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The paper presents a new method for shape and topology optimization based onan efficient and scalable boundary integral formulation for elasticity. Tooptimize topology, our approach uses iterative extraction of isosurfaces of atopological derivative. The numerical solution of the elasticity boundary valueproblem at every iteration is performed with the boundary element formulationand the kernel-independent fast multipole method. Providing excellent singlenode performance, scalable parallelization and the best available asymptoticcomplexity, our method is among the fastest optimization tools available today.The performance of our approach is studied on few illustrative examples,including the optimization of engineered constructions for the minimumcompliance and the optimization of the microstructure of a metamaterial for thedesired macroscopic tensor of elasticity.

What Lies Beneath the Surface: Topological-Shape Optimization With the Kernel-Independent Fast Multipole Method