On the convergence of algebraically defined multigrid methods.
- Fuhrmann, Jürgen
- Multigrid methods, Algebraic multigrid, Schar complement iterative methods, Iterative methods for convection-diffusion equations
Based on the theory for multigrid methods with nonnested spaces and noninherited quadratic forms, a V-cycle convergence proof for an algebraically defined multigrid method using the approximation and smoothing property from the theory of algebraic multigrid is given. The estimation of the approximation property is carried out by means of strengthened Cauchy inequalities. Further, a method is suggested which allows to construct multigrid algorithms for special nonsymmetric problems. The ideas of the paper are illustrated by some examples of multigrid methods for problems with strongly varying coefficients in two- and three-dimensional rectangular domains.