4.6 Article

THE TARGET-MATRIX OPTIMIZATION PARADIGM FOR HIGH-ORDER MESHES

期刊

SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 41, 期 1, 页码 B50-B68

出版社

SIAM PUBLICATIONS
DOI: 10.1137/18M1167206

关键词

target-matrix optimization paradigm; high-order meshes; high-order finite elements; mesh optimization

资金

  1. U.S. Department of Energy [DE-AC52-07NA27344 (LLNL-JRNL-744725)]

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We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of [P. Knupp, Eng. Comput., 28 (2012), pp. 419-429]. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Lagrangian-Eulerian (ALE) application [BLAST: High-order curvilinear finite elements for shock hydrodynamics, http://www.llnl.gov/CASC/blast] . Our implementation is freely available in an open-source library form [MFEM: Modular parallel finite element methods library, http://mfem.org].

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