Time-Dependent Adjoint Formulation for Metamaterial Optimization using Petrov-Galerkin Methods
Keywords:
Adjoint-based sensitivity analysis, design optimization, finite element method, metamaterial, Petrov-GalerkinAbstract
A time-dependent discrete adjoint algorithm for electromagnetic problems is presented. The governing equations are discretized with a semi-discrete Petrov- Galerkin method. Time advancement is accomplished using an implicit, second-order backward differentiation formula (BDF2). An all-dielectric metamaterial is proposed and gradient-based shape design optimization is conducted. Hicks-Henne functions are utilized for shape parameterization to ensure smooth surfaces, and linear elasticity employed to adapt interior mesh points to boundary modifications. The cost function used in the design optimization attempts to widen the bandwidth of the metamaterial over a desired frequency range. Optimization results demonstrate an increase of the full width at half maximum (FWHM) of reflection from 111 THz to 303 THz.
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References
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