Filtering algebraic multigrid and adaptive strategies

Solving linear systems arising from partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. It is shown, how the class of filtering multigrid methods can be integrated into an adaptive, self-correcting framework. Numerical experiments, which are performed for a class of scaled operators, underline the results.