Abstract: A relaxation algorithm is developed to simulate sphere packing with arbitrary diameter distribution.An adaptive iteration period is employed to keep the packing density stable with various number of spheres.The packing density and the coordinate number of the algorithm are higher than those of previous approaches.The efficiency of contact detection is considerably increased by background grids and double link group structure.The time complexity of the algorithm is O(N),where N is the number of spheres.It needs only CPU time of 217s to achieve a packing density of 0.64 for random close packing of 10 000 equal spheres with an AMD Athlon 3200+PC.New classification of numerical methods for sphere packing is also presented.

Key words: sphere packing, relaxation algorithm, random close packing, background grid, arbitrary diameter distribution