Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficul...Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.展开更多
We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwi...We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are required in the combine step, for each point that lies in the 25-wide vertical slab. The correctness of the algorithm is shown for all Minkowski distances with p ≥ 1. We also show empirically that, although the time complexity of the algorithm is still O（n lgn）, the reduction in the total number of comparisons leads to a significant reduction in the total execution time, for inputs with size sufficiently large.展开更多
1)Figure of the earth as a geometrical problem.In anoient times,people thought that the surface of the earth is essentially flat.This notion hadbeen kept in the minds of the primitive peoples until the beginning of th...1)Figure of the earth as a geometrical problem.In anoient times,people thought that the surface of the earth is essentially flat.This notion hadbeen kept in the minds of the primitive peoples until the beginning of the sixthcentury before Ohrist.The first clear and unequivocal statement of the sphericity of the earth was due to the Greek philosopher Pythogoras(died 582 B.C.).展开更多
基金Project supported by the National 973 Program (No.2004CB719402), the National Natural Science Foundation of China (No. 10372030)the Open Research Projects supported by the Project Fund of the Hubei Province Key Lab of Mechanical Transmission & Manufacturing Engineering Wuhan University of Science & Technology (No.2003A16).
文摘Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
文摘We present an engineered version of the divide-and-conquer algorithm for finding the closest pair of points, within a given set of points in the XY-plane. For this version of the algorithm we show that only two pairwise comparisons are required in the combine step, for each point that lies in the 25-wide vertical slab. The correctness of the algorithm is shown for all Minkowski distances with p ≥ 1. We also show empirically that, although the time complexity of the algorithm is still O（n lgn）, the reduction in the total number of comparisons leads to a significant reduction in the total execution time, for inputs with size sufficiently large.
文摘1)Figure of the earth as a geometrical problem.In anoient times,people thought that the surface of the earth is essentially flat.This notion hadbeen kept in the minds of the primitive peoples until the beginning of the sixthcentury before Ohrist.The first clear and unequivocal statement of the sphericity of the earth was due to the Greek philosopher Pythogoras(died 582 B.C.).
