We have recently presented modified version of the smoothed aggregation
multigrid suitable for application on problems featuring large variation of
coefficients. For the modified version, we have been able to prove convergence
independent of the size of the coefficient jump under certain assumptions
on the jump distribution.
However, numerical experiments suggest that our assumptions may be too restrictive and one may expect good convergence rates even in situations where our assumptions do not hold. In this talk, we present an extension of the convergence theory to certain configurations excluded by our theory to date.