A new approach for the algebraic multigrid method^*

^*This research was supported by the Natural Sciences and Engineering Research Council of Canada.

Abstract

In this paper, a new approach for the algebraic multigrid (AMG) method is presented. As opposed to the standard AMG method developed by Ruge and Stüben, new algorithms for the interpolation formula, the restriction and the coarse grid operators are presented. The effectiveness of the proposed new AMG algorithm is demonstrated by numerical experiments, in particular, a wider range of applications has been achieved to include some non-diagonally dominant matrices for which the standard AMG method fails to converge.

Keywords:

• Multigrid
• algebraic multigrid
• large sparse matrix computations

C.R Categories:

• G.1.3 Numerical Linear Algebr
• J.2 Physical Sciences and Engineering

^*This research was supported by the Natural Sciences and Engineering Research Council of Canada.

^†Present address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China.

^*This research was supported by the Natural Sciences and Engineering Research Council of Canada.

^†Present address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China.

Notes

^*This research was supported by the Natural Sciences and Engineering Research Council of Canada.

^†Present address: Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China.