Algebraic multigrid based on element interpolation (AMGe) (Q2706453)

Algebraic multigrid (AMG) is a method for solving matrix equations that is based on multigrid concepts, but constructs the coarsening process in an algebraic way that requires no explicit knowledge of the geometry. For any multigrid method the errors that remain after relaxation must be well approximated by the range of interpolation. NEWLINENEWLINENEWLINEThis paper introduces an AMG method for solving partial differential equations discretized by the Ritz finite element method. The new method, called AMGe, assumes access to element stiffness matrices. It is based on the use of two local measures, which are derived from global ones that appear in the actual multigrid theory. These new measures are used to determine local representations of algebraically ``smooth'' error components that provide the basis for constructing effective interpolation and the corresponding coarsening process for AMG. A theoretical foundation for the new AMGe is developed and numerical results showing better convergence rates for it are presented.