We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the element stiffness matrices, AMGe is based on the use of two local measures, which are derived from global measures that appear in existing multigrid theory. These new measures are used to determine local rep...

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

We apply a recently proposed ([3]) robust overlapping Schwarz method with a certain spectral construction of the coarse space in the setting of element agglomeration algebraic multigrid methods (or agglomeration AMGe) for elliptic problems with high-contrast coefficients. Our goal is to design multilevel iterative methods that converge independent of the contrast in the coefficients. We present...

We provide some extensions to the AMGe method (algebraic multigrid method based on element interpolation), concerning the agglomeration process, the application to non-conforming elements, and the application to the mixed finite element discretization of the Oseen-linearized Navier-Stokes equations. This last point, using AMGe for mixed finite elements, gets straight-forward because of the avai...

We introduce spectral AMGe (ρAMGe), a new algebraic multigrid method for solving systems of algebraic equations that arise in Ritz-type finite element discretizations of partial differential equations. The method requires access to the element stiffness matrices, which enables accurate approximation of algebraically “smooth” vectors (i.e., error components that relaxation cannot effectively eli...

Th e improvement of new genotypes with acceptable yield stability in diff erent environments is an important issue in breeding programs. In order to study genotype × environment (GE) interaction and to determine the most stable durum wheat genotypes, fi eld experiments were conducted with 20 genotypes for three years (20072009). Results showed highly signifi cant GE interaction indicating the p...