Fast multipole boundary element method using the binary tree structure with tight bounds: application to a calculation of an electrostatic force for the manipulation of a metal micro particle? ?
Boundary element method is one of the most powerful tools to solve partial differential equations. However, it takes a lot of computational time when applied to an actual problem with a large number of unknowns. In this research, the binary tree structure with tight bounds and the downward pass for this structure are adopted for the fast multipole method to reduce the number of M2L translations, thereby further reducing the computational time. Furthermore, the recurrence formulae to calculate the multipole moments of a triangular element are derived. The fast multipole boundary element method using the binary tree structure with tight bounds is developed and the analyses of an electrostatic force acting on a metal micro particle above a complex structure are performed to confirm the effectiveness of this method.
boundary element method tree structure electrostatic force fast multipole method multipole moment micro manipulation micro machine