Topology optimization in Bernoulli free boundary problems

In this work we consider the topology optimization of systems governed by the external Bernoulli free boundary problem arising, for example, from the mathematical modelling of electro-chemical machining. In this work we combine, for the first time, the so-called pseudo-solid approach to the solution of governing free boundary problems and the level set method, which is used to define the design domain. Previous studies of the problem showed a tendency towards topological changes in the design, which can now automatically take place thanks to level set parametrization. The scalar function used in the level set method is parametrized using radial basis functions, converting the problem into a parametric optimization problem, which is solved using a gradient-based method.