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Defining Quality Measures for Validation and Generation of High-Order Tetrahedral Meshes

Gargallo-Peiro, Abel, Xevi Roca, Jaime Peraire, and Josep Sarrate

22nd International Meshing Roundtable, Springer-Verlag, pp.109-126, October 13-16 2013

IMR
PROCEEDINGS

22nd International Meshing Roundtable
Orlando, FL
October 13-16,2013

Laboratori de Calcul Numeric (LaCaN), Universitat Politecnica de Catalunya, Barcelona 08034, Spain
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Email: {abel.gargallo,jose.sarrate}@upc.edu, {xeviroca,peraire}@mit.edu

Summary
A procedure to quantify the distortion (quality) of a high-order mesh composed by curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed by valid and high-quality high-order tetrahedral elements. To this end, we describe a method to simultaneously smooth and untangle high-order tetrahedral meshes by minimizing the proposed mesh distortion. Finally, we present several results to illustrate the two main applications of the proposed technique.

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