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Destruction Effects and Sparse Matrix Factorization

Tuesday, November 22, 3:30PM – 5PM
POB 6.304

James F. O'Brien

In this talk I will briefly discuss the use of finite element simulations for generating destruction effects in games and film. With this context as motivation I will then present 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 while avoiding the need for expensive refactorization each time step, and allowing a controlled trade-off between accuracy and speed. 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.

Hosted by Chandrajit Bajaj and Thomas Hughes