A consistent operator splitting algorithm and a two-metric variant: Application to topology optimization

TL;DR

This paper introduces a novel operator splitting algorithm and a two-metric variant for topology optimization, improving convergence and computational efficiency in regularized structural design problems.

Contribution

The work presents a new splitting algorithm tailored for topology optimization and a two-metric variant that reduces computational overhead without sacrificing solution quality.

Findings

Improved convergence characteristics with the proposed algorithm.

The two-metric variant reduces computational overhead.

Numerical results demonstrate effectiveness across various parameters.

Abstract

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant mechanism design), parameterized by means of density functions, whose ill-posendess is addressed by introducing a Tikhonov regularization term. The proposed forward-backward splitting algorithm treats the constituent terms of the cost functional separately which allows suitable approximations of the structural objective. We will show that one such approximation, inspired by the optimality criteria algorithm and reciprocal expansions, improves the convergence characteristics and leads to an update scheme that resembles the well-known heuristic sensitivity filtering method. We also discuss a two-metric variant of the splitting algorithm that removes the computational overhead associated with bound constraints on the density field without compromising convergence and quality of optimal solutions. We present several numerical results and investigate the influence of various algorithmic parameters.