MGPBD: A Multigrid Accelerated Global XPBD Solver
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912382441226240 |
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| author | Li, Chunlei Yu, Peng Liu, Tiantian Yu, Siyuan Xiao, Yuting Li, Shuai Hao, Aimin Gao, Yang Zhao, Qinping |
| author_facet | Li, Chunlei Yu, Peng Liu, Tiantian Yu, Siyuan Xiao, Yuting Li, Shuai Hao, Aimin Gao, Yang Zhao, Qinping |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MGPBD: A Multigrid Accelerated Global XPBD Solver Li, Chunlei Yu, Peng Liu, Tiantian Yu, Siyuan Xiao, Yuting Li, Shuai Hao, Aimin Gao, Yang Zhao, Qinping Graphics I.3.6 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. |
| title | MGPBD: A Multigrid Accelerated Global XPBD Solver |
| topic | Graphics I.3.6 |
| url | https://arxiv.org/abs/2505.13390 |