Exponential Rosenbrock-Euler integrators for elastodynamic simulation
Authors
Yu Ju (Edwin) Chen, Uri M. Ascher, Dinesh K. Pai
Code (coming soon)
Abstract
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.
Citation
@article{10.1109/TVCG.2017.2768532,
author = {Chen, Yu Ju and Ascher, Uri M. and Pai, Dinesh K.},
title = {Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation},
year = {2018},
issue_date = {October 2018},
publisher = {IEEE Educational Activities Department},
address = {USA},
volume = {24},
number = {10},
issn = {1077-2626},
url = {https://doi.org/10.1109/TVCG.2017.2768532},
doi = {10.1109/TVCG.2017.2768532},
abstract = {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.},
journal = {IEEE Transactions on Visualization and Computer Graphics},
month = oct,
pages = {2702–2713},
numpages = {12}
}