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Maintaining Large Time Steps in Explicit Finite Element Simulations using Shape Matching

Basil Fierz, Jonas Spillmann, Iker Aguinaga, Matthias Harders
IEEE Transactions on Visualization and Computer Graphics


We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case a co-rotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.

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  author = {Basil Fierz and Jonas Spillmann and Iker Aguinaga and Matthias Harders},
  title = {Maintaining Large Time Steps in Explicit Finite Element Simulations using Shape Matching},
  journal = {IEEE Transactions on Visualization and Computer Graphics},
  year = {2011},
  month = {},
  pages = {},
  volume = {},
  number = {},
  keywords = {Animation, Physically based modeling, Computational Geometry and Object Modeling, Real time, Computers in Other Systems, Computer Applications, Virtual reality, Three-Dimensional Graphics and Realism, Computer Graphics, Computing Methodologies}