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<p>This paper presents a residual-driven Chebyshev-accelerated Jacobi solver for block Neo-Hookean extended position-based dynamics. Neo-Hookean constraints solved with Jacobi iteration are attractive for parallel simulation, but they often show weak sensitivity to stiffness parameters and visually soft behavior under high stiffness. We address this limitation by combining invariant-based block Neo-Hookean formulation with Chebyshev semi-iteration. The hydrostatic and deviatoric constraints are solved as an element-wise block system, and an effective spectral radius estimate for Chebyshev acceleration is updated online from block residuals. The resulting Chebyshev parameters adapt to residual behavior, reducing manual tuning and suppressing oscillations near rest. Across benchmark models, our method reaches same-order aggregate constraint errors as Gauss–Seidel block solvers while achieving a 5<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>–9<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> speedup in real-time settings. It also provides controllable stiffness responses over a wide range of Young’s moduli. We further validate the method in a Unity3D SMPL-X human body interaction scene, where it visually maintains more consistent volume and mitigates hand and foot jitter compared with the small steps scheme using Neo-Hookean constraints. These results indicate that residual-driven Chebyshev acceleration is a practical parallel solver strategy for stable real-time deformable simulation.</p>

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Residual-driven Chebyshev acceleration for Jacobi Neo-Hookean XPBD solver

  • 期刊论文

  • 发表日期：

    2026年6月28日

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  • Xu Wang,
  • Jian Liu,
  • Soichi Murakami,
  • Takashi Shimoe,
  • Taku Senoo,
  • Hiroaki Date,
  • Toshiaki Shichinohe,
  • Takashige Abe,
  • Satoshi Kanai,
  • Atsushi Konno

摘要

This paper presents a residual-driven Chebyshev-accelerated Jacobi solver for block Neo-Hookean extended position-based dynamics. Neo-Hookean constraints solved with Jacobi iteration are attractive for parallel simulation, but they often show weak sensitivity to stiffness parameters and visually soft behavior under high stiffness. We address this limitation by combining invariant-based block Neo-Hookean formulation with Chebyshev semi-iteration. The hydrostatic and deviatoric constraints are solved as an element-wise block system, and an effective spectral radius estimate for Chebyshev acceleration is updated online from block residuals. The resulting Chebyshev parameters adapt to residual behavior, reducing manual tuning and suppressing oscillations near rest. Across benchmark models, our method reaches same-order aggregate constraint errors as Gauss–Seidel block solvers while achieving a 5 \(\times \) × –9 \(\times \) × speedup in real-time settings. It also provides controllable stiffness responses over a wide range of Young’s moduli. We further validate the method in a Unity3D SMPL-X human body interaction scene, where it visually maintains more consistent volume and mitigates hand and foot jitter compared with the small steps scheme using Neo-Hookean constraints. These results indicate that residual-driven Chebyshev acceleration is a practical parallel solver strategy for stable real-time deformable simulation.