Parallel Iterative Solvers for Ill-conditioned Problems with Heterogeneous Material Properties

AbstractThe efficiency and robustness of preconditioned parallel iterative solvers, based on domain decomposition for ill-conditioned problems with heterogeneous material properties, are evaluated in the present work. The preconditioning method is based on the BILUT(p,d,t) method proposed by the author in a previous study, and two types of domain decomposition procedures, LBJ (Localized Block Jacobi) and HID (Hierarchical Interface Decomposition), are considered. The proposed methods are implemented using the Hetero3D code, which is a parallel finite-element benchmark program for solid mechanics problems, and the code provides excellent scalability and robustness on up to 240 nodes (3,840 cores) of the Fujitsu PRIMEHPC FX10 (Oakleaf-FX) at the Information Technology Center, the University of Tokyo. Generally, HID provides better efficiency and robustness than LBJ for a wide range of values of parameters