On Some Versions of the Element Agglomeration AMGe Method

Journal Article · Thu Aug 09 04:00:00 EDT 2007 · Numerical Linear Algebra with Applications, vol. 15, n/a, February 21, 2008, DOI: 10.1002/nla.585

OSTI ID:942043

Lashuk, I; Vassilevski, P

The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate element based AMG method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V-cycle utilizing simple interpolation matrices and nested conjugate gradient (CG) based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 942043
• Report Number(s): UCRL-JRNL-233772
• Journal Information: Numerical Linear Algebra with Applications, vol. 15, n/a, February 21, 2008, DOI: 10.1002/nla.585, Journal Name: Numerical Linear Algebra with Applications, vol. 15, n/a, February 21, 2008, DOI: 10.1002/nla.585 Vol. 15
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
AGGLOMERATION
ALGORITHMS
DEGREES OF FREEDOM
EIGENVALUES
IMPLEMENTATION
INTERPOLATION
MATRICES
TARGETS
TOPOLOGY