期刊
ACM TRANSACTIONS ON GRAPHICS
卷 27, 期 5, 页码 -出版社
ASSOC COMPUTING MACHINERY
DOI: 10.1145/1409060.1409118
关键词
Dimensional model reduction; reduced-order modeling; subspace integration; quadrature; subspace dynamics; dynamic deformations; nonlinear solid mechanics; real-time simulation
资金
- NIBIB NIH HHS [R01 EB006615-04, R01 EB006615-03, R01 EB006615-01A1, R01 EB006615, R01 EB006615-02] Funding Source: Medline
We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r(2)) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St. Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration.
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