, Volume 25, Issue 1-3, pp 287-304

An algebraic multigrid method for finite element systems on criss-cross grids

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Abstract

In this paper, we design and analyze an algebraic multigrid method for a condensed finite element system on criss-cross grids and then provide a convergence analysis. Criss-cross grid finite element systems represent a large class of finite element systems that can be reduced to a smaller system by first eliminating certain degrees of freedoms. The algebraic multigrid method that we construct is analogous to many other algebraic multigrid methods for more complicated problems such as unstructured grids, but, because of the specialty of our problem, we are able to provide a rigorous convergence analysis to our algebraic multigrid method.

Communicated by A. Zhou
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
The work was supported in part by NSAF(10376031) and National Major Key Project for basic researches and by National High-Tech ICF Committee in China.