A Primal-Dual Box-Constrained QP Pressure Poisson Solver With Topology-Aware Geometry-Inspired Aggregation AMG

Abstract

We propose a new barrier-based box-constrained convex QP solver based on a primal-dual interior point method to efficiently solve large-scale pressure Poisson problems with non-negative pressure constraints, which commonly arise in liquid animation. The performance of prior active-set-based approaches is limited by the need to repeatedly update the active set. Our solver eliminates this issue by entirely avoiding the use of an active set, which in turn makes the inner problems of our Newton iteration process fully unconstrained. For efficiency, exploiting the solution uniqueness of convex QPs and the fact that the pressure constraints are simple box constraints, we aggressively update solution candidates without performing any step selection procedure (such as line search) and instead directly clamp candidates back to the bounds wherever constraint violations occur. Additionally, to accelerate the inner linear solves, we present a topology-aware geometry-inspired aggregation algebraic multigrid preconditioner and describe in detail several key performance optimizations that we incorporate. We demonstrate the efficacy of our solver in various practical scenarios and show that it often surpasses various alternatives in terms of speed and memory usage.