Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

• Published in: Advances in engineering software (1992) Vol. 80; pp. 12 - 24
• Main Authors: Ruiz-Gironés, E., Roca, X., Sarrate, J., Montenegro, R., Escobar, J.M.
• Format: Journal Article Publication
• Language: English
• Published: Elsevier Ltd 01.02.2015
• Subjects: ALGORITHM; Algorithms; Anàlisi numèrica; Computational efficiency; CONDITION NUMBER; DECOMPOSITION; ELEMENT MESHES; Elements finits, Mètode dels; GENERATION; Hexahedral mesh; IMPROVEMENT; JACOBIAN MATRIX; Matemàtica aplicada a les ciències; Matemàtiques i estadística; Mesh generation; Mesh smoothing; Mesh untangling; Numerical grid generation (Numerical analysis); Object oriented; Object-oriented framework; Object-oriented programming; OPTIMIZATION; Quadrilaterals; Quality measure; QUALITY METRICS; Robustness; Smoothing; TETRAHEDRAL MESH; Àrees temàtiques de la UPC; Object-oriented framework; Hexahedral mesh; Mesh smoothing; Quality measure; Mesh untangling; Mesh generation
• ISSN: 0965-9978
• DOI: 10.1016/j.advengsoft.2014.09.021

In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and hexahedral meshes. The algorithm iteratively improves a quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a regularized algebraic distortion measure of the elements. We propose several techniques to improve the robustness and the computational efficiency of the optimization algorithm. In addition, we have adopted an object-oriented paradigm to create a common framework to smooth meshes composed by any type of elements, and using different minimization techniques. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when the initial meshes contain a large number of tangled elements.