Improvement in Computation Time of the Finite Multipole Method by Using K-Means Clustering

Acceleration of the Multi-Level Fast Multipole Algorithm Using K-Means Clustering

“…The ratio of |D| to |d| is increased by using the K-means clustering compared with the regular cube grouping [17]. Figure 2 compares the clustering methods of basis functions in a canonical sphere computer-aided design (CAD) model.…”

“…When using the existing octree clustering technique, both FMM and MLFMA The key advantage that can be obtained when the K-means clustering is applied to the MLFMA is the reduction in the transfer function pre-calculation time. As shown in Figure 5, we pointed out the limitation of the rapid increase in pre-processing time in the FMM [17]. However, the MLFMA efficiently reduces the transfer function calculations by using a tree hierarchy, as shown in Figure 6.…”

“…In this paper, we propose the MLFMA using K-means clustering to accelerate the scattering analysis of large complex targets. In particular, compared to the method presented by the authors in the past [17], the effectiveness of the proposed method is further increased. As a result of the K-means clustering, the locations of the cluster centroids are not regular.…”

“…Various reports have been published on the acceleration of the MLFMA for electrically large scattering problems. The preconditioner is primarily used to mitigate the condition number of the impedance matrix to improve the convergence rate in the iterative solver [4,8,[13][14][15][16][17]. The diagonal preconditioner and MN preconditioner enhance the convergence rate of the electric field integral equation (EFIE) case [13,14].…”

“…The K-means clustering is applied to partition parallel hierarchical N-body interactions in the N-body simulation that can approximate the direct summation [16]. Recently, we proposed applying K-means clustering to the FMM to improve the computation time of scattering analysis [17]. By replacing the conventional cube grouping with K-means clustering [18], the addition theorem is more accurately approximated.…”