Robust isogeometric Schwarz preconditioners for composite elastic materials

The system of linear elasticity for compressible composite materials is discretized with Isogeometric Analysis and the resulting discrete system is solved iteratively by PCG with an Overlapping Schwarz preconditioner, requiring the solution of local elasticity problems on overlapping subdomains and the solution of a coarse elasticity problem associated with the subdomain coarse mesh. The proposed preconditioner has an optimal convergence rate bound that is scalable in the number of subdomains and is linear in the ratio between subdomain and overlap sizes. This study also shows the preconditioner robustness with respect to the presence of discontinuous elastic coefficients in composite materials and to domain deformation.