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. Then, we discuss how it can be used for other simulation problems, including particle-based simulations and rigid bodies.

翻译：我们提出了顶点块下降法，这是一种通过顶点级高斯-赛德尔迭代求解隐式欧拉变分形式的块坐标下降解法。该方法通过局部顶点位置更新实现全局变分能量的降低，并具有最大化的并行性。这构成了一种能够实现数值收敛、具备无条件稳定性与卓越计算性能的物理求解器。通过简单地限制迭代次数，该方法可在保持稳定性与优越收敛速率的同时，适应给定的计算预算。我们以弹性体动力学为背景对该方法进行展示与评估，并详述所有核心组件的实现细节。随后，我们探讨其在包括基于粒子的模拟和刚体在内的其他仿真问题中的应用方法。