Preconditioning Schur complement matrices based on an aggregation multigrid method for shell structures

An aggregation multigrid method is utilized in constructing a preconditioner for a Schur complement system of automatically partitioned, non-overlapping subdomains. Preserving the relationship of the partitioned subdomains, we apply a rigid body based aggregation method, which employ geometric data, as a coarsening procedure. And then, we derive a new Schur complement coarse grid matrix by an approach of a condensation after the coarsening procedure. Therefore, we generate a multi-level preconditioner of a Krylov subspace method for Schur complement matrices using the coarse grid matrix. Through numerical experiments, the proposed preconditioner shows efficient performance and robust convergences irrespect of the size of elements and subdomains. It also shows better performance than the preconditioned conjugate gradient method (PCG) for the partitioned system and the aggregation multigrid method for the original domain in shell problems of structural mechanics.