Performance analysis of GPU-based parallel solvers for rigid body dynamics

doi:10.11996/JG.j.2095-302X.2025030642

Abstract

Abstract:

Multi-body dynamic simulation involving rigid bodies and constraints plays a critical role in physical simulation and has widespread applications in engineering analysis, virtual reality, and game animation. Traditional rigid-body physics engines primarily rely on CPUs for computation. However, in modern computer graphics and real-time physics simulation, the parallel computing power of GPUs has been demonstrated to significantly enhance performance. This study explored the implementation of five Jacobian-based constraint solvers on the GPU and analyzed their performance and stability. These solvers included the projected Jacobi (PJ) solver, the combined projected Jacobi and nonlinear Jacobi (PJNJ) solver, the projected Jacobi with soft constraints (PJSoft) solver, the substep-based Jacobi (TJ) solver, and the substep-based Jacobi with soft constraints (TJSoft) solver. Benchmark tests revealed that the soft-constraint method provided smoother constraint impulse responses, while employing a substep strategy results in more stable solutions, particularly for high mass ratios and complex scenarios. Overall, this work offered a fresh perspective on evaluating GPU-based constraint solver strategies in multi-body simulations and served as an important reference for real-time physics simulation and interactive computer graphics.

Key words: multi-body dynamic simulation, GPU implementation, Jacobi method, soft constraints, substep, performance and stability analysis

CLC Number:

TP391

LIANG Ruikai, LUO Xukun, GUO Yuzhong, HE Xiaowei. Performance analysis of GPU-based parallel solvers for rigid body dynamics[J]. Journal of Graphics, 2025, 46(3): 642-654.

Figures/Tables 13

Fig. 1 Collision constraint definition

Fig. 2 Solvers algorithm flow

Table 1 Solver evaluation results

算法求解器	步长	数值稳定性	数值精度	性能表现	应用场景
PJ	★★	★★	★★	★★★	性能优先的实时场景
PJSoft	★★	★★★	★★	★★★	性能优先且需要更高稳定性的实时场景
TJ	★★★	★★★★	★★★	★★	高精度大步长的实时场景
TJSoft	★★★	★★★★★	★★★	★★	高精度大步长且需要更高稳定性的实时场景
PJNJ	★★	★★	★★	★	单帧位置误差限度要求较高的场景

Fig. 3 Verification of various joint correctness ((a) Ball-and-socket joint; (b) Hinge joint; (c) Siding joint)

Fig. 4 Crank-rocker multi-joint motion ((a) Rest; (b) Motion)

Fig. 5 Box stack scene ((a) Box stacking scene performance; (b) System energy change before and after solving; (c) Constraint error variation curve)

Fig. 6 Chain and ball scene ((a) Ball and chain scene performance; (b) System energy change before and after solving; (c) Constraint error variation curve)

Fig. 7 Overlap scene ((a) Overlap scene performance; (b) System energy change before and after solving; (c) Constraint error variation curve)

Table 2 Time consumption comparison/ms

算法	场景
算法	Box stack	Ball and chain	Overlap
PJ	7.093 2	7.212 8	6.804 4
PJNJ	54.825 1	53.645 8	45.276 9
PJSoft	7.652 4	7.376 4	6.419 0
TJ	10.338 9	9.641 3	8.920 8
TJSoft	10.503 3	9.326 5	7.833 7

Fig. 8 Single-frame iterative residual change curve

Fig. 9 Time consumption of key step

Fig. 10 Performance of different solvers in complex scenarios—cars crossing suspension bridges ((a) PJ; (b) PJNJ; (c) PJSoft; (d) TJ; (e) TJSoft)

Fig. 11 Performance of different solvers in complex scenarios—windmill rotation impacting stacked blocks ((a) PJ; (b) PJNJ; (c) PJSoft; (d) TJ; (e) TJSoft)

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