Coordinate Condensation: Subspace-Accelerated Coordinate Descent for Physics-Based Simulation

Abstract: We introduce Coordinate Condensation, a variant of coordinate descent that accelerates physics-based simulation by augmenting local coordinate updates with a Schur-complement-based subspace correction. Recent work by Lan et al. 2025 (JGS2) uses perturbation subspaces to augment local solves to account for global coupling, but their approach introduces damping that can degrade convergence. We reuse this subspace but solve for local and subspace displacements independently, eliminating this damping. For problems where the subspace adequately captures global coupling, our method achieves near-Newton convergence while retaining the efficiency and parallelism of coordinate descent. Through experiments across varying material stiffnesses and mesh resolutions, we show substantially faster convergence than both standard coordinate descent and JGS2. We also characterize when subspace-based coordinate methods succeed or fail, offering insights for future solver design.