Skip to main content

Research Repository

Advanced Search

A multiresolution Discrete Element Method for triangulated objects with implicit time stepping

Noble, Peter; Weinzierl, Tobias

A multiresolution Discrete Element Method for triangulated objects with implicit time stepping Thumbnail


Peter Noble
PGR Student Doctor of Philosophy


Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are nonspherical. The most expensive part within such a simulation code is the collision detection. We propose a family of novel multiscale collision detection algorithms that can be applied to triangulated objects within explicit and implicit time stepping methods. They are well suited to handle objects that cannot be represented by analytical shapes or assemblies of analytical objects. Inspired by multigrid methods and adaptive mesh refinement, we determine collision points iteratively over a resolution hierarchy and combine a functional minimization plus penalty parameters with the actual comparision-based geometric distance calculation. Coarse surrogate geometry representations identify “no collision” scenarios early on and otherwise yield an educated guess which triangle subsets of the next finer level might yield collisions. They prune the search tree and furthermore feed conservative contact force estimates into the iterative solve behind an implicit time stepping. Implicit time stepping and nonanalytical shapes often yield prohibitive high compute cost for rigid body simulations. Our approach reduces the object-object comparison cost algorithmically by one to two orders of magnitude. It also exhibits high vectorization efficiency due to its iterative nature.

Journal Article Type Article
Acceptance Date Mar 14, 2022
Online Publication Date Jul 28, 2022
Publication Date 2022-08
Deposit Date Mar 18, 2022
Publicly Available Date Dec 19, 2022
Journal SIAM Journal on Scientific Computing
Print ISSN 1064-8275
Electronic ISSN 1095-7197
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 44
Issue 4
Pages A2121-A2149
Public URL
Related Public URLs


You might also like

Downloadable Citations