CG-Based Subdomain Local Solver with ICT Factorization Preconditioner for Domain Decomposition Method

Abstract

To analyze large-scale problems by a domain decomposition method (DDM), it is important to accelerate the subdomain local solver. For utilizing cache memory e ff ectively and for saving main memory usage, we employ the preconditioner of incomplete Cholesky factorization with threshold (ICT) optimized for the subdomain local solver of the DDM. Though the ICT preconditioner was originally proposed for ill-conditioned problems, we employ it in this study because it can freely control the number of nonzeros of the preconditioning matrix. By controlling the number of nonzeros, both the coe ffi cient and the preconditioning matrices can fit on the cache memory. By using the cache memory e ff ectively, the computation time of the ICT-based subdomain local solver becomes comparable to that of the direct LDL-based solver. In addition, when the number of degrees of freedom (DOFs) of an analysis model becomes very large, the LDL-based DDM solver su ff ers from overflow of the main memory whereas the ICT-based solver can complete the analysis. Using this solver, we succeeded in analyzing a structural problem of 64 million DOFs in 8 minutes on a parallel computing cluster of 8 nodes. Local Solver, Conjugate Gradient Preconditioners, Incomplete Cholesky Factorization with Threshold