Reaction-diffusion equation based topology optimization combined with the modified conjugate gradient method

Abstract The reaction-diffusion equation (RDE) based design method is a type of topology optimization methods generally employing the finite element method for physical field analysis. It uses the RDE as the design variable update scheme and its diffusion term contributes to regularize the density field. The drawback of the method is that the diffuse interfacial layer which affects the complexity of the optimization result contains the gray scale area. Moreover, the update scheme of the RDE based optimization method has employed the steepest descent method so far, although its convergence rate becomes slow near the optimum. To overcome such drawbacks, this study proposes a modified conjugate gradient method for the RDE based design method to stabilize the convergence with some numerical restrictions. It also contributes for effective elimination of intermediate materials by supplying the implicit mechanism to change the influence between the reaction and the diffusion term in the RDE. Electromagnetic as well as structural design results are given to confirm the validity of the proposed approach.

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