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Published November 2019 | public
Journal Article

Material-adapted refinable basis functions for elasticity simulation


In this paper, we introduce a hierarchical construction of material-adapted refinable basis functions and associated wavelets to offer efficient coarse-graining of linear elastic objects. While spectral methods rely on global basis functions to restrict the number of degrees of freedom, our basis functions are locally supported; yet, unlike typical polynomial basis functions, they are adapted to the material inhomogeneity of the elastic object to better capture its physical properties and behavior. In particular, they share spectral approximation properties with eigenfunctions, offering a good compromise between computational complexity and accuracy. Their construction involves only linear algebra and follows a fine-to-coarse approach, leading to a block-diagonalization of the stiffness matrix where each block corresponds to an intermediate scale space of the elastic object. Once this hierarchy has been precomputed, we can simulate an object at runtime on very coarse resolution grids and still capture the correct physical behavior, with orders of magnitude speedup compared to a fine simulation. We show on a variety of heterogeneous materials that our approach outperforms all previous coarse-graining methods for elasticity.

Additional Information

© 2019 Association for Computing Machinery. This work was supported by National Key R&D Program of China (No. 2017YFB1002703), NSFC (No. 61522209). MD acknowledges generous support from Pixar Animation Studios, and early discussion with Rasmus Tamstorf. Finally, we thank Santiago V. Lombeyda for the teaser, Tianyu Wang for generating elastic materials, and Chongyao Zhao for help with rendering.

Additional details

August 19, 2023
October 18, 2023