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Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaled Error Estimates

Conference ·

We give an overview of a number of algebraic multigrid methods targeting finite element discretization problems. The focus is on the properties of the constructed hierarchy of coarse spaces that guarantee (two-grid) convergence. In particular, a necessary condition known as 'weak approximation property', and a sufficient one, referred to as 'strong approximation property' are discussed. Their role in proving convergence of the TG method (as iterative method) and also on the approximation properties of the AMG coarse spaces if used as discretization tool is pointed out. Some preliminary numerical results illustrating the latter aspect are also reported.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA
Sponsoring Organization:
USDOE
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
1010832
Report Number(s):
LLNL-PROC-432896
Country of Publication:
United States
Language:
English

References (11)

General Constrained Energy Minimization Interpolation Mappings for AMG journal January 2010
Algebraic Multigrid Based on Element Interpolation (AMGe) journal January 2001
On some versions of the element agglomeration AMGe method journal September 2008
On two-grid convergence estimates
  • Falgout, Robert D.; Vassilevski, Panayot S.; Zikatanov, Ludmil T.
  • Numerical Linear Algebra with Applications, Vol. 12, Issue 5-6 https://doi.org/10.1002/nla.437
journal January 2005
AMG by element agglomeration and constrained energy minimization interpolation journal January 2006
AMGE Based on Element Agglomeration journal January 2001
On an energy minimizing basis for algebraic multigrid methods journal October 2004
Two-grid Method for Linear Elasticity on Unstructured Meshes journal January 1999
Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs journal October 2009
A New Convergence Proof for the Multigrid Method Including the V -Cycle journal October 1983
An Energy-minimizing Interpolation for Robust Multigrid Methods journal January 1999

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Related Subjects

97 MATHEMATICS AND COMPUTING
APPROXIMATIONS
CONVERGENCE
ITERATIVE METHODS