An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

TL;DR

This paper introduces an open-source GPU solver optimized for large-scale inverse homogenization problems, enabling rapid high-resolution microstructure design with minimal code and high computational efficiency.

Contribution

The paper presents a novel GPU-based solver with optimized data structures and algorithms, achieving fast high-resolution microstructure optimization and ease of use.

Findings

Optimizes homogenized stiffness tensors efficiently

Handles 512^3 finite element models in under 40 seconds per iteration

Requires less than 20 lines of code for customization

Abstract

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3=134.2 million finite elements run in less than 40 seconds per iteration with a peak GPU memory of 9 GB on an NVIDIA GeForce GTX 1080Ti GPU. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d.