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The objective of this work is to compare topologies resulting from direct BEM (Boundary Element Method) with a BEM accelerated by Fast Multipole Method (FMM). A formulation of fast multipole boundary element (FMBEM) is introduced in order to turn the optimization process more attractive in the point of view of the computational cost. The formulation of the fast multipole 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. A benchmark is investigated by imposing different FMBEM parameters. For effect of comparison the topology resulting from an analytical BEM optimization process is used. The topologies resulting due to this set of parameters imposed are presented. The CPU time x DOF's are also investigated. The accelerated BEM demonstrated good feasibility in an optimization routine.

OPTIMIZATION USING TOPOLOGICAL DERIVATIVE AND BOUNDARY ELEMENT METHOD WITH FAST MULTIPOLE