Fakultät Informatik

A Multigrid Framework for Real-Time Simulation of Deformable Bodies

 Joachim Georgii, Rüdiger Westermann

Computer Graphics and Visualization Group, Technische Universität München, Germany


In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and non-linear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates.

The deformation of a tetrahedral horse model is shown. From left to right we show the initial model, the model exhibiting
homogeneous and inhomogeneous stiffness under gravity, and the heterogenous model under external forces. In all images, interal stress is visualized with red color.

Associated publications

  A Multigrid Framework for Real-Time Simulation of Deformable Bodies
J. Georgii, R.Westermann,  Computers & Graphics, Vol. 30, No. 3, 2006 [Bibtex]


Accompanying video of the paper [30 MB AVI]



Matthias Niessner, our new Professor from Stanford University, offers a number of interesting topics for  master theses.


PhD positions on   Computational Fabrication and 3D Printing and  Photorealistic Rendering for Deep Learning and Online Reconstruction are available at the Computer Graphics & Visualization group.