  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.
