High scalable non-overlapping domain decomposition method using a direct method for finite element analysis

Abstract

In this paper, a novel domain decomposition method is introduced to solve a large finite element model. In this method, the decomposed domains do not overlap and are connected using a simple connective finite element, which influences the nodal point equilibrium between adjacent finite elements. This approach has the advantage that it allows use of a direct method such as Gauss elimination even in a singular problem. The singular stiffness matrices from the floating domain without the Dirichlet boundary conditions are changed into invertible stiffness matrices by assembling the connective elements. Another advantage is that computational time and storage can be reduced by using a banded matrix in the direct solver. In order to describe this proposed method, we first review the FETI method, which is the most popular domain decomposition method. Then the proposed method is introduced with a technical approach in a distributed computer system. Finally, the high scalability and computational efficiency of the proposed method are verified by comparing with the traditional FETI method for 2D and 3D finite element examples which have floating subdomains. In the result, we demonstrate high scalability for a large finite element model.