Exponential integrators for deformable objects using finite elements

Simulating deformable objects is often done with implicit integrator since they can robustly simulate large time steps. However, these integrators introduce significant artificial damping into the simulation. Recently, exponential integrators have attracted attention as an alternative to implicit integrators. They have shown to the potential to achieve large time steps without introducing artificial damping. In this thesis we implement and compare five promising exponential integrator on deformable object simulation tasks. They are the non-linear exponential time integrator (NETI), co-rotational exponential time integrator (CETI), exponential Rosenbrock-Euler (ERE) and two exponential propagation iterative methods of Runge-Kutta type (EPIRK). Additionally, we also propose a new way to compute the exponential-like functions inside ERE and EPIRK integrators. Four of the exponential integrators we present have been used before for deformable object simulation but their performance has not been compared on the same task. In our experiment we compare how well the exponential integrators preserve the energy of the system, how accurate they are, their runtime requirements, how damping effects the integrator and how important internal variables scale with the task. We show that the exponential integrators preserve energy much better than the popular semi-implicit Euler integrator. Of the exponential integrators the ERE integrator is the most stable on our experiments and performs well in terms of accuracy. However, ERE is not as stable as the semi-implicit Euler integrator. Our new computation of the exponential functions in ERE and EPIRK slightly improves their stability but also slightly increases runtime requirements.