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Title: αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods

Abstract

Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. In this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.

Authors:
 [1];  [2]
  1. ICAR-CNR, Napoli (Italy)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). CASC
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1144751
Report Number(s):
LLNL-CONF-656131
Journal ID: ISSN 1612--3956
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Conference
Resource Relation:
Journal Volume: 22; Conference: 18. European Conference on Mathematics for Industry, Taormina (Italy), 9-13 Jun 2014
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

Citation Formats

D'Ambra, P., and Vassilevski, P. S. αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods. United States: N. p., 2014. Web. doi:10.1007/978-3-319-23413-7_142.
D'Ambra, P., & Vassilevski, P. S. αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods. United States. https://doi.org/10.1007/978-3-319-23413-7_142
D'Ambra, P., and Vassilevski, P. S. 2014. "αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods". United States. https://doi.org/10.1007/978-3-319-23413-7_142. https://www.osti.gov/servlets/purl/1144751.
@article{osti_1144751,
title = {αAMG based on Weighted Matching for Systems of Elliptic PDEs Arising From Displacement and Mixed Methods},
author = {D'Ambra, P. and Vassilevski, P. S.},
abstractNote = {Adaptive Algebraic Multigrid (or Multilevel) Methods (αAMG) are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near-null kernel of the underlined matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, αAMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as “the compatible weighted matching”. In this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.},
doi = {10.1007/978-3-319-23413-7_142},
url = {https://www.osti.gov/biblio/1144751}, journal = {},
issn = {1612--3956},
number = ,
volume = 22,
place = {United States},
year = {Fri May 30 00:00:00 EDT 2014},
month = {Fri May 30 00:00:00 EDT 2014}
}

Conference:
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