A Domain Decomposition Method Based on Augmented Lagrangian with a Penalty Term in Three Dimensions

Summary

In our earlier work [4], a dual iterative substructuring method for two dimensional problems was proposed, which is a variant of the FETI-DP method. The proposed method imposes continuity on the interface by not only the pointwise matching condition but also uses a penalty term which measures the jump across the interface. For a large penalization parameter, it was proven that the condition number of the resultant dual problem is bounded by a constant independent of both the subdomain size H and the mesh size h. In this paper, we extend the method to three dimensional problems. For this extension, we consider two things; one is the construction of a penalty term in 3D to give the same convergence speed as in 2D and the other is how to treat the ill-conditioning of the subdomain problems due to a large penalization parameter. To resolve these two key issues, we need to be aware of the difference between 2D and 3D in the geometric complexity of the interface.