Abstract
Mesh quality can affect both the accuracy and efficiency of numerical solutions. This paper first proposes a geometry-based smoothing and untangling method for 2D meshes based on explicit element geometric transformation and element stitching. A new explicit element geometric transformation (EEGT) operation for polygonal elements is firstly presented. The transformation, if applied iteratively to an arbitrary polygon (even inverted), will improve its regularity and quality. Then a well-designed element stitching scheme is introduced, which is achieved by carefully choosing appropriate element weights to average the temporary nodes obtained by the above individual element transformation. Based on the explicit element geometric transformation and element stitching, a new mesh smoothing and untangling approach for 2D meshes is proposed. The proper choice of averaging weights for element stitching ensures that the elements can be transitioned smoothly and uniformly throughout the calculation domain. Numerical results show that the proposed method is able to produce high-quality meshes with no inverted elements for highly tangled meshes. Besides, the inherent regularity and fine-grained parallelism make it suitable for implementation on Graphic Processor Unit (GPU).
Highlights
Mesh quality has great effects on both the accuracy and efficiency of numerical solutions based on the finite element method and the finite volume method [1,2,3]
Local mesh modification and topological transformations methods are valuable in mesh untangling, we focus on mesh smoothing or optimization via node-movement in this paper
The purpose of this paper is to develop a geometry-based mesh untangling and smoothing approach for 2D meshes
Summary
Mesh quality has great effects on both the accuracy and efficiency of numerical solutions based on the finite element method and the finite volume method [1,2,3]. Franks and Knupp proposed two new metrics for simultaneous mesh untangling and smoothing using the target matrix paradigm [21] This method can effectively eliminate inverted elements and do not require that one specify a parameter as in Reference [20]. Escobar et al [24,25] proposed a method incorporating a modified quality metric that ensured higher penalty for inverted elements This method is effective and does not guarantee an untangled output mesh. Kim et al [27] proposed a novel approach for simultaneous mesh untangling and smoothing using a Pointer network This method predicts the approximate solutions for free nodes using a pre-trained network, and there is no need to solve complex numerical optimization problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
