Pixel-Exact Rendering of Spacetime Finite Element Solutions

Yuan Zhou, Michael Garland, Robert Haber
Center for Process Simulation and Design, University of Illinois at Urbana-Champaign
IEEE Visualization, 2004, p.425-432


   title={Pixel-exact rendering of spacetime finite element solutions},

   author={Zhou, Y. and Garland, M. and Haber, R.},

   booktitle={Visualization, 2004. IEEE},






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Computational simulation of time-varying physical processes is of fundamental importance for many scientific and engineering applications. Most frequently, time-varying simulations are performed over multiple spatial grids at discrete points in time. We investigate a new approach to time-varying simulation: spacetime discontinuous Galerkin finite element methods. The result of this simulation method is a simplicial tessellation of spacetime with per-element polynomial solutions for physical quantities such as strain, stress, and velocity. To provide accurate visualizations of the resulting solutions, we have developed a method for per-pixel evaluation of solution data on the GPU. We demonstrate the importance of per-pixel rendering versus simple linear interpolation for producing high quality visualizations. We also show that our system can accommodate reasonably large datasets – spacetime meshes containing up to 20 million tetrahedra are not uncommon in this domain.
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