Momentum-preserving inversion alleviation for elastic material simulation

This paper proposes a novel method that enhances the optimization-based elastic body solver. The proposed method tackles the element inversion problem, which is prevalent in the prediction-projection approach for numerical simulation of elastic bodies. At the prediction stage, our method alleviates inversions such that the subsequent projection solver can benefit in stability and efficiency. To prevent excessive suppression of predicted inertial motion when alleviating, we introduce a velocity decomposition method and adapt only the non-rigid motion while preserving the rigid motion, that is, linear and angular momenta. Thanks to the respected inertial motion in the prediction stage, our method produces lively motions while keeping the entire simulation more stable. The experiments demonstrate that our alleviation method successfully stabilizes the simulation and improves the efficiency particularly when large deformations hamper the solver.