A Multilevel Active-Set Preconditioner for Box-Constrained Pressure Poisson Solvers
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Date
2023
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ACM Association for Computing Machinery
Abstract
Efficiently solving large-scale box-constrained convex quadratic programs (QPs) is an important computational challenge in physical simulation.We propose a new multilevel preconditioning scheme based on the active-set method and combine it with modified proportioning with reduced gradient projections (MPRGP) to efficiently solve such QPs arising from pressure Poisson equations with non-negative pressure constraints in fluid animation. Our method employs a purely algebraic multigrid method to ensure the solvability of the coarser level systems and to merge only algebraically-connected components, thereby avoiding performance degradation of the preconditioner. We present a filtering scheme to efficiently apply our multilevel preconditioning only to unconstrained subsystems of the pressure Poisson system while reusing the hierarchy constructed per simulation step. We demonstrate the effectiveness of our method over previous approaches in various examples.
Description
CCS Concepts: Computing methodologies -> Physically-based simulation Fluid simulation, quadratic program, multigrid"
@inproceedings{10.1145:3606939,
booktitle = {Proceedings of the ACM on Computer Graphics and Interactive Techniques},
editor = {Wang, Huamin and Ye, Yuting and Victor Zordan},
title = {{A Multilevel Active-Set Preconditioner for Box-Constrained Pressure Poisson Solvers}},
author = {Takahashi, Tetsuya and Batty, Christopher},
year = {2023},
publisher = {ACM Association for Computing Machinery},
ISSN = {2577-6193},
ISBN = {},
DOI = {10.1145/3606939}
}