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Material-adapted refinable basis functions for elasticity simulation

Published: 08 November 2019 Publication History

Abstract

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.

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    cover image ACM Transactions on Graphics
    ACM Transactions on Graphics  Volume 38, Issue 6
    December 2019
    1292 pages
    ISSN:0730-0301
    EISSN:1557-7368
    DOI:10.1145/3355089
    Issue’s Table of Contents
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    Publication History

    Published: 08 November 2019
    Published in TOG Volume 38, Issue 6

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    Author Tags

    1. deformable body simulation
    2. material-adapted basis functions
    3. numerical coarsening
    4. operator-adapted wavelets

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