Exponential integrators for stiff elastodynamic problems

Dominik Michels*, Gerrit A. Sobottka, Andreas G. Weber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

We investigate the application of exponential integrators to stiff elastodynamic problems governed by second-order differential equations. Classical explicit numerical integration schemes have the shortcoming that the stepsizes are limited by the highest frequency that occurs within the solution spectrum of the governing equations, while implicit methods suffer from an inevitable and mostly uncontrollable artificial viscosity that often leads to a nonphysical behavior. In order to overcome these specific detriments, we devise an appropriate class of exponential integrators that solve the stiff part of the governing equations of motion by employing a closed-form solution. As a consequence, we are able to handle up to three orders of magnitude larger time-steps as with conventional implicit integrators and at the same time achieve a tremendous increase in the overall long-term stability due to a strict energy conservation. The advantageous behavior of our approach is demonstrated on a broad spectrum of complex deformablemodels like fibers, textiles, and solids, including collision response, friction, and damping.

Original languageEnglish (US)
Article numbera7
JournalACM Transactions on Graphics
Volume33
Issue number1
DOIs
StatePublished - Jan 1 2014

Keywords

  • Co-rotational elasticity
  • Collision response
  • Controlled damping
  • Deformable models
  • Energy conservation
  • Exponential integrators
  • Large step sizes
  • Long-term stability
  • Molecular modeling
  • Stiff differential equations
  • Textile simulation

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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