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A Mixed-Integer PDE-Constrained Optimization Formulation for Electromagnetic Cloaking

Ryan Vogt(rvogt2***at***ncsu.edu)
Sven Leyffer(leyffer***at***anl.gov)
Todd Munson(tmunson***at***mcs.anl.gov)

Abstract: 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.

Keywords: PDE-constrained optimization, mixed-integer nonlinear optimization, Helmholtz equation, electromagnetic cloaking

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 3: Integer Programming ((Mixed) Integer Nonlinear Programming )

Citation: Argonne MCS Preprint ANL/MCS-P9277-0120

Download: [PDF]

Entry Submitted: 01/29/2020
Entry Accepted: 02/01/2020
Entry Last Modified: 01/29/2020

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