Filling domains with disks: an advancing front approach

Abstract

SUMMARYAn advancing front-based algorithm is proposed to constructively generate a random initial packing for disks with di erent radii within a 2D domain, which is often required in discrete element methods (DEM). Depending on whether the domain boundary is included in the initial front and how the front is formed, two di erent versions of the algorithm, termed the closed and open form, respectively, are presented. The open form version has an inherent linear complexity. The closed form can achieve the same complexity under a relatively weak condition. The generated packing is not a globally optimal arrangement but achieves a locally highest density from the algorithmic point of view. The performance of the algorithm is illustrated in several examples. The major beneÿt of this development is the significant reduction of CPU time required for the preparation of an initial discrete object conÿguration in DEM simulations. It is demonstrated that it takes only 3:77 s for the proposed algorithm to generate one million disks on a PC with a one 1 GHz processor.

Modified algorithm for generating high volume fraction sphere packings

“…Regarding dynamic methods, wall compression [2], particle expansion [2,3] and gravity deposition [2] can be mentioned. Constructive methods include sequential inhibition [4], triangulation [5], dropping [6] and advancing front [1,2,7,8].…”

“…Constructive methods include sequential inhibition [4], triangulation [5], dropping [6] and advancing front [1,2,7,8]. The above mentioned particle packing methods are briefly explained in the next paragraphs.…”

“…The above mentioned particle packing methods are briefly explained in the next paragraphs. More detailed reviews on packing methods can be found in [1,2,4,7,9].…”

“…The problem of disk packing has been efficiently solved using an advancing front approach [1,2]. The previously cited results allow to obtain high density disk packings in very short times.…”

A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

“…Most studies were carried out for the packing of uniform and arbitrary sized spheres [1], considering the problem of optimal packing [2][3][4][5], (and its dual, the sphere cutting problem [6,7]) or space-filling [8][9][10][11][12][13][14].…”