在杆系结构的受力分析中,应用弯矩迭代法计算框架的杆端弯矩时,常遇到迭代过程收敛缓慢的问题。本文提供的方法,可以提高迭代收敛速度。令 M<sub>?k</sub>′、M<sub>ki</sub>′、M<sub>ik</sub>″...在杆系结构的受力分析中,应用弯矩迭代法计算框架的杆端弯矩时,常遇到迭代过程收敛缓慢的问题。本文提供的方法,可以提高迭代收敛速度。令 M<sub>?k</sub>′、M<sub>ki</sub>′、M<sub>ik</sub>″表示刚架中杆 ik 两端的转角弯矩和侧移弯矩,P<sub>?</sub> 表示杆 ik 所属第 r 楼层的楼层剪力。展开更多
In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the so...In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.展开更多
KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the...KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF)scheme.To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms,we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox.We compare the performance of KSSOLV-GPU on three types of GPU,including RTX3090,V100,and A100,with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.展开更多
The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor form...The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.展开更多
We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements...We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.展开更多
文摘在杆系结构的受力分析中,应用弯矩迭代法计算框架的杆端弯矩时,常遇到迭代过程收敛缓慢的问题。本文提供的方法,可以提高迭代收敛速度。令 M<sub>?k</sub>′、M<sub>ki</sub>′、M<sub>ik</sub>″表示刚架中杆 ik 两端的转角弯矩和侧移弯矩,P<sub>?</sub> 表示杆 ik 所属第 r 楼层的楼层剪力。
基金Supported by the Yildiz Technical University Scientific Research Projects Coordination Department.Project Number:2012-10-01 KAP 02
文摘In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.
基金supported by the National Natural Science Foundation of China (No.21688102,No.21803066,and No.22003061)the Chinese Academy of Sciences Pioneer Hundred Talents Program (KJ2340000031,KJ2340007002)+7 种基金the National Key Research and Development Program of China(2016YFA0200604)the Anhui Initiative in Quantum Information Technologies (AHY090400)the Strategic Priority Research of Chinese Academy of Sciences(XDC01040100)CAS Project for Young Scientists in Basic Research (YSBR-005)the Fundamental Research Funds for the Central Universities (WK2340000091,WK2060000018)the Hefei National Laboratory for Physical Sciences at the Microscale (SK2340002001)the Research Start-Up Grants (KY2340000094)the Academic Leading Talents Training Program(KY2340000103) from University of Science and Technology of China
文摘KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF)scheme.To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms,we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox.We compare the performance of KSSOLV-GPU on three types of GPU,including RTX3090,V100,and A100,with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.
基金supported by National Natural Science Foundation of China (Grant No.10961010)Science and Technology Foundation of Guizhou Province (Grant No. LKS[2009]03)
文摘The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper.By fully exploiting the structure of the tensor equation,we propose a projection method based on the tensor format,which needs less flops and storage than the standard projection method.The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product(NKP) preconditioner,which is easy to construct and is able to accelerate the convergence of the iterative solver.Numerical experiments are presented to show good performance of the approaches.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010MS080)the Research Fund for Doctoral Program of Higher Education of China (Grant No. 20070487403)
文摘We apply the fast multipole method (FMM) accelerated boundary element method (BEM) for the three-dimensional (3D) Helmholtz equation, and as a result, large-scale acoustic scattering problems involving 400000 elements are solved efficiently. This is an extension of the fast multipole BEM for two-dimensional (2D) acoustic problems developed by authors recently. Some new improvements are obtained. In this new technique, the improved Burton-Miller formulation is employed to over-come non-uniqueness difficulties in the conventional BEM for exterior acoustic problems. The computational efficiency is further improved by adopting the FMM and the block diagonal preconditioner used in the generalized minimum residual method (GMRES) iterative solver to solve the system matrix equation. Numerical results clearly demonstrate the complete reliability and efficiency of the proposed algorithm. It is potentially useful for solving large-scale engineering acoustic scattering problems.
