Vertex Block Descent (VBD)

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.

Source Code

An implementation of our vertex block descent (VBD) method is included in Anka He Chen's Gaia simulation engine.

Stability Tests

Our VBD method is unconditionally stable. Here, a deformable teapot simulation is started after randomly placing all its vertices, forming a complex mess, and a deformable armadillo model is completely flattened prior to simulation. In either case, models quickly recover their shapes without any instability issues. These extreme tests showcase the exceptional stability characteristics of VBD.

Paper Video

Project Publications

Anka He Chen, Ziheng Liu, Yin Yang, Cem YukselVertex Block DescentACM Transactions on Graphics (Proceedings of SIGGRAPH 2024), 43, 4, 2024