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

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:
 [1];  [2];  [2]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. 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):
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.
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
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.
@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}
}