A multiresolution Discrete Element Method for triangulated objects with implicit timestepping

TL;DR

This paper introduces a multiresolution collision detection algorithm for triangulated objects that significantly reduces computational costs in rigid body simulations with implicit time stepping.

Contribution

The paper presents a novel multiscale collision detection method inspired by multigrid techniques, suitable for non-analytical shapes and implicit time stepping, improving efficiency.

Findings

Reduces collision detection cost by 10 to 100 times.

Efficiently identifies non-collision scenarios early.

High vectorisation efficiency due to iterative approach.

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 non-spherical. 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 minimisation 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 potentially 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 non-analytical shapes often yield prohibitive high compute cost for rigid body simulations. Our approach reduces these cost algorithmically by one to two orders of magnitude. It also exhibits high vectorisation efficiency due to its iterative nature.