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-赛德尔迭代求解隐式欧拉法变分形式的块坐标下降方案。该方法通过局部顶点位置更新实现全局变分能量的降低，同时最大化并行计算效率。由此构建的物理求解器能够在无条件稳定性的前提下实现数值收敛，并具备卓越的计算性能。该方法还可通过简单限制迭代次数来适应特定计算预算，同时保持其稳定性与优越的收敛速度。我们在弹性体动力学背景下阐述并评估了本方法，详述了所有核心组件，并证明其性能优于现有技术。此外，我们通过实例探讨了该方法在其他仿真系统中的应用潜力，包括基于粒子的仿真与刚体仿真。