Ministerio de Educación, Cultura y Deporte MINECO; FEDE

Brovka, Marina

Escobar, José María

López González, José Iván

Montenegro Armas, Rafael

Socorro-Marrero, Guillermo Valentín

English

Gestion del Repositorio Documental de la Universidad de Salamanca

ECCOMAS Congress 2016Analysis of several objective functions for optimization of hexahedral meshesJosé Iván López González1*, Marina Brovka1, José María Escobar Sánchez1, Rafael MontenegroArmas1, Guillermo Valentín Socorro Marrero11University Institute for Intelligent Systems and Numerical Applications in Engineering, SIANIUniversity of Las Palmas de Gran CanariaCampus Universitario de Tafira, Spain{jilopez,mbrovka,jmescobar,rmontenegro,gvsocorro}@siani.es ABSTRACTFor many simulation processes, hexahedral meshes present several numerical advantages over tetrahedralones. For example, in Finite Element Method simulations, hexahedral meshes are best suited to solveelastic, structural or fluid mechanics problems.The quality of the mesh has high repercussion on the numerical behaviour of FEM. In some cases, meshgenerators construct poor quality meshes or, even worse, with inverted elements. Indeed, a good qualitymesh could degenerate into a mesh with inverted or not valid elements when the simulation requires nodemovement. For this reason, it is of the major importance to apply a mesh optimization algorithm to untanglethe inverted elements and increase the quality of the mesh.A widely used technique for optimizing a mesh consists on an iterative process in which each node ismoved to a new position in order to improve the quality of the local mesh, that is, the set of elementsconnected to the free node. This new position of the node is determined by minimizing certain objectivefunction based on the distortion of the elements of the local mesh.In 2D, the optimization of a quadrilateral mesh is carried out by decomposing each element in fourtriangles. The nondegeneracy of these triangles is a necessary and sufficient condition for the validity of aquadrilateral element. Nevertheless, it is not known a set of necessary and sufficient conditions based ontetrahedra that guarantees the validity of a hexahedron. For example, the conditions proposed in [1, 2] aresufficient but not necessary conditions.In this work we analyze the ability of several objective functions to untangle and smooth hexahedralmeshes. The construction of the objective functions is addressed from different perspectives. In one hand,we form the objective function through the decomposition of the hexahedral elements into tetrahedra [1, 3,4]. On the other hand, the objective function is built up from shape distortion measures derived from the tri-linear mapping between the reference and physical hexahedron [5].Although, in general, the analyzed objective functions are able to optimize a not extremely distorted mesh,some of them do not work properly in complicated situations. We have designed two experiments to test thecapabilities of the objective functions to achieve valid meshes. References[1] O. V. Ushakova, Nondegeneracy tests for hexahedral cells, Computer Methods in Applied Mechanicsand Engineering 200 (17-20) (2011) 1649–1658[2] P. Knabner, S. Korotov, G. Summ, Conditions for the invertibility of the isoparametric mapping forhexahedral finite elements, Finite Elements in Analysis and Design 40 (2003) 159–172[3] P. M. Knupp, A method for hexahedral mesh shape optimization, International Journal for NumericalMethods in Engineering 58 (2) (2003) 319–332[4] T.J. Wilson, J. Sarrate, X. Roca, R. Montenegro, J.M. Escobar, Untangling and smoothing ofquadrilateral and hexahedral meshes, in: Proceedings of the Eighth International Conference on EngineeringComputational Technology, 2012[5] A. Gargallo-Peiró, Generation of curved meshes for high-order unstructured methods, Ph.D. thesis,Universitat Politècnica de Catalunya (2014)  Powered by TCPDF (www.tcpdf.org)                               1 / 1

Analysis of several objective functions for optimization of hexahedral meshes

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Analysis of several objective functions for optimization of hexahedral meshes

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Gestion del Repositorio Documental de la Universidad de Salamanca