Efficient large-scale 3D topology optimization with matrix-free MATLAB code

Abstract

This paper presents an efficient MATLAB framework for large-scale density-based topology optimization and porous infill optimization in 3D. Besides showing comparable computational efficiency with existing MATLAB implementations at equivalent simulation scales, this framework supports significantly larger models with up to 128 million hexahedral simulation elements on a standard PC equipped with 64 GB RAM. Furthermore, it can handle arbitrary non-cuboid design domains and does not require powers-of-two differences in the elements’ spatial resolutions. To achieve this, the technical contribution concentrates on solving the linear system of static finite element method (FEM). A tailored element-based matrix-free computing stencil is demonstrated to circumvent the vast memory consumption in large-scale FEM. Its computational efficiency is assured by fully leveraging the efficient matrix–vector operations and indexing functionalities in MATLAB. We further improve the computational efficiency and memory consumption of the MATLAB-implemented geometric multigrid method with a non-dyadic Galerkin coarsening and a diagonal relaxation scheme.