GPU optimization of material point methods

The Material Point Method (MPM) has been shown to facilitate effective simulations of physically complex and topologically challenging materials, with a wealth of emerging applications in computational engineering and visual computing. Borne out of the extreme importance of regularity, MPM is given attractive parallelization opportunities on high-performance modern multiprocessors. Parallelization of MPM that fully leverages computing resources presents challenges that require exploring an extensive design-space for favorable data structures and algorithms. Unlike the conceptually simple CPU parallelization, where the coarse partition of tasks can be easily applied, it takes greater effort to reach the GPU hardware saturation due to its many-core SIMT architecture. In this paper we introduce methods for addressing the computational challenges of MPM and extending the capabilities of general simulation systems based on MPM, particularly concentrating on GPU optimization. In addition to our open-source high-performance framework, we also conduct performance analyses and benchmark experiments to compare against alternative design choices which may superficially appear to be reasonable, but can suffer from suboptimal performance in practice. Our explicit and fully implicit GPU MPM solvers are further equipped with a Moving Least Squares MPM heat solver and a novel sand constitutive model to enable fast simulations of a wide range of materials. We demonstrate that more than an order of magnitude performance improvement can be achieved with our GPU solvers. Practical high-resolution examples with up to ten million particles run in less than one minute per frame.