Balancing domain decomposition method whose coarse grid is defined using local coordinate systems

Abstract

The balancing domain decomposition (BDD) method is an effective preconditioner for the substructuring-based iterative solver, which is a kind of the domain decomposition method. The BDD method is a powerful tool for the large-scale implicit structural analysis using the finite element method. It is a kind of the multi-grid method whose coarse grid is defined by the null spaces in subdomain problems. Shioya et al. proposed a method to construct the null spaces for the structural analysis using the rigid body modes of each subdomain. In the present study, the Shioya's method is improved, that is, the rigid body modes are defined using a local coordinate system of each subdomain instead of using the global coordinate system. In the original method, components with very different values are contained in the prolongation and restriction matrices that are used for making the coarse grid stiffness matrix. The proposed method reduces the difference of the values and improves the property of the coarse-grid stiffness matrix. In the numerical experiments, the proposed method reduces computation time and amount of used memory when the coarse grid problem is solved by a sparse direct solver with the pivoting. In addition, the convergence property of the CG method is improved in some numerical examples.