A general mesh smoothing method for finite elements

• Published in: Finite elements in analysis and design Vol. 158; pp. 17 - 30
• Main Authors: Durand, R., Pantoja-Rosero, B.G., Oliveira, V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2019; Elsevier BV
• Subjects: Algorithms; Deformation analysis; Finite elements; Least-squares fitting; Mesh smoothing; Smoothing; Least-squares fitting; Finite elements; Mesh smoothing
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2019.01.010

This paper presents a general mesh smoothing method for finite elements. The method deals with two and three-dimensional meshes with virtually any type of element. To evaluate the quality of different element types, the paper also introduces a broad quality function. The proposed method works by solving a standard deformation analysis where nodal forces aim to deform each element into an optimally placed reference element. A detailed algorithm of the proposed smoothing method is presented which is suitable for a straightforward computer implementation. Several application examples in two and three-dimensions are presented and analyzed in order to demonstrate the capabilities of the proposed algorithm. In all cases very good quality improvements were obtained with very few iterations. Also, the proposed method provided greater improvements when compared to conventional Laplacian-based methods. •A physics-based mesh smoothing method that uses reference elements and least squares fitting is presented.•The method works in 2D and 3D with virtually any type of finite element including higher order elements.•A broad quality metric definition is presented to deal with meshes with mixed-type elements.•All examples show rapid convergence rate; in fact, in most practical cases just one or two iterations are required.