Higher-Order Time Integration for Deformable Solids

dc.contributor.authorLöschner, Fabianen_US
dc.contributor.authorLongva, Andreasen_US
dc.contributor.authorJeske, Stefanen_US
dc.contributor.authorKugelstadt, Tassiloen_US
dc.contributor.authorBender, Janen_US
dc.contributor.editorBender, Jan and Popa, Tiberiuen_US
dc.date.accessioned2020-10-16T06:25:42Z
dc.date.available2020-10-16T06:25:42Z
dc.date.issued2020
dc.description.abstractVisually 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.en_US
dc.description.number8
dc.description.sectionheadersCloth and Deformable Solids
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume39
dc.identifier.doi10.1111/cgf.14110
dc.identifier.issn1467-8659
dc.identifier.pages157-169
dc.identifier.urihttps://doi.org/10.1111/cgf.14110
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14110
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectComputing methodologies
dc.subjectPhysical simulation
dc.titleHigher-Order Time Integration for Deformable Solidsen_US
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