NDLI: Optimizing cubature for efficient integration of subspace deformations

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Optimizing cubature for efficient integration of subspace deformations

Content Provider	ACM Digital Library
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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