Augmented Vertex Block Descent

Vertex Block Descent is a fast physics-based simulation method that is unconditionally stable, highly parallelizable, and capable of converging to the implicit Euler solution. We extend it using an augmented Lagrangian formulation to address some of its fundamental limitations. First, we introduce a mechanism to handle hard constraints with infinite stiffness without introducing numerical instabilities. Second, we substantially improve the convergence in the presence of high stiffness ratios. These changes we introduce allow simulating complex contact scenarios involving rigid bodies with stacking and friction, articulated bodies connected with hard constraints, including joints with limited degrees of freedom, and stiff systems interacting with soft bodies. We present evaluations using a parallel GPU implementation that can deliver real-time performance and stable simulations with low iteration counts for millions of objects interacting via collisions, various joint/attachment constraints, and springs of various stiffness. Our results show superior performance, convergence, and stability compared to the state-of-the-art alternatives.