Smoothers for MatrixFree Algebraic Multigrid Preconditioning of HighOrder Finite Elements
Abstract
We investigate smoothers for use in matrixfree algebraic multigrid (AMG) preconditioning of highorder finite element problems. These AMG preconditioners are matrixfree in the sense that they are built from a related loworder refined finite element problem whose system matrix can be much more rapidly assembled than the highorder problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many loworder refined meshes which feature a clustering of nodes near the boundaries between highorder finite elements. For solving the loworder refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.
 Authors:

 California Institute of Technology (CalTech), Pasadena, CA (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 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):
 LLNLTR814531
1023036
 DOE Contract Number:
 AC5207NA27344
 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 MatrixFree Algebraic Multigrid Preconditioning of HighOrder Finite Elements. United States: N. p., 2020.
Web. doi:10.2172/1660522.
Epperly, Ethan N., Barker, Andrew T., & Falgout, Robert D.. Smoothers for MatrixFree Algebraic Multigrid Preconditioning of HighOrder Finite Elements. United States. https://doi.org/10.2172/1660522
Epperly, Ethan N., Barker, Andrew T., and Falgout, Robert D.. 2020.
"Smoothers for MatrixFree Algebraic Multigrid Preconditioning of HighOrder Finite Elements". United States. https://doi.org/10.2172/1660522. https://www.osti.gov/servlets/purl/1660522.
@article{osti_1660522,
title = {Smoothers for MatrixFree Algebraic Multigrid Preconditioning of HighOrder Finite Elements},
author = {Epperly, Ethan N. and Barker, Andrew T. and Falgout, Robert D.},
abstractNote = {We investigate smoothers for use in matrixfree algebraic multigrid (AMG) preconditioning of highorder finite element problems. These AMG preconditioners are matrixfree in the sense that they are built from a related loworder refined finite element problem whose system matrix can be much more rapidly assembled than the highorder problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many loworder refined meshes which feature a clustering of nodes near the boundaries between highorder finite elements. For solving the loworder 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}
}