Direct-current electric invisibility through topology optimization

Based on the covariance matrix adaptation evolution strategy (CMA-ES), advanced designs of direct-current (DC) electric cloaks composed of bulk isotropic materials are presented through a topology optimization using a level set method. The designed DC electric cloaks succeed in providing DC electric invisibility of an electrical insulator in DC flow; specifically, an electric potential distribution is found that closely reproduces a distribution when no insulator is present. To produce this invisibility, we minimized the difference between distributions for the DC electric cloak and one without insulating obstacles as the objective function. CMA-ES explores optimal sets of level set functions as design variables that minimize the objective function with a perimeter constraint. In the best case in our simulation, the minimized objective function under cloaking reaches 0.00194% of that in the absence of cloaking. Toward multidirectional DC electric cloaks, a topology optimization subject to four-axial structural symmetries is demonstrated.