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On curving high-order hexahedral meshes

Gargallo-Peiro, Abel, Eloi Ruiz-Girones, Xevi Roca,c, Jose Sarrate

24th International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-14 2015


24th International Meshing Roundtable
Austin, TX
October 12-14,2014

Laboratori de Calcul Numeric (LaCaN), Departament de Matematica Aplicada III (MA III), Universitat Politecnica de Catalunya (UPC), Barcelona, Spain.
Computer Applications in Science and Engineering, Barcelona Supercomputing Center, Barcelona, Spain.
Aerospace Computational Design Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA.

We present a new definition of distortion and quality measures for high-order hexahedral (quadrilateral) elements. This definition leads to two direct applications. First, it can be used to check the validity and quality of a high-order hexahedral (quadrilateral) mesh. Second, it allows the generation of high-order curved meshes composed of valid and high-quality hexahedral (quadrilateral) elements. We describe a method to simultaneously smooth and untangle high-order hexahedral (quadrilateral) meshes by minimizing the proposed mesh distortion. Finally, we analyze the behavior of the proposed distortion measure and we present several results to illustrate the benefits of the mesh generation framework.

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