Numerical solution of the elastic body-plate problem by nonoverlapping domain decomposition type techniques

The purpose of this paper is to provide two numerical methods for solving the elastic body-plate problem by nonoverlapping domain decomposition type techniques, based on the discretization method by Wang. The first one is similar to an older method, but here the corresponding Schur complement matrix is preconditioned by a specific preconditioner associated with the plate problem. The second one is a “displacement-force” type Schwarz alternating method. At each iteration step of the two methods, either a pure body or a pure plate problem needs to be solved. It is shown that both methods have a convergence rate independent of the size of the finite element mesh.