Deflation preconditioning is one of the preconditioners to accelerate the convergence of iterative method. Deflation preconditioning uses the linearly independent vectors（deflation bases）. In this paper, we propose the deflation preconditioning using incremental singular value decomposition and hierarchical domain decomposition. Incremental singular value decomposition enables adaptive updating of singular vectors in response to the problem’s state. Hierarchical domain decomposition enables independent configuration of the region used for parallel computation and the region where deflation bases are obtained. We incorporate the proposed method into conjugate gradient method and apply the proposed method to nonlinear dynamic structure analysis and evaluate its performance.
SHIMIZU et al. (Wed,) studied this question.