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

This project aims to provide an code framework for efficiently solving the inverse homogenization problems to design microstructure.

dependency

• OpenVDB
• CUDA11
• gflags
• glm
• Eigen3

We have packed dependencies into a conda environment (except CUDA and compilers), you can create it by:

conda env create -f environment.yml

Then you activate it by:

conda activate homo3d

Compilation

After the dependency is installed, the code can be compiled using cmake:

mkdir build
cd build
cmake ..
make -j4

If the conda environment is activated, cmake will automatically checkout the dependencies in this environment.

Usage

command line

• -reso : the resolution of the discretized domain, e.g., -reso 128 defines an $128\times128\times128$ domain. Default value is 128.
• -obj : the objective to be optimized, options are bulk,shear,npr and custom, which optimizes the bulk modulus, shear modulus, Poisson's ratio and custom objective respectively. Default is bulk
• -init: the method for initializing the density field, the common and default option is randc, which set the initialization via a set of trigonometric function basis. You can set this option to manual to set the initialization from a OpenVDB file.
• -sym: symmetry requirement on the structure, only reflect3, reflect6 and rotate3 are supported. Default is reflect6.
• -vol: volume ratio for material usage ranging from $(0,1)$, default is 0.3
• -E: Young's modulus of base material. Default is 1e1 (Recommanded, inappropriate value will cause numerical problem due to poor representation range of Fp16. You can rescale the elastic matrix latter).
• -mu: Poisson's ratio of base material. Default is 0.3
• -prefix: output path suffixed with /
• -in: variable input determined by other options, e.g., a OpenVDB file path when the argument of -init is manual.
• -N: maximal iteration number, default is 300.
• -relthres: the relative residual tolerance on FEM equation, default is 1e-2. (The master branch may not work well with tolerance smaller than 1e-5. Usually, the default value is enough to produce a satisfactory result).

example

optimizing the bulk modulus :

./homo3d -reso 128 -obj bulk -init randc -sym reflect6 -vol 0.3 -mu 0.3

After the optimization finished, the optimized density field is stored in <prefix>/rho in OpenVDB format.

3rd party softwares like Rhino (with grasshopper plugin Dendro) or Blender may be used to extract the solid part.

The optimized elastic matrix is stored in <prefix>/C in binary format, which is an array of 36 float precision numbers.

custom objective

To optimizing custom objective, option -obj custom should be used and add your objective and optimization routine in Framework.cu file, where we have provide few examples：

void example_opti_bulk(cfg::HomoConfig config) {
    // ...
}
void example_opti_npr(cfg::HomoConfig config) {
    // ...
}
void example_yours(cfg::HomoConfig config) {
	// Add your routines here....
}
void runCustom(cfg::HomoConfig config) {
	//example_opti_bulk(config);
	//example_opti_npr(config);
	example_yours(cfg::HomoConfig config); // uncomment this line
}

Version illustration

If you care more about accuracy rather than performance, please checkout the branch mix-fp64 and uses a smaller tolerance on the relative residual of FEM equation:

./homo3d -reso 128 -vol 0.1 -relthres 1e-6 # set tolerence to 1e-6

Other version (branch) such as mix-fp64fp32 uses a mixed precision scheme and requires less memory.

Citation

If you are using this project in your academic research, please include the following citation

@ARTICLE{Zhang2023-ti,
  title    = "An optimized, easy-to-use, open-source {GPU} solver for
              large-scale inverse homogenization problems",
  author   = "Zhang, Di and Zhai, Xiaoya and Liu, Ligang and Fu, Xiao-Ming",
  journal  = "Structural and Multidisciplinary Optimization",
  volume   =  66,
  pages    =  "Article 207",
  month    =  sep,
  year     =  2023
}