An indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints

Abstract

SUMMARYA new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper. It is an indirect all-quad mesh generation and presented in the following steps: (1) discretizing the constrained lines within the domain; (2) converting the above domain to a triangular mesh together with the line constraints; (3) transforming the generated triangular mesh with line constraints to an all-quad mesh through performing an advancing front algorithm from the line constraints, which enables the construction of quadrilaterals layer by layer, and roughly keeps the feature of the initial triangular mesh; (4) optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes; (5) smoothing the generated mesh toward high-quality all-quad mesh generation. Finally, a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm.

A boundary focused quadrilateral mesh generation algorithm for multi-material structures

“…(3) Quadrilateral mesh optimization: a general pattern named ''Pisces'' is proposed to decrease the number of irregular nodes. It covers most of the specified patterns proposed by authors in Liu et al [27].…”

“…But they still encountered the same difficulty of ''paving''. To overcome this difficulty, Liu et al [27] proposed a robust quadrilateral mesh generation method. Based on the Catmull-Clark subdivision [28], it could automatically generate meshes with high quality elements comparable to the Catmull and Clark [28] approach.…”

Geração De Malha De Elementos Finitos Com Inserção De Restrições a Posteriori

“…Em geral, essa etapaé realizada através de alguma variação da clássica Triangulação de Delaunay (10) (12).…”

“…Um exemplo dessa conversão pode ser observada na Figura 2.5. No método proposto por Liu et al (12), os triângulos são convertidos em quadriláteros utilizando o método proposto por Catmull-Clark. Para contornar os problemas inerentes a essa conversão, os quadriláteros resultantes são combinados utilizando um método baseado em avanço de fronteiras.…”

“…Contudo, de acordo com Liu et al (12), a malha de quadriláterosé mais adequada para uma análise realizada com o método de elementos finitos. Diferente da triangulação, a geração automática de malhas de quadriláteros aindaé umaárea com problemas em aberto, especialmente quando aplicada a domínios complexos (10).…”