Constraint interface preconditioning for topology optimization problems

TL;DR

This paper introduces a new interface preconditioning technique for topology optimization problems that combines interior-point methods with a novel domain decomposition approach, significantly improving solution efficiency for large-scale problems.

Contribution

It presents a novel interface preconditioner that accelerates domain decomposition methods, making topology optimization computations more scalable and efficient.

Findings

Performance is independent of problem size.

The method effectively accelerates large-scale linear system solutions.

The approach improves convergence in topology optimization problems.

Abstract

The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size. In this work we propose a methodology which brings together existing fast algorithms, namely, interior-point for the optimization problem and a novel substructuring domain decomposition method for the ensuing large-scale linear systems. The main contribution is the choice of interface preconditioner which allows for the acceleration of the domain decomposition method, leading to performance independent of problem size.