Phase field-based topology optimization of metallic structures for microwave applications using adaptive mesh refinement

An important issue in the metallic structure design for microwave applications is the skin depth which may significantly degrade the intended performance. In order to address the skin depth issue, a perfect electric conductor or an impedance boundary condition can be imposed on the outer surface of the metallic structure. However, it is hard to impose such boundary conditions in topology optimization-based design because clear boundary definition with the best performance is difficult in ordinary topology optimization. To overcome such difficulties, this study proposes the phase field-based topological design process of the metallic structure using the adaptive mesh refinement for improved boundary representation. The reaction-diffusion equations combined with the double-well potentials are used as the update scheme. An exponential function using logarithmic interpolation with penalization is used for electrical conductivity definition of gray materials to replace the PEC boundary conditions for the metallic structure with the adaptive mesh refinement. The design process consists of two steps; the first step derives a roughly optimized shape which is used for the initial shape in the next step, where the finally optimized shape is derived using adapted mesh with respect to the material distribution. The validity of the proposed approach is confirmed through three numerical examples.