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Content Provider | ACM Digital Library |
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Author | James, Doug L. Kim, Theodore An, Steven S. |
Abstract | 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 sub-space 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 multi-modal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. |
Starting Page | 1 |
Ending Page | 10 |
Page Count | 10 |
File Format | PDF QT / MOV |
ISBN | 9781450318310 |
DOI | 10.1145/1457515.1409118 |
Language | English |
Publisher | Association for Computing Machinery (ACM) |
Publisher Date | 2008-12-10 |
Publisher Place | New York |
Access Restriction | Subscribed |
Subject Keyword | Quadrature Subspace integration Nonlinear solid mechanics Subspace dynamics Dynamic deformations Real-time simulation Reduced-order modeling Dimensional model reduction |
Content Type | Video Text |
Resource Type | Article |
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