Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements

Epperly, Ethan N.; Barker, Andrew T.; Falgout, Robert D.

doi:10.2172/1660522

Title: Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements

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Abstract

We investigate smoothers for use in matrix-free algebraic multigrid (AMG) preconditioning of high-order finite element problems. These AMG preconditioners are matrix-free in the sense that they are built from a related low-order refined finite element problem whose system matrix can be much more rapidly assembled than the high-order problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many low-order refined meshes which feature a clustering of nodes near the boundaries between high-order finite elements. For solving the low-order refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.

Authors:

Epperly, Ethan N. ^[1]; Barker, Andrew T. ^[2]; Falgout, Robert D. ^[2]

California Institute of Technology (CalTech), Pasadena, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: 2020-09-04

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1660522

Report Number(s):: LLNL-TR-814531
1023036

DOE Contract Number:: AC52-07NA27344

Resource Type:: Technical Report

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Epperly, Ethan N., Barker, Andrew T., and Falgout, Robert D.. Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements.  United States: N. p., 2020. 
        Web.  doi:10.2172/1660522.

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                    Epperly, Ethan N., Barker, Andrew T., & Falgout, Robert D.. Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements.  United States.  https://doi.org/10.2172/1660522

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                    Epperly, Ethan N., Barker, Andrew T., and Falgout, Robert D.. 2020.  
        "Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements".  United States.  https://doi.org/10.2172/1660522.  https://www.osti.gov/servlets/purl/1660522.

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@article{osti_1660522,

  title        = {Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements},

  author       = {Epperly, Ethan N. and Barker, Andrew T. and Falgout, Robert D.},

  abstractNote = {We investigate smoothers for use in matrix-free algebraic multigrid (AMG) preconditioning of high-order finite element problems. These AMG preconditioners are matrix-free in the sense that they are built from a related low-order refined finite element problem whose system matrix can be much more rapidly assembled than the high-order problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many low-order refined meshes which feature a clustering of nodes near the boundaries between high-order finite elements. For solving the low-order refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.},

  doi          = {10.2172/1660522},

  url          = {https://www.osti.gov/biblio/1660522},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {2020},

  month        = {9}

}

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https://doi.org/10.2172/1660522

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