  The paper presents a new method for shape and topology optimization based on
an efficient and scalable boundary integral formulation for elasticity. To
optimize topology, our approach uses iterative extraction of isosurfaces of a
topological derivative. The numerical solution of the elasticity boundary value
problem at every iteration is performed with the boundary element formulation
and the kernel-independent fast multipole method. Providing excellent single
node performance, scalable parallelization and the best available asymptotic
complexity, 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 minimum
compliance and the optimization of the microstructure of a metamaterial for the
desired macroscopic tensor of elasticity.
