This paper describes the effectiveness of the geometric multi-grid method in a current density analysis using a numerical human body model. The scalar potential finite difference (SPFD) method is used as a numerical method for analyzing the current density inside a human body due to contact with charged objects in a low-frequency band, and research related to methods to solve faster large-scale simultaneous equations based on the SPFD method has been conducted. In previous research, the block incomplete Cholesky conjugate gradients (ICCG) method is proposed as an effective method to solve the simultaneous equations faster. However, even though the block ICCG method is used, many iterations are still needed. Therefore, in this study, we focus on the geometric multi-grid method as a method to solve the problem. We develop the geometric-multi-grid method and evaluate performances by comparing it with the block ICCG method in terms of computation time and the number of iterations. The results show that the number of iterations needed for the geometric multi-grid method is much less than that for the block ICCG method. In addition, the computation time is much shorter, depending on the number of threads and the number of coarse grids. Also, by using multi-color ordering, the parallel performance of the geometric multi-grid method can be greatly improved.

In this paper we report the convergence acceleration effect of the extended node patch preconditioner for the iterative full-wave electromagnetic finite element method with more than ten million degrees of freedom. The preconditioner, which is categorized into the multiplicative Schwarz scheme, effectively works with conventional numerical iterative matrix solving methods on a parallel computer. We examined the convergence properties of the preconditioner combined with the COCG, COCR and GMRES algorithms for the analysis domain encompassed by absorbing boundary conditions (ABC) such as perfectly matched layers (PML). In those analyses the properties of the convergence are investigated numerically by sweeping frequency range and the number of PMLs. Memory-efficient nature of the preconditioner is numerically confirmed through the experiments and upper bounds of the required memory size are theoretically proved. Finally it is demonstrated that this extended node patch preconditioner with GMRES algorithm works well with the problems up to one hundred million degrees of freedom.

A domain decomposition method is widely utilized for analyzing large-scale electromagnetic problems. The method decomposes the target model into small independent subdomains. An electromagnetic analysis has inherently suffers from late convergence analyzed with iterative algorithms such as Krylov subspace algorithms. The DDM remedies this issue by decomposing the total system into subdomain problems and gathering the local results as an interface problem to adjust to achieve the total solution. In this paper we report the convergence properties of the domain decomposition method while modifying the size of local domain and the region shape on several mesh sizes. As experimental results show, the convergence speed depends on the number of interface problem variables and the selection of the local region shapes. In addition to that the convergence property differs according to the target frequencies. In general it is demonstrated that the convergence speed can be accelerated with large cubic subdomain shape. We propose the subdomain selection strategies based on the analysis of the condition numbers of the governing equation.