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Material-adapted refinable basis functions for elasticity simulation

Chen, Jiong and Budninskiy, Max and Owhadi, Houman and Bao, Hujun and Huang, Jin and Desbrun, Mathieu (2019) Material-adapted refinable basis functions for elasticity simulation. ACM Transactions on Graphics, 38 (6). Art. No. 161. ISSN 0730-0301.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Owhadi, Houman0000-0002-5677-1600
Desbrun, Mathieu0000-0003-3424-6079
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.
Funding AgencyGrant Number
National Key Research and Development Program of China2017YFB1002703
National Natural Science Foundation of China61522209
Pixar Animation StudiosUNSPECIFIED
Subject Keywords:Numerical coarsening, deformable body simulation, material-adapted basis functions, operator-adapted wavelets
Issue or Number:6
Record Number:CaltechAUTHORS:20191111-134055447
Persistent URL:
Official Citation:Jiong Chen, Max Budninskiy, Houman Owhadi, Hujun Bao, Jin Huang, and Mathieu Desbrun. 2019. Material-adapted Refinable Basis Functions for Elasticity Simulation. ACM Trans. Graph. 38, 6, Article 161 (November 2019), 15 pages.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99780
Deposited By: Tony Diaz
Deposited On:12 Nov 2019 17:35
Last Modified:12 Nov 2019 17:35

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