Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A modification to the usual coarse-grid equations is derived, both in Correction Scheme and in Full Approximation Scheme. With this modification, the algorithm exhibits the usual multigrid efficiency.