===firstname:
Hongxuan
===firstname3:
Jinchao
===affil6:

===lastname3:
Xu
===email:
huz114@psu.edu
===keyword_other2:
Multigrid
===lastname6:

===affil5:

===lastname4:

===lastname7:

===affil7:

===postal:
109B McAllister Building,
Penn State University,
Unverisity Park, PA, 16802
===ABSTRACT:
In this work, we developed a unified theory for both classical and aggregation based AMG. The coarse space in this theory is defined by the sum of locally low frequency spaces. A theorem is proved that if the AMG restriction operator preserves locally minimum eigenspaces, then the approximation property is satisfied. And by additionally estimating the local Poincar{\'e}  constants, we can get an estimate of the convergence rate of two-level methods. As an application, the two-level uniform convergence of classical AMG and unsmoothed aggregation AMG for finite element discretized Poisson equation on a shape regular mesh is proved using this theory.
===affil3:
Penn State University
===title:
 A unified theory for classical and aggregation based AMG.
===affil2:
Penn State University
===lastname2:
Zikatanov
===firstname4:

===keyword1:
APP_OTHER
===workshop:
no
===lastname:
Zhang
===firstname5:

===keyword2:
APP_OTHER
===otherauths:

===affil4:

===competition:
no
===firstname7:

===firstname6:

===keyword_other1:
AMG
===lastname5:

===affilother:

===firstname2:
Ludmil