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

摘要

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 expamples demonstrating the efficiency of developed multigrid methods are included.