Neumann-Neumann methods for vector field problems (Q1568842)

The author introduces and discusses some Schwarz preconditioners for the solution of systems arising from the finite element approximation of some vector field problems (Dirichlet-type boundary value problems). An iterative substructuring method, related to a partition of the original domain into non-overlapping subdomains, is proposed. A hybrid Schwarz preconditioner, called Neumann-Neumann preconditioner, for the Schur complement system corresponding to a variational problem, are built. A logarithmic bound for the condition number of the hybrid Schwarz operator is obtained. Numerical experiments for the hybrid Neumann-Neumann method are presented.