Packing congruent hyperspheres into a hypersphere |
| |
Authors: | Yuriy Stoyan Georgiy Yaskov |
| |
Institution: | 1.Department of Mathematical Modeling and Optimal Design,Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine,Kharkov,Ukraine |
| |
Abstract: | The paper considers a problem of packing the maximal number of congruent nD hyperspheres of given radius into a larger nD hypersphere of given radius where n = 2, 3, . . . , 24. Solving the problem is reduced to solving a sequence of packing subproblems provided that radii of hyperspheres
are variable. Mathematical models of the subproblems are constructed. Characteristics of the mathematical models are investigated.
On the ground of the characteristics we offer a solution approach. For n ≤ 3 starting points are generated either in accordance with the lattice packing of circles and spheres or in a random way.
For n > 3 starting points are generated in a random way. A procedure of perturbation of lattice packings is applied to improve
convergence. We use the Zoutendijk feasible direction method to search for local maxima of the subproblems. To compute an
approximation to a global maximum of the problem we realize a non-exhaustive search of local maxima. Our results are compared
with the benchmark results for n = 2. A number of numerical results for 2 ≤ n ≤ 24 are given. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|