A stiffly accurate integrator for elastodynamic problems

Dominik L. Michels, Vu Thai Luan, Mayya Tokman

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We present a new integration algorithm for the accurate and efficient solution of stiff elastodynamic problems governed by the second-order ordinary differential equations of structural mechanics. Current methods have the shortcoming that their performance is highly dependent on the numerical stiffness of the underlying system that often leads to unrealistic behavior or a significant loss of efficiency. To overcome these limitations, we present a new integration method which is based on a mathematical reformulation of the underlying differential equations, an exponential treatment of the full nonlinear forcing operator as opposed to more standard partially implicit or exponential approaches, and the utilization of the concept of stiff accuracy which ensures that the efficiency of the simulations is significantly less sensitive to increased stiffness. As a consequence, we are able to tremendously accelerate the simulation of stiff systems compared to established integrators and significantly increase the overall accuracy. The advantageous behavior of this approach is demonstrated on a broad spectrum of complex examples like deformable bodies, textiles, bristles, and human hair. Our easily parallelizable integrator enables more complex and realistic models to be explored in visual computing without compromising efficiency.
Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalACM Transactions on Graphics
Volume36
Issue number4
DOIs
StatePublished - Jul 21 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work has been partially supported by the National Science Foundation of the United States or America (grant 1419105), the King Abdullah University of Science and Technology (KAUST baseline funding), the Max Planck Center for Visual Computing and Communication (MPC-VCC) funded by Stanford University and the Federal Ministry of Education and Research of the Federal Republic of Germany (grants FKZ-01IMC01 and FKZ-01IM10001).

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