High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes

TL;DR

This paper introduces a high-order finite element method for elastodynamic simulation on curved meshes that maintains non-penetration guarantees and large time steps by leveraging the linearity of IPC optimization steps, improving accuracy and reliability.

Contribution

It presents a novel high-order FE formulation with contact handling for curved meshes, enabling accurate and reliable elastodynamic simulations while preserving key IPC properties.

Findings

Effective in graphics, fabrication, and scientific computing applications.

Retains non-penetration guarantees and large time steps.

Benefits from high-order geometry and bases.

Abstract

High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order finite element (FE) formulation (high-order bases) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact (IPC) model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of nonlinear meshes or nonlinear FE bases. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order bases and high-order geometry. We accomplish this by mapping displacements and resulting contact forces between a linear collision proxy and the underlying high-order representation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.