Multigrid and conjugate gradient methods as convergence acceleration techniques

Abstract

Multigrid and conjugate gradient type techniques for the acceleration of iterative methods are discussed.A detailed discussion is given of incomplete factorizations.The theoretical background of the classical conjugate gradient method and preconditioning is briefly reviewed.A conjugate gradient type method for ngn-symmetric-positive-definite systems is presented.Multigrid methods are discussed, and two portable, autonomous computer codes are introduced.Multigrid treatment of convection-diffusion entails special difficulties, and ways to overcome these are outlined.Numerical experiments on a set of test problems are reported.Efficiency and robustness of several conjugate gradient and multigrid methods are compared and discussed.