The Target-Matrix Optimization Paradigm for High-Order Meshes

Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Tomov, Vladimir

doi:10.1137/18M1167206

Title: The Target-Matrix Optimization Paradigm for High-Order Meshes

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Abstract

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].

Authors:

Dobrev, Veselin ^[1]; Knupp, Patrick ^[2];

^[1]; Mittal, Ketan ^[3]; Tomov, Vladimir ^[1]

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

Publication Date:: Tue Jan 29 00:00:00 EST 2019

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1729749

Report Number(s):: LLNL-JRNL-744725
Journal ID: ISSN 1095-7197; 900022

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing (Online)

Additional Journal Information:: Journal Name: SIAM Journal on Scientific Computing (Online); Journal Volume: 41; Journal Issue: no. 1; Journal ID: ISSN 1095-7197

Publisher:: Society for Industrial and Applied Mathematics (SIAM)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; target-matrix optimization paradigm; high-order meshes; high-order finite elements; mesh optimization

Citation Formats


                    Dobrev, Veselin, Knupp, Patrick, Kolev, Tzanio, Mittal, Ketan, and Tomov, Vladimir. The Target-Matrix Optimization Paradigm for High-Order Meshes.  United States: N. p., 2019. 
Web.  doi:10.1137/18M1167206.

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                    Dobrev, Veselin, Knupp, Patrick, Kolev, Tzanio, Mittal, Ketan, & Tomov, Vladimir. The Target-Matrix Optimization Paradigm for High-Order Meshes.  United States.  https://doi.org/10.1137/18M1167206

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                    Dobrev, Veselin, Knupp, Patrick, Kolev, Tzanio, Mittal, Ketan, and Tomov, Vladimir. Tue .  
"The Target-Matrix Optimization Paradigm for High-Order Meshes".  United States.  https://doi.org/10.1137/18M1167206.  https://www.osti.gov/servlets/purl/1729749.

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@article{osti_1729749,

  title        = {The Target-Matrix Optimization Paradigm for High-Order Meshes},

  author       = {Dobrev, Veselin and Knupp, Patrick and Kolev, Tzanio and Mittal, Ketan and Tomov, Vladimir},

  abstractNote = {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].},

  doi          = {10.1137/18M1167206},

  journal      = {SIAM Journal on Scientific Computing (Online)},

  number       = no. 1,

  volume       = 41,

  place        = {United States},

  year         = {Tue Jan 29 00:00:00 EST 2019},

  month        = {Tue Jan 29 00:00:00 EST 2019}

}

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