QLB: Collision-Aware Quasi-Newton Solver with Cholesky and L-BFGS for Nonlinear Time Integration

Abstract

We advocate for the straightforward applications of the Cholesky and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms in the context of nonlinear time integration of deformable objects with dynamic collisions. At the beginning of each time step, we form and factor the Hessian matrix, accounting for all internal forces while omitting the implicit cross-coupling terms from the collision forces between multiple dynamic objects or self collisions. Then during the nonlinear solver iterations of the time step, we implicitly update this Hessian with L-BFGS. This approach is simple to implement and can be readily applied to any nonlinear time integration scheme, including higher-order schemes and quasistatics. We show that this approach works well in a wide range of settings involving complex nonlinear materials, including heterogeneity and anisotropy, as well as collisions, including frictional contact and self collisions.