Distortion and quality measures for validating and generating high-order tetrahedral meshes

A procedure to quantify the distortion (quality) of a high-order mesh composed of 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 of valid and high-quality high-order tetrahedral elements. To this end, we describe a method to smooth and untangle high-order tetrahedral meshes simultaneously by minimizing the proposed mesh distortion. Moreover, we present a $$p$$p-continuation procedure to improve the initial configuration of a high-order mesh for the optimization process. Finally, we present several results to illustrate the two main applications of the proposed technique.

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