Restarted Anderson Acceleration with Monotonicity Control and L₁-norm Minimization for Projective Dynamics

In physical simulation, improving the efficiency and accuracy of real-time simulation of elastic deformable objects becomes paramountly significant. Projective dynamics (PD), as a foundamental method for real-time simulation, holds great necessity in acceleration implementation, such as using Anderson acceleration (AA). However, introducing AA into PD has certain limitations, including insufficient convergence rates or numerical stagnation. To tackle these challenges, we propose the restarted Anderson acceleration with monotonicity control and L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm minimization for projective dynamics (RAM-L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>) to improve the algorithm’s robustness and global convergence speed, as well as surmount the high computational costs and numerical stagnation. Experiments on triangular and tetrahedral meshes show that the RAM-L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> provides a more efficient and accurate real-time simulation algorithm from both physical and numerical perspectives, proposing a potential framework for designing fast algorithms in physical simulation.