# Efficient topology optimization using compatibility projection in micromechanical homogenization

@article{Jdicke2021EfficientTO, title={Efficient topology optimization using compatibility projection in micromechanical homogenization}, author={Indre J{\"o}dicke and Richard J. Leute and Till Junge and Lars Pastewka}, journal={ArXiv}, year={2021}, volume={abs/2107.04123} }

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas Fourier-based solvers have recently shown large efficiency gains for homogenization problems. In this paper, we derive the discrete adjoint method for Fourier-based solvers that employ compatibility projection. We demonstrate the method on the optimization…

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