TY - JOUR
T1 - The rapid assessment for three-dimensional potential model of large-scale particle system by a modified multilevel fast multipole algorithm
AU - Li, Junpu
AU - Gu, Yan
AU - Qin, Qing Hua
AU - Zhang, Lan
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/5/1
Y1 - 2021/5/1
N2 - In this study, a modified multilevel fast multipole algorithm is constructed for investigating large-scale particle systems. The algorithm expands the number of levels of the modified dual-level fast multipole algorithm from dual-level grids to multipole levels by a layer-by-layer correction and recursive calculation. The linear equations on coarse grid are recursively solved by a two-level grid. The single sparse matrix having higher filling rate is decomposed into a set of sparse matrices with much lower filling rate. Subsequent theoretical analysis and examples demonstrate that the total storage space of sparse matrices is significantly reduced, yet efficiency of the algorithm is almost unaffected. The fast multipole method is applied to expedite the matrix–vector multiplications. Complexity analysis demonstrates the algorithm has O(N) operation efficiency and storage complexity for three-dimensional potential model. A potential example with 10 million degrees of freedom is accurately computed via a single laptop with 16GB RAM. Finally, the development process of the modified multilevel fast multipole algorithm is briefly overviewed.
AB - In this study, a modified multilevel fast multipole algorithm is constructed for investigating large-scale particle systems. The algorithm expands the number of levels of the modified dual-level fast multipole algorithm from dual-level grids to multipole levels by a layer-by-layer correction and recursive calculation. The linear equations on coarse grid are recursively solved by a two-level grid. The single sparse matrix having higher filling rate is decomposed into a set of sparse matrices with much lower filling rate. Subsequent theoretical analysis and examples demonstrate that the total storage space of sparse matrices is significantly reduced, yet efficiency of the algorithm is almost unaffected. The fast multipole method is applied to expedite the matrix–vector multiplications. Complexity analysis demonstrates the algorithm has O(N) operation efficiency and storage complexity for three-dimensional potential model. A potential example with 10 million degrees of freedom is accurately computed via a single laptop with 16GB RAM. Finally, the development process of the modified multilevel fast multipole algorithm is briefly overviewed.
KW - Fast multipole algorithm
KW - Large-scale potential field
KW - Modified dual-level algorithm
KW - Modified multilevel algorithm
KW - Modified multilevel fast multipole algorithm
UR - http://www.scopus.com/inward/record.url?scp=85102866557&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2021.03.003
DO - 10.1016/j.camwa.2021.03.003
M3 - Article
SN - 0898-1221
VL - 89
SP - 127
EP - 138
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
ER -