Algebraic multigrid based on computational molecules. 1: Scalar elliptic problems
A positive semidefinite matrix is called an edge matrix if the nonzero entries refer only to variables associated to two nodes. If the given stiffness matrix is an \(L\)-matrix, then it can be decomposed into a sum of edge matrices. Otherwise an approximation by \(L\)-matrices is considered. Once a decomposition is determined, a distinction between strongly and weakly connected variables is natural. In this way, one has a basis for selecting coarse-grid nodes in algebraic multigrid algorithms.
scientific article; zbMATH DE number 5014080