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
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.
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.
