We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.

翻译：我们提出顶点块下降法，一种通过顶点级高斯-赛德尔迭代实现隐式欧拉变分形式的块坐标下降法。该方法通过局部顶点位置更新，以最大化并行度降低全局变分能量。由此形成的物理求解器能够在无条件稳定性和卓越计算性能下实现数值收敛。通过简单限制迭代次数，该方法可在保持稳定性和优越收敛速度的同时适应给定计算预算。我们在弹性体动力学背景下对所提方法进行阐述与评估，详细说明所有核心组件，并证明其优于替代技术。此外，我们讨论并展示了该方法如何应用于其他模拟系统（包括基于粒子的模拟和刚体系统）的实例。