Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation

High quality simulations of the dynamics of soft flexible objects can be rather costly, because the assembly of internal forces through an often nonlinear stiffness at each time step is expensive. Many standard implicit integrators introduce significant, time-step dependent artificial damping. Here we propose and demonstrate the effectiveness of an exponential Rosenbrock-Euler (ERE) method which avoids discretization-dependent artificial damping. The method is relatively inexpensive and works well with the large time steps used in computer graphics. It retains correct qualitative behaviour even in challenging circumstances involving non-convex elastic energies. Our integrator is designed to handle and perform well even in the important cases where the symmetric stiffness matrix is not positive definite at all times. Thus we are able to address a wider range of practical situations than other related solvers. We show that our system performs efficiently for a wide range of soft materials.