Auxiliary space multigrid based on domain decomposition

Priv.-Doz. Dr. Johannes Kraus

Dec. 17, 2013, 12:45 p.m. S2 059

A non-variational multigrid algorithm for general symmetric positive definite problems is introduced.

This method is based on exact two-by-two block factorization of local (stiffness) matrices that correspond to a sequence of coverings of the domain by overlapping or non-overlapping subdomains. The coarse-grid matrix is defined via additive Schur complement approximation. Its sparsity can be controlled by the size and overlap of the subdomains. The two-level method is analyzed in the framework of auxiliary space preconditioning.

Several applications are addressed, e.g., scalar elliptic problems modeling highly heterogeneous media or locking-free discontinuous Galerkin discretizations of the equations of linear elasticity.