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ACM Transactions on Mathematical Software (TOMS)
ACM SIGGRAPH 2008 papers
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ACM Transactions on Mathematical Software (TOMS)
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ACM SIGGRAPH 2009 papers
Real-time deformation and fracture in a game environment
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
Unified simulation of elastic rods, shells, and solids
ACM SIGGRAPH 2010 papers
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IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Fast simulation of mass-spring systems
ACM Transactions on Graphics (TOG)
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We present warp-canceling corotation, a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation's linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization at each time step. This finite element formulation combines the widely used corotational method with stiffness warping so that changes in the per-element rotations are initially approximated by inexpensive per-node rotations. When the errors of this approximation grow too large, the per-element rotations are selectively corrected by updating parts of the matrix chosen according to locally measured errors. These changes to the system matrix are propagated to its Cholesky factor by incremental updates that are much faster than refactoring the matrix from scratch. A nested dissection ordering of the system matrix gives rise to a hierarchical factorization in which changes to the system matrix cause limited, well-structured changes to the Cholesky factor. We show examples of simulations that demonstrate that the proposed formulation produces results that are visually comparable to those produced by a standard corotational formulation. Because our method requires computing only partial updates of the Cholesky factor, it is substantially faster than full refactorization and outperforms widely used iterative methods such as preconditioned conjugate gradients. Our method supports a controlled trade-off between accuracy and speed, and unlike most iterative methods its performance does not slow for stiffer materials but rather it actually improves.