Introduction of a Direct Method at Subdomains in Non-linear Magnetostatic Analysis with HDDM

This paper deals with a large-scale 3D non-linear magneto static 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 solution strategy of Finite Element Analysis (FEA) in sub domains is reexamined. Because our employed equation is singular, it has been solved by the iterative method such as the ICCG method. However, by applying the direct method for solving FEA in sub domains, it is expected that the convergence of the interface problem is improved by improvement of precision in sub domains and the computation time is reduced by storing matrices that are results of the LU decomposition on the main memory. Then, to solve FEA in sub domains by the direct method, the A method with the Lagrange multiplier p is considered. As a result, the convergence of the interface problem is much improved by improvement of precision in sub domain-wise analysis. Then, the computation time is reduced by 10 - 20 %. Moreover, a nonlinear magneto static problem with 1.2 billion degrees of freedom is solved in about 4.8 hours on the T2K Open Supercomputer (64 nodes, 1,024 cores).