On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study

TL;DR

This paper investigates the use of the virtual element method on polygonal meshes for topology optimization problems, demonstrating its advantages over traditional methods through numerical experiments.

Contribution

It introduces a polygonal VEM approach for topology optimization, addressing mesh-related issues and improving solution accuracy for elasticity and Stokes flow problems.

Findings

Polygonal VEM improves solution quality in topology optimization.

The method handles complex geometries effectively.

Numerical results outperform standard discretization techniques.

Abstract

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the method employed to discretize the underlying differential problem, which may not be able to correctly capture the physics of the problem. In light of the above remarks, in this paper we consider polygonal meshes and employ the virtual element method (VEM) to solve two classes of paradigmatic topology optimization problems, one governed by nearly-incompressible and compressible linear elasticity and the other by Stokes equations. Several numerical results show the virtues of our polygonal VEM based approach with respect to more standard methods.