Physics-Based Animation

Stefan Jeschke, Chris Wojtan

This paper presents a method for simulating water surface waves as a displacement field on a 2D domain. Our method relies on Lagrangian particles that carry packets of water wave energy; each packet carries information about an entire group of wave trains, as opposed to only a single wave crest. Our approach is unconditionally stable and can simulate high resolution geometric details. This approach also presents a straightforward interface for artistic control, because it is essentially a particle system with intuitive parameters like wavelength and amplitude. Our implementation parallelizes well and runs in real time for moderately challenging scenarios.

Water Wave Packets

Jieyu Chu, Nafees Bin Zafar, Xubo Yang

We present an algorithmically efficient and parallelized domain decomposition based approach to solving Poisson’s equation on irregular domains. Our technique employs the Schur complement method, which permits a high degree of parallel efficiency on multi-core systems. We create a novel Schur complement preconditioner which achieves faster convergence, and requires less computation time and memory. This domain decomposition method allows us to apply different linear solvers for different regions of the flow. Subdomains with regular boundaries can be solved with an FFT based Fast Poisson Solver. We can solve systems with 10243 degrees of freedom, and demonstrate its use for the pressure projection step of incompressible liquid and gas simulations. The results demonstrate considerable speedup over preconditioned conjugate gradient methods commonly employed to solve such problems, including a multigrid preconditioned conjugate gradient method.

A Schur Complement Preconditioner for Scalable Parallel Fluid Simulation

Zherong Pan and Dinesh Manocha

We present a novel algorithm to control the physically-based animation of smoke. Given a set of keyframe smoke shapes, we compute a dense sequence of control force fields that can drive the smoke shape to match several keyframes at certain time instances. Our approach formulates this control problem as a PDE constrained spacetime optimization and computes locally optimal control forces as the stationary point of the Karush-Kuhn-Tucker conditions. In order to reduce the high complexity of multiple passes of fluid resimulation, we utilize the coherence between consecutive fluid simulation passes and update our solution using a novel spacetime full approximation scheme (STFAS). We demonstrate the benefits of our approach by computing accurate solutions on 2D and 3D benchmarks. In practice, we observe more than an order of magnitude improvement over prior methods.

Efficient Optimal Control of Smoke using Spacetime Multigrid

Alexey Stomakhin, Andrew Selle

We present a novel approach to guiding physically based particle simulations using boundary conditions. Unlike commonly used ad hoc particle techniques for adding and removing the material from a simulation, our approach is principled by utilizing the concept of volumetric flux. Artists are provided with a simple yet powerful primitive called a fluxed animated boundary (FAB), allowing them to specify a control shape and a material flow field. The system takes care of enforcing the corresponding boundary conditions and necessary particle reseeding. We show how FABs can be used artistically or physically. Finally, we demonstrate production examples that show the efficacy of our method.

Fluxed Animated Boundary Method