Building blocks for odd–even multigrid with applications to reduced systems

Building blocks yielding an efficient implementation of the odd–even multigrid method for the Poisson problem in the reference domain (0,1)d, d=2,3, are described. Modifications needed to transform these techniques to solve reduced linear systems representing boundary value problems in arbitrary domains are given. A new way to define enriched coarser subspaces in the multilevel realization is proposed. Numerical examples demonstrating the efficiency of developed multigrid methods are included.