations of fluid flow are discretized using the finite volume method(FVM),and the pressure-velocity coupling equations are solved using the SIMPLE(semi-implicit method for pressure linked equations)algorithm.Volume of fluid(VOF)method is employed to capture the interface between air and water phases.A fine discretization is performed in between these two phases to get a higher mesh resolution.The fluid-structure interaction(FSI)is modeled with the dynamic fluid-body interaction(DFBI)module within the STAR-CCM+.The numerical results are verified using the results available in the literatures.Grid convergence studies are also carried out to determine the dependence of results on the grid quality.In comparison to previous findings,the current CFD analysis shows the satisfactory results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11902085 and 11832009)the Science and Technology Association Young Scientific and Technological Talents Support Project of Guangzhou City(Grant No.SKX20210304)the Natural Science Foundation of Guangdong Province(Grant No.2021Al515010320).
文摘Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.
基金supported by the National Natural Science Foundation of China (Nos.11731013,11871453 and 11971089)Young Elite Scientists Sponsorship Program by CAST (No.2018QNRC001)+1 种基金Youth Innovation Promotion Association,CASFundamental Research Funds for the Central Universities,UCAS.
文摘In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order oracles.To encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search condition.Otherwise,a small step size will be taken to help induce desired good properties.Then we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain conditions.We also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen output.Furthermore,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high probability.At last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.
基金supported by National Natural Science Foundation of China (No. 10771120)Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this paper, we present a modified projection method for the linear feasibility problems （LFP）. Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.
