Investigation of Convergence of Linear Solvers in Electromagnetic Finite Element Analysis with Electric Circuit

A fast linear solver for electromagnetic finite element analysis with electric circuit using a deflation technique with Proper Orthogonal Decomposition (POD) is discussed. The authors have presented a deflated Preconditioned Conjugate Gradient (PCG) method that can reduce the cost of finite element analysis. The deflation technique decomposes the solution into fast and slowly converging components. The slow components can be solved by direct methods with low computational cost due to small dimensions. Therefore, the deflated PCC method can improve the convergence of PCG. However, the deflated PCG requires to find the slow components. In this study, a POD method with snapshots is introduced. Orthogonal vectors for the deflation are constructed from the snapshots. In contrast with well-known model order reduction with POD, the present method has same accuracy of solution as the PCG method. The authors have shown the present method in magnetostatic problem. In this study, the present method is applied to the electromagnetic finite element analysis with electric circuit. Moreover, the performance of the present method is compared with a subspace correction method. The numerical results show that the present method has good convergence in comparison with the conventional PCG method.