The fast multipole boundary element method performance evaluation for topological optimization procedure

Abstract

The objective of this work is to evaluate the performance of a Boundary Element Method (BEM) accelerated by the Fast Multipole Method (FMM) compared with a direct (BEM) in an optimization topology problem. The formulation of the Fast Multipole Boundary Element Method (FMBEM) is introduced in order to make the optimization process more attractive from the point of view of the computational cost. The fast multipole formulation is briefly summarized. A topological-shape sensitivity approach is used to select the points showing the lowest sensitivities, where material is removed by opening a cavity. As the iterative process evolves, the original domain has holes progressively removed, until a given stop criteria is achieved. For comparison, the topology resulting from a direct BEM optimization process is used. The CPU time x DOF’s is also investigated. The accelerated BEM shows good performance in an optimization routine.