In this paper, we propose and analyze a series of novel algorithms based on projection-free accelerated gradient flows to minimize bending energies for nonlinear plates with non-convex metric constraints. We discuss the stability and constraint consistency in a semi-discrete setting for both bilayer and prestrained plates. Our proposed algorithms demonstrate substantial improvements, in both efficiency and accuracy, over current state-of-the-art methods based on gradient flows.

翻译：本文提出并分析了一系列基于无投影加速梯度流的新型算法，用于最小化具有非凸度量约束的非线性板的弯曲能量。我们在半离散框架下讨论了双层板和预应力板的稳定性与约束一致性。与当前基于梯度流的先进方法相比，所提算法在效率和精度上均实现了显著提升。