An augmented spatial digital tree algorithm for contact detection in computational mechanics

Based on the understanding of existing spatial digital tree-based contact detection approaches, and the alternating digital tree (ADT) algorithm in particular, a more e cient algorithm, termed the augmented spatial digital tree (ASDT) algorithm, is proposed in the present work. The ASDT algorithm adopts a di erent point representation scheme that uses only the lower corner vertex to represent a (hyper-)rectangle, with the upper corner vertex serving as the augmented information. Consequently, the ASDT algorithm can keep the working space the same as the original n-dimensional space and, in general, a much better balanced tree can be expected. This, together with the introduction of an additional bounding subregion for the rectangles associated with each tree node, makes it possible to signi cantly reduce the number of node visits in the region search, although each node visit may be slightly more expensive. Three examples arising in computational mechanics are presented to provide an assessment of the performance of the ASDT. The numerical results indicate that the ASDT is, at least, over 3.9 times faster than the ADT