# A parameterized level set topology optimization strategy using FEniCS and radial basis functions with compact support

## Palavras-chave:

level sets, Topology Optimization, radial basis functions## Resumo

This work addresses level-set based methods for structural topology optimization. Compact support C2-

Wendland radial-based functions are employed to parameterize the level sets. Structures are assumed to be in static

equilibrium, under plane stress state and built with isotropic linear elastic materials, and the classical compliance

minimization problem is considered. Aiming to save the computational effort of the potentially large number of

linear systems to be solved, the computational linear algebra of the resulting sparse interpolation matrix is explored

in contrast with the use of classic multiquadric radial basis functions, with dense matrices in the related systems.

Implementation is made in Python using the FEniCS project for the resolution of the equilibrium system and

the sensitivity analysis, based on a recent work of Laurain, that uses direct numerical resolution of the Hamilton-

Jacobi equation for the level set update. Both strategies are, therefore, compared. Additionally, our approach is

put into perspective with the radial basis function parameterization Matlab code of Wei et al. Numerical results

of experiments with classical benchmark problems are presented.