2015 年 7 巻 1 号 p. 1-9
In this study, we investigated the convergence of parallel iterative linear solvers in structural finite element analyses with multipoint constraints (MPCs) treated by implicit and explicit master-slave elimination. Iterative linear solvers are indispensable in large-scale analyses due to its superior parallel scalability compared to direct solvers. For stable convergence of iterative linear solvers, it is important not to deteriorate condition of matrices when imposing MPCs. We previously proposed an implicit implementation of master-slave elimination, MPC-CG method, which had a drawback that it is difficult to implement effective preconditioners. In this paper, we compared MPC-CG method and explicit master-slave elimination by estimating condition numbers of preconditioned matrices, and by studying convergence of preconditioned iterative linear solvers. The results showed that the explicit elimination provided better convergence than the MPC-CG method. It was also observed that the overhead for explicit computation of matrix to be solved was small enough with respect to the total solution time. It was concluded that the explicit masterslave elimination is effective when iterative linear solvers are used for large problems with MPCs.
