Higher‐Order Time Integration for Deformable Solids

Computer Graphics Forum, vol. 39, pp. 157–169

Abstract

Abstract Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first‐order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second‐order methods, their use is not widespread. Many of these well‐known methods have significant drawbacks such as severe numerical damping or scene‐dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first‐order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge‐Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher‐order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor‐corrector approach that leads to consistent behavior with higher‐order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.

Authors 5

1. Fabian Löschner Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Germany

   RWTH Aachen University, Germany

2. Andreas Longva Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Germany

   RWTH Aachen University, Germany

3. Stefan Rhys Jeske Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Germany

   RWTH Aachen University, Germany

4. Tassilo Kugelstadt Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Germany

   RWTH Aachen University, Germany

5. Jan Bender Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University Germany

   RWTH Aachen University, Germany