INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2004; 61:1977–1991 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1068 A general advancing front technique for filling space with arbitrary objects Rainald Löhner 1, ∗, † and Eugenio Oñate 2 1 School of Computational Sciences, MS 4C7 George Mason University, Fairfax, VA 22030-4444, U.S.A. 2 CIMNE, Universidad Politécnica de Catalunya Barcelona, Spain SUMMARY An advancing front space-filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance in space and an initial triangulation of the surface. One object at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active objects are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Different deposition or layering patterns can be achieved by selecting the order in which objects are eliminated from the active front. Timings show that for simple objects like spheres the scheme is considerably faster than volume mesh generators based on the advancing front technique, making it possible to generate large (> 10 6 ) yet optimal clouds of points in a matter of minutes on a PC. For more general objects, the performance may degrade depending on the complexity of the penetration checks. Several examples are included that demonstrate the capabilities of the technique. Copyright  2004 John Wiley & Sons, Ltd. KEY WORDS: grid generation; mesh free techniques; discrete element method; SPH; finite point method 1. INTRODUCTION Many simulation techniques in computational mechanics require a space-filling cloud of arbitrary objects. For the case of ‘gridless’ or ‘mesh free’ partial differential equation (PDE) solvers (see References [1–9]) these are simply points. For discrete element methods (see References [10–13]), these could be spheres, ellipsoids, polyhedra, or any other arbitrary shape. The task is therefore to fill a prescribed volume with these objects so that they are close but do not overlap in an automatic way. ∗ Correspondence to: Rainald Löhner, School of Computational Sciences, MS 4C7 George Mason University, Fairfax, VA 22030-4444, U.S.A. † E-mail: rlohner@gmu.edu Received 22 August 2003 Revised 29 December 2003 Copyright  2004 John Wiley & Sons, Ltd. Accepted 28 January 2004