We formulate a mixed-integer partial-differential equation constrained optimization problem for designing an electromagnetic cloak governed by the 2D Helmholtz equation with absorbing boundary conditions. Our formulation is an alternative to the topology optimization formulation of electromagnetic cloaking design. We extend the formulation to include uncertainty with respect to the angle of the incidence wave, and we develop a mixed-integer trust-region approach for solving both the deterministic and the uncertain formulation. We present detailed numerical results that show that our trust-region approach obtains effective cloaks.
Argonne MCS Preprint ANL/MCS-P9277-0120