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

Noble, Peter; Weinzierl, Tobias

Abstract

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.

Citation

Noble, P., & Weinzierl, T. (2022). A multiresolution Discrete Element Method for triangulated objects with implicit time stepping. SIAM Journal on Scientific Computing, 44(4), A2121-A2149. https://doi.org/10.1137/21m1421842

• 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
• DOI: https://doi.org/10.1137/21m1421842
• Public URL: https://durham-repository.worktribe.com/output/1209672
• Related Public URLs: https://arxiv.org/abs/2105.12415