Planar Delaunay Mesh Smoothing Method Based on Angle and a Deep Q-Network

Abstract

Mesh quality is critical to the accuracy and efficiency of finite element calculations, and mesh smoothing is an essential means of reducing the number of poor elements and improving mesh quality. The deep Q-network-based optimization algorithm for planar Delaunay mesh (unconstrained DQN) has attracted increasing attention due to its advantages in autonomous optimization. However, the unconstrained DQN model does not constrain the movement area of the central node during the training process, and element quality easily falls into a local optimum, resulting in a low generalization of the DQN model. In this paper, an updateable iterative inner polygon is proposed as a constraint to limit the central node’s movement and control the element’s angle. Next, the performance of different neural networks when training the same dataset is analyzed, and the appropriate neural network is selected. After that, the effectiveness and generalization of the method were analyzed. Finally, the results were compared with those obtained by existing methods. The results show that the proposed algorithm can improve the minimum angle of global elements and the shape of poor elements, and the trained DQN model has a high generalization.