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：我们提出顶点块下降法，这是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解法。该方法通过局部顶点位置更新，在最大化并行性的同时降低全局变分能量。由此形成的物理求解器能够实现数值收敛，兼具无条件稳定性与卓越的计算性能。通过简单限制迭代次数，该方法可在保持稳定性与优越收敛速率的前提下适应给定的计算预算。我们在弹性体动力学背景下对方法进行展示与评估，详细阐述所有核心组件的技术细节。最后，讨论该方法如何应用于其他仿真问题，包括基于粒子的仿真与刚体动力学。