HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-980724-A

  
Model problem analysis

As outlined above we intend to analyse the full multigrid method for defining the basis transformation $B_I$. Due to the very complex matter however we have to restrict the analysis to the full two-grid operator and the model problem 1 instead.

In this section the basic formulae to evaluate $\, \mu =\varrho \, (S_C^{-1} T_C^{\phantom{\!\!\!\!-1}}) \,$ are derived first, followed by the analysis of the full two-grid operator. For the special case where the relaxation parameter is chosen to be $\omega = 1.0$ a proof of the growth of $\mu$ is presented in the remainder of this section.

HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-980724-A