Robustness of the additive and multiplicative frequency decomposition multi-level method
A multiplicative variant of the frequency decomposition multi-level method (FDMLM) developed earlier by W. Hackbusch is studied. The abstract finite element spaces and their subspaces decomposition that underlies the FDMLM are defined. The additive and multiplicative FDMLM are described as subspace correction methods. Robustness of both the methods applied to second-order symmetric singular perturbation problems is proven. Results of numerical experiments for a two-dimensional anisotropic equation and the Helmholtz equation are presented. They show that the additive FDMLM is superior to standard BPX for these problems. The BPX (Bramble-Pasciak-Xu) preconditioner is a parallel subspace correction method corresponding to the overlapping decomposition with one Jacobi iteration as a smoother.
frequency decomposition multi-level method
scientific article; zbMATH DE number 769257