Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stocha...Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.展开更多
Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is ...Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is approximated by the two-pass model which increases computational cost. A new kind of discretization scheme for the Laplacian is proposed in this paper, then a method with higher precision and better stability, called Improved KGF-SPH, is developed by modifying KGF-SPH with this new Laplacian model. One-dimensional （1D） and two-dimensional （2D） heat conduction problems are used to test the precision and stability of the Improved KGF-SPH. The numerical results demonstrate that the Improved KGF-SPH is more accurate than SPH, and stabler than KGF-SPH. Natural convection in a closed square cavity at different Rayleigh numbers are modeled by the Improved KGF-SPH with shifting particle position, and the Improved KGF-SPH results are presented in comparison with those of SPH and finite volume method （FVM）. The numerical results demonstrate that the Improved KGF-SPH is a more accurate method to study and model the heat transfer problems.展开更多
针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景...针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景下的布图规划问题的不同优化阶段处理为该泛化模型的特例,并利用共轭次梯度算法(conjugate sub-gradient algorithm,CSA)对其进行求解。针对固定轮廓布图规划问题,通过统一框架下的全局布图规划、合法化、局部优化三个阶段,实现了在固定轮廓约束下的线长优化。针对无固定轮廓约束问题,提出了带黄金分割策略的共轭次梯度算法(conjugate sub-gradient algorithm with golden section strategy,CSA_GSS),利用黄金分割策略缩小固定轮廓的面积,达到面积和线长双优化的效果。实验在GSRC测试电路上与基于B*-树表示的布图规划算法进行比较,该算法对于大规模电路在线长和时间方面均占据优势。实验结果表明,该算法能以更低的时间复杂度获得更优的线长。展开更多
The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis ...The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.展开更多
文摘Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.
文摘Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is approximated by the two-pass model which increases computational cost. A new kind of discretization scheme for the Laplacian is proposed in this paper, then a method with higher precision and better stability, called Improved KGF-SPH, is developed by modifying KGF-SPH with this new Laplacian model. One-dimensional （1D） and two-dimensional （2D） heat conduction problems are used to test the precision and stability of the Improved KGF-SPH. The numerical results demonstrate that the Improved KGF-SPH is more accurate than SPH, and stabler than KGF-SPH. Natural convection in a closed square cavity at different Rayleigh numbers are modeled by the Improved KGF-SPH with shifting particle position, and the Improved KGF-SPH results are presented in comparison with those of SPH and finite volume method （FVM）. The numerical results demonstrate that the Improved KGF-SPH is a more accurate method to study and model the heat transfer problems.
文摘针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景下的布图规划问题的不同优化阶段处理为该泛化模型的特例,并利用共轭次梯度算法(conjugate sub-gradient algorithm,CSA)对其进行求解。针对固定轮廓布图规划问题,通过统一框架下的全局布图规划、合法化、局部优化三个阶段,实现了在固定轮廓约束下的线长优化。针对无固定轮廓约束问题,提出了带黄金分割策略的共轭次梯度算法(conjugate sub-gradient algorithm with golden section strategy,CSA_GSS),利用黄金分割策略缩小固定轮廓的面积,达到面积和线长双优化的效果。实验在GSRC测试电路上与基于B*-树表示的布图规划算法进行比较,该算法对于大规模电路在线长和时间方面均占据优势。实验结果表明,该算法能以更低的时间复杂度获得更优的线长。
基金supported by the Portuguese Foundation for Science and Technology(FCT)through project UID/CTM/00264/2019 of 2C2T—Centro de Ciência e Tecnologia Têxtil,hold by National Founds of FCT/MCTES,and project UID/EEA/04436/2013,COMPETE 2020 with the code POCI-01-0145-FEDER-006941.
文摘The combination of a 4-node quadrilateral mixed interpolation of tensorial components element(MITC4)and the cell-based smoothed finite element method(CSFEM)was formulated and implemented in this work for the analysis of free vibration and unidirectional buckling of shell structures.This formulation was applied to numerous numerical examples of non-woven fabrics.As CSFEM schemes do not require coordinate transformation,spurious modes and numerical instabilities are prevented using bilinear quadrilateral element subdivided into two,three and four smoothing cells.An improvement of the original CSFEM formulation was made regarding the calculation of outward unit normal vectors,which allowed to remove the integral operator in the strain smoothing operation.This procedure conducted both to the simplification of the developed formulation and the reduction of computational cost.A wide range of values for the thickness-to-length ratio and edge boundary conditions were analysed.The developed numerical model proved to overcome the shear locking phenomenon with success,revealing both reduced implementation effort and computational cost in comparison to the conventional FEM approach.The cell-based strain smoothing technique used in this work yields accurate results and generally attains higher convergence rate in energy at low computational cost.
