An Algebraic Multigrid Method for a Class of Elliptic Differential Systems

The development, numerical investigation, and analysis of an algebraic multigrid (AMG) method for the numerical solution of a representative class of elliptic differential systems are presented. Our AMG scheme is based on the AMG strategy of Brandt, Ruge, and Stüben. However, the present approach may be implemented within other AMG schemes. By means of numerical experiments with model problems arising from some application areas, it is demonstrated that the computational performance of the proposed AMG scheme is comparable to that of AMG applied to a single scalar equation. An AMG convergence theory is presented that extends convergence results for AMG methods for scalar problems to the case of AMG applied to elliptic systems. Some details of our AMG implementation are given.