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.

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  This paper deals with a large-scale 3D time-harmonic eddy current analysis using the Hierarchical Domain Decomposition Method (HDDM). To improve the convergence of the interface problem of the HDDM and to reduce the computation time, the HDDM is applied to the mixed formulation with the Lagrange multiplier. Because the conventional formulation is singular, it is expected that the characteristic of convergence of the interface problem is made bad. Therefore, in this paper, the mixed formulation of the A method with the Lagrange multiplier that is not singular is considered. As a result, the convergence of the interface problem is much improved, and the time-harmonic eddy current problem with 3.5 billion degrees of freedom is solved in about 9 hours.

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  The Crout variant of ILU preconditioner devised recently has been to have some advan-tages over conventional row-based ILU preconditioner. One of advantages is to be able to adopt a dropping strategy for estimating column norm of inverse U⁻¹. This paper shows how to extend this inverse-based dropping strategy to solve a linear system of equations with symmetric positive definite matrix. Furthermore this paper reveals significant characteristics of inverse-based dropping strategy through numerical experi-ments.

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