Condensation Jacobian with Adaptivity

TL;DR

ConJac introduces an adaptive condensation method for dynamic simulations that enables large time steps, stability, and accurate modeling of complex materials by reducing degrees of freedom through a velocity-level mapping.

Contribution

This work presents a novel condensation-based approach, ConJac, that adaptively selects dynamic nodes and derives reduced equations for stable, large time step simulations with complex nonlinear materials.

Findings

ConJac remains stable at large time steps.

It accurately reproduces full space configurations after static state.

Supports complex nonlinear, anisotropic, and heterogeneous materials.

Abstract

We present a new approach that allows large time steps in dynamic simulations. Our approach, ConJac, is based on condensation, a technique for eliminating many degrees of freedom (DOFs) by expressing them in terms of the remaining degrees of freedom. In this work, we choose a subset of nodes to be dynamic nodes, and apply condensation at the velocity level by defining a linear mapping from the velocities of these chosen dynamic DOFs to the velocities of the remaining quasistatic DOFs. We then use this mapping to derive reduced equations of motion involving only the dynamic DOFs. We also derive a novel stabilization term that enables us to use complex nonlinear material models. ConJac remains stable at large time steps, exhibits highly dynamic motion, and displays minimal numerical damping. In marked contrast to subspace approaches, ConJac gives exactly the same configuration as the full space approach once the static state is reached. Furthermore, ConJac can automatically choose which parts of the object are to be simulated dynamically or quasistatically. Finally, ConJac works with a wide range of moderate to stiff materials, supports anisotropy and heterogeneity, handles topology changes, and can be combined with existing solvers including rigid body dynamics.