An efficient topology optimization method based on adaptive reanalysis with projection reduction

TL;DR

This paper introduces an adaptive topology optimization method that combines auxiliary reduced models and projection reduction to significantly enhance computational efficiency and scalability for large-scale problems.

Contribution

The paper proposes a novel adaptive auxiliary reduced model reanalysis method integrating projection reduction, improving efficiency and scalability in topology optimization.

Findings

Significantly reduces computational time for large-scale problems.

Enables solving problems that exceed memory limits of direct solvers.

Demonstrates effectiveness through numerical examples.

Abstract

Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the combined approximation reduced model (CARM) to reduce the dimension of the model in different aspects. First, the CARM restricts the solution space to avoid large matrix factorization. Second, the PARM is proposed to construct the CARM dynamically to save computational cost. Furthermore, the multi-grid conjugate gradient method is suggested to update PARM adaptively. Finally, several classic numerical examples are tested to show that the proposed method not only significantly improves computational efficiency, but also can solve large-scale problems that are difficult to solve by direct solvers due to the memory limitations.