Variational Elastodynamic Simulation

Leticia Mattos Da Silva, Silvia Sellán, Natalia Pacheco-Tallaj, Justin Solomon

Numerical schemes for time integration are the cornerstone of dynamical simulations for deformable solids. The most popular time integrators for isotropic distortion energies rely on nonlinear root-finding solvers, most prominently, Newton’s method. These solvers are computationally expensive and sensitive to ill-conditioned Hessians and poor initial guesses; these difficulties can particularly hamper the effectiveness of variational integrators, whose momentum conservation properties require reliable root-finding. To tackle these difficulties, this paper shows how to express variational time integration for a large class of elastic energies as an optimization problem with a “hidden” convex substructure. This hidden convexity suggests uses of optimization techniques with rigorous convergence analysis, guaranteed inversion-free elements, and conservation of physical invariants up to tolerance/numerical precision. In particular, we propose an Alternating Direction Method of Multipliers (ADMM) algorithm combined with a proximal operator step to solve our formulation. Empirically, our integrator improves the performance of elastic simulation tasks, as we demonstrate in a number of examples.

Variational Elastodynamic Simulation