  During design optimization, a smooth description of the geometry is
important, especially for problems that are sensitive to the way interfaces are
resolved, e.g., wave propagation or fluid-structure interaction. A levelset
description of the boundary, when combined with an enriched finite element
formulation, offers a smoother description of the design than traditional
density-based methods. However, existing enriched methods have drawbacks,
including ill-conditioning and difficulties in prescribing essential boundary
conditions. In this work we introduce a new enriched topology optimization
methodology that overcomes the aforementioned drawbacks; boundaries are
resolved accurately by means of the Interface-enriched Generalized Finite
Element Method (IGFEM), coupled to a levelset function constructed by radial
basis functions. The enriched method used in this new approach to topology
optimization has the same level of accuracy in the analysis as standard the
finite element method with matching meshes, but without the need for remeshing.
We derive the analytical sensitivities and we discuss the behavior of the
optimization process in detail. We establish that IGFEM-based levelset topology
optimization generates correct topologies for well-known compliance
minimization problems.
