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Non-Polynomial Galerkin Projection on Deforming Meshes

Matt Stanton, Yu Sheng, Martin Wicke, Federico Perazzi, Amos Yuen, Srinivasa Narasimhan, Adrien Treuille

This paper extends Galerkin projection to a large class of non-polynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.

Non-Polynomial Galerkin Projection on Deforming Meshes

Posted by christopherbatty on April 27th, 2013 Posted in Fluids
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