Shape optimization of waveguide filter

We propose an optimization method for the boundary shape of a waveguide for a high-pass filter that passes electric signals. The waveguide is modeled as a boundary-value problem having the electromagnetic wave equation. The domain variation is chosen as a design variable, while the weighted power consumption on the input port is used as an objective function. Its shape derivative is derived theoretically using the adjoint variable method. To solve the shape-optimization problem, we use an iterative algorithm based on the $H^{1}$ gradient method. The numerical results obtained show the effectiveness of the proposed method.