逆手順版ツリー法による三次元直交等間隔格子上低周波磁界分布の数値計算

抄録

In this paper, we undertake the numerical calculation of 50-Hz magnetic fields on three-dimensional orthogonal equidistant grids. The usual calculation method using the Biot-Savart law (BS) is accelerated by the Barnes-Hut tree method executed in reverse order (TMR). This method reduces the computation time from O(MN) to O(MlogN) + O(N), where N is the number of calculation points and M is the number of infinitesimal source current elements. Adopting a tree structure corresponding to the grid structure of calculation points further reduces calculation time. Two parallelization schemes of TMR, TMR1 and TMR2, are implemented to investigate computational performance. The calculation time, accuracy, and required memory capacity were investigated by calculating the field distribution generated by the Helmholtz coil and solenoid-like coil. The speedup of the TMR2 compared to the BS ranged from 2693 to 32391, when N and M were 1400³ and 2×10⁶, respectively. It is concluded that this method is efficient and practical for magnetic-field calculation on three-dimensional orthogonal equidistant grids.