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Peter Kaufmann, Sebastian Martin, Mario Botsch, Markus Gross
The discontinuous Galerkin Finite Element Method (DG FEM) is currently a topic of high interest
in the applied mathematics and mechanical engineering communities. The method differs from
standard continuous FEM
in that basis functions are no longer required to be continuous across element boundaries,
allowing for simple and efficient h- and p-refinement.
In this project we extend DG FEM to make it suitable for the simulation of
deformable models in Computer Graphics. In order to perform efficient and stable
simulations of large deformations, we use a linear model and generalize the corotated stiffness warping
approach to DG FEM. We use simple polynomial basis functions in each element and present
a fast and accurate volumetric integration technique for the computation of the stiffness matrix.
Because discontinuities between elements are not desirable in graphics applications,
we show how to reconstruct a smooth deformation field based on moving least squares (MLS) interpolation
which can then be used to embed a high-resolution surface mesh into the coarse and discontinuous
simulation mesh.
Our method supports arbitrary polyhedral convex and non-convex elements and allows
for efficient topological changes without the need for remeshing.
We present examples of element refinement (static and dynamic adaptivity) and progressive cutting.
We also point out that DG FEM can be understood as a generalization
of CG FEM and the PriMo framework (see
Nonlinear Deformation Based on Rigid Cells),
by showing how DG FEM can approximate both methods as limit cases.
- P. Kaufmann, S. Martin, M. Botsch, E. Grinspun, M. Gross, Enrichment Textures for Detailed Cutting of Shells, Proceedings of ACM SIGGRAPH (New Orleans, USA, August 3-7, 2009), ACM Transactions on Graphics, vol. 28, no. 3, pp. 50:1-50:10
[Abstract]
[PDF] [Video]
- P. Kaufmann, S. Martin, M. Botsch, M. Gross, Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM, Journal of Graphical Models, vol. 71, no. 4, 2009, Special Issue of ACM SIGGRAPH / Eurographics Symposium on Computer Animation 2008, pp. 153-167
[Abstract]
[PDF] [Video] [Video]
- P. Kaufmann, S. Martin, M. Botsch, M. Gross, Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM, Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Dublin, Ireland, July 7-9, 2008), pp. 105-115
[Abstract]
[PDF] [Video]
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