经典的高效全局优化(efficient global optimization,EGO)算法搜寻得到的最优解,受代理模型精度及过早收敛等问题的制约,其精度仍存在进一步改善的空间。围绕最优解精度进一步改善的问题,研究了面向精确最优解的EGO算法。该算法基于Krig...经典的高效全局优化(efficient global optimization,EGO)算法搜寻得到的最优解,受代理模型精度及过早收敛等问题的制约,其精度仍存在进一步改善的空间。围绕最优解精度进一步改善的问题,研究了面向精确最优解的EGO算法。该算法基于Kriging代理模型,涉及的最优加点策略采用考虑Kriging信任的改善期望函数法,使得优化迭代后期更偏向于局部寻优。此外,文中还考虑了与成熟的拟牛顿法和Powell法等局部优化方法协同的算法,以提高最优解的搜寻精度。选用了若干典型的检验函数,对优化算法的具体实施过程进行了模拟与分析,发现改进后的优化算法能以相对较少的额外函数评估次数得到比经典的EGO算法更精确的全局最优解,从而验证了算法的有效性和准确性。最后,把发展的算法应用到具体的跨音速翼型优化问题,算例表明,改进后的EGO算法翼型阻力较原EGO算法减小了1.11%,显示了其工程实用性。展开更多
A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU...A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)model.The CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG method.The corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar Navier-Stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi&Rebay,respectively.A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical solutions.The resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be achieved.The numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU speedups.This shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.展开更多
文摘经典的高效全局优化(efficient global optimization,EGO)算法搜寻得到的最优解,受代理模型精度及过早收敛等问题的制约,其精度仍存在进一步改善的空间。围绕最优解精度进一步改善的问题,研究了面向精确最优解的EGO算法。该算法基于Kriging代理模型,涉及的最优加点策略采用考虑Kriging信任的改善期望函数法,使得优化迭代后期更偏向于局部寻优。此外,文中还考虑了与成熟的拟牛顿法和Powell法等局部优化方法协同的算法,以提高最优解的搜寻精度。选用了若干典型的检验函数,对优化算法的具体实施过程进行了模拟与分析,发现改进后的优化算法能以相对较少的额外函数评估次数得到比经典的EGO算法更精确的全局最优解,从而验证了算法的有效性和准确性。最后,把发展的算法应用到具体的跨音速翼型优化问题,算例表明,改进后的EGO算法翼型阻力较原EGO算法减小了1.11%,显示了其工程实用性。
基金partially supported by the National Natural Science Foundation of China(No.11972189)the Natural Science Foundation of Jiangsu Province(No.BK20190391)+1 种基金the Natural Science Foundation of Anhui Province(No.1908085QF260)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)model.The CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG method.The corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar Navier-Stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi&Rebay,respectively.A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical solutions.The resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be achieved.The numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU speedups.This shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.
