MGPBD: A Multigrid Accelerated Global XPBD Solver

TL;DR

This paper presents a multigrid accelerated solver for XPBD that enhances stability and efficiency in high-resolution, high-stiffness simulations by combining algebraic multigrid techniques with innovative setup strategies.

Contribution

It introduces a novel multigrid method with lazy prolongator updates and simplified near-kernel construction to improve XPBD performance.

Findings

Significantly faster convergence rates.

Enhanced numerical stability in high-resolution simulations.

Reduced computational overhead with lazy setup strategy.

Abstract

We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and high-stiffness simulations. While XPBD excels in simulating deformable objects due to its speed and simplicity, its nonlinear Gauss-Seidel (GS) solver often struggles with low-frequency errors, leading to instability and stalling issues, especially in high-resolution, high-stiffness simulations. Our multigrid approach addresses these issues efficiently by leveraging AMG. To reduce the computational overhead of traditional AMG, where prolongator construction can consume up to two-thirds of the runtime, we propose a lazy setup strategy that reuses prolongators across iterations based on matrix structure and physical significance. Furthermore, we introduce a simplified method for constructing near-kernel components by applying a few sweeps of iterative methods to the homogeneous equation, achieving convergence rates comparable to adaptive smoothed aggregation (adaptive-SA) at a lower computational cost. Experimental results demonstrate that our method significantly improves convergence rates and numerical stability, enabling efficient and stable high-resolution simulations of deformable objects.