Analysis of Current Density Inside Human Body Using Geometric Multi-Grid Method

Abstract

This paper describes the effectiveness of a geometric multi-grid (GMG) method in current density analysis using numerical human body models. The scalar potential finite difference (SPFD) method is used as a current analysis method inside a human body in the low-frequency domain, and studies have been conducted to solve faster large-scale linear equations made by the SPFD method. In the previous research, the block incomplete Cholesky conjugate gradients (ICCG) method is proposed as an effective method to solve linear equations faster. However, even though the block ICCG method is applied, many iterations are still needed. Therefore, in this research, the GMG method is considered as an effective solver for the problem. GMG method is developed and evaluated performances comparing with the block ICCG method with multi-color (MC) ordering in terms of computation time and the number of iterations. The results show that the number of iterations needed for GMG method is much smaller than that for the block ICCG and the ICCG with MC ordering. In addition, computation times are much shorter, depending on the number of threads and the number of coarse grids. Also, by using MC ordering, the scalability of the GMG method can be greatly improved.