  We propose a method to modify a polygonal mesh in order to fit the
zero-isoline of a level set function by extending a standard body-fitted
strategy to a tessellation with arbitrarily-shaped elements. The novel level
set-fitted approach, in combination with a Discontinuous Galerkin finite
element approximation, provides an ideal setting to model physical problems
characterized by embedded or evolving complex geometries, since it allows
skipping any mesh post-processing in terms of grid quality. The proposed
methodology is firstly assessed on the linear elasticity equation, by verifying
the approximation capability of the level set-fitted approach when dealing with
configurations with heterogeneous material properties. Successively, we combine
the level set-fitted methodology with a minimum compliance topology
optimization technique, in order to deliver optimized layouts exhibiting crisp
boundaries and reliable mechanical performances. An extensive numerical test
campaign confirms the effectiveness of the proposed method.

Computational Engineering, Finance, and Science