Primal-dual interior-point multigrid method for topology optimization

TL;DR

This paper introduces a primal-dual interior-point method combined with multigrid preconditioning for efficient large-scale topology optimization, demonstrating superior performance over existing methods.

Contribution

It presents a novel interior point approach with multigrid preconditioning for topology optimization, improving scalability and efficiency for large problems.

Findings

Superior performance for large-scale problems

Effective linear system solution with multigrid preconditioning

Outperforms existing optimality condition methods

Abstract

An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared with the so-called optimality condition method, an established technique in topology optimization. This method is also equipped with the multigrid preconditioned conjugate gradient algorithm. We conclude that, for large scale problems, the interior point method with an inexact iterative linear solver is superior to any other variant studied in the paper.