The Target-Matrix Optimization Paradigm for High-Order Meshes

Journal Article · 29 January 2019 · SIAM Journal on Scientific Computing (Online)

DOI: https://doi.org/10.1137/18M1167206 · OSTI ID:1729749

Dobrev, Veselin ^[1]; Knupp, Patrick ^[2]; Kolev, Tzanio  ^[1]; Mittal, Ketan ^[3]; Tomov, Vladimir ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2. Dihedral LLC, Bozeman, MT (United States)
3. Univ. of Illinois at Urbana-Champaign, IL (United States)

Here, 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].

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1729749
• Report Number(s): LLNL-JRNL--744725; 900022
• Journal Information: SIAM Journal on Scientific Computing (Online), Journal Name: SIAM Journal on Scientific Computing (Online) Journal Issue: no. 1 Vol. 41; ISSN 1095-7197
• Publisher: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
• Country of Publication: United States
• Language: English