: Left: Real-time simulation of 105 deformable solids consisting of 356k tetrahedral elements (without collision handling). Right: Large scene with 320 solids consisting of 1.42 million tetrahedral elements are colliding with each other as they are falling through a funnel after they have been shot through the air. The simulation of the deformation required only 140ms per step on a standard CPU. In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss-Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.
Kugelstadt et al. REF proposed a novel operator splitting method for joint FEM simulation, and the method enables a very efficient simulation of complex scenes with more than a million elements.
Fast Corotated FEM using Operator Splitting
Comput. Graph. Forum
Comput. Graph. Forum
Computer Science