===firstname:
Tristan
===firstname3:
Delyan
===affil6:

===lastname3:
Kalchev
===email:
tristan.konolige@colorado.edu
===keyword_other2:
Adaptive Multigrid
===lastname6:

===affil5:
CU Boulder
===lastname4:
McCormick
===lastname7:

===affil7:

===postal:
College of Engineering and Applied Science
University of Colorado Boulder
1111 Engineering Drive
ECOT 717, 430 UCB
Boulder, CO 80309-0430 USA
===ABSTRACT:
Smoothed Aggregation (SA) multigrid has proved to be a useful AMG method for solving discretizations of elliptic problems. However, SA requires knowledge of slow to converge near-nullspace vectors in order to achieve good performance. Previous work in adaptively finding near-nullspace vectors relied on heuristics and had trouble when near-nullspace vectors were too similar. Our improved version of Adaptive Smoothed Aggregation (aSA) uses a more principled approach to find near-nullspace vectors. By leveraging the Weak Approximation Property and global and local orthogonalization processes, we ensure that our candidates better match the near-nullspace vectors. We extend this method to find candidates on all multigrid levels. Our technique can be used as a tool to find near-nullspace vectors for developing new multigrid methods or as a stand alone solver for difficult problems.
===affil3:
CU Boulder
===title:
Improved Adaptive Smoothed Aggregation
===affil2:
CU Boulder
===lastname2:
Southworth
===firstname4:
Stephen
===keyword1:
APP_OTHER
===workshop:
no
===lastname:
Konolige
===firstname5:
Thomas
===keyword2:
APP_OTHER
===otherauths:

===affil4:
CU Boulder
===competition:
no
===firstname7:

===firstname6:

===keyword_other1:
Iterative Adaptive Methods
===lastname5:
Manteuffel
===affilother:

===firstname2:
Ben