Abstract
Poorly-shaped and/or inverted elements negatively affect numerical simulation accuracy and efficiency. Most current approaches consider mesh quality improvement and mesh untangling problems as numerical optimization problems and solve them using nonlinear optimization. However, these optimization-based approaches require users to set and solve complex numerical optimization problems with no guarantee that the output meshes are valid meshes with good element qualities. Therefore, this paper proposes a data-driven approach for simultaneous mesh untangling and smoothing using a Pointer network. The proposed approach generates various triangular meshes and employs a novel sequence generation algorithm to train the Pointer network and predicts competitive approximate solutions using the trained network. The strength of the proposed framework lies in its simplicity to predict the best free vertex candidate, providing high-quality output meshes, since it does not require solving complex numerical optimization for prediction. Experimental results show that the proposed framework successfully eliminates inverted elements on the meshes and improved average and worst element quality up to 85.9% and 97.8%, respectively, compared to current optimization-based methods.
Highlights
Mesh quality significantly affects both solution accuracy and speed for numerical simulations [1]–[3]
We do not tune all hyper-parameters of the Pointer networks (Ptr-Net) model, such as the learning rate, regularization, and batch size, since our goal is to show the possibility of using a data-driven approach for performing simultaneous mesh untangling and smoothing
Average element quality, i.e., the sum of all element quality in the mesh divided by the total number of elements
Summary
Mesh quality significantly affects both solution accuracy and speed for numerical simulations [1]–[3]. Poor-quality mesh elements have large condition numbers of the resulting systems, which negatively affect the accuracy of the numerical solution [1], [3]–[5]. Mesh smoothing is a common method to improve mesh quality by moving the vertices while fixing the mesh topology. One of the simplest and most popular mesh smoothing methods is Laplacian smoothing, which moves the position of a vertex by the average of its neighborhood positions [6], [7]. Laplacian smoothing can produce inverted elements for non-convex polygons [4], [7], where inverted.
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