New Domain Decomposition Algorithm for Nonlinear Substructures

For large-scale finite element analysis, using a numerical method to reduce the problem size is a standard strategy to analyze a problem efficiently. For the analysis with reduction, the most time-consuming process is reducing the degrees of freedom, not solving the global sparse system in the standard analysis. Therefore, improving the efficiency of the reduction process is the key to further speedup the analyses of large-scale problems. Nonlinear analysis is much more computationally intensive than linear elastic analysis. There is a need to investigate a more efficient reduction method for nonlinear problems. This paper presents a new domain decomposition method for nonlinear substructures, which can greatly reduce the analyses time for large-scale nonlinear problems. In the proposed method, the nonlinear behavior of a substructure is updated by adding correcting modes, instead of totally repeating the whole reduction process. The efficiency can be further improved by cooperating with a parallel processing technique. The proposed method was implemented in a parallel object-oriented finite element analysis program, and its performance and accuracy were verified on various examples.