Adaptive AMG based on Weighted Matching for Systems of Elliptic PDEs arising from Displacement and Mixed Methods

Adaptive Algebraic Multigrid (or Multilevel) Methods (?AMG)are introduced to improve robustness and efficiency of classical algebraic multigrid methods in dealing with problems where no a-priori knowledge or assumptions on the near null kernel of the underlined Matrix are available. Recently we proposed an adaptive (bootstrap) AMG method, ?AMG, aimed to obtain a composite solver with a desired convergence rate. Each new multigrid component relies on a current (general) smooth vector and exploits pairwise aggregation based on weighted matching in a matrix graph to define a new automatic, general-purpose coarsening process, which we refer to as "the compatible weighted matching". In this work, we present results that broaden the applicability of our method to different finite element discretizations of elliptic PDEs. In particular, we consider systems arising from displacement methods in linear elasticity problems and saddle-point systems that appear in the application of the mixed method to Darcy problems.