A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals
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1-s2.0-S2590055219300320-main.pdf
Description
Published version
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1.97 MB
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Adobe PDF
Checksum (MD5)
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Author(s)
Vidal-Codina, Ferran
Saà-Seoane, J.
Nguyen, N.-C.
Peraire, Jaime
Date Issued
March 2019
Journal
Journal of Computational Physics: X
Publisher
Elsevier BV
Citation
Vidal-Codina, F. et al. "A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals." Journal of Computational Physics: X, 2 (March 2019): 100016 © 2019 The Author(s)
Version
Final published version
Abstract
We present a multiscale continuous Galerkin (MSCG) method for the fast and accurate stochastic simulation and optimization of time-harmonic wave propagation through photonic crystals. The MSCG method exploits repeated patterns in the geometry to drastically decrease computational cost and incorporates the following ingredients: (1) a reference domain formulation that allows us to treat geometric variability resulting from manufacturing uncertainties; (2) a reduced basis approximation to solve the parametrized local subproblems; (3) a gradient computation of the objective function; and (4) a model and variance reduction technique that enables the accelerated computation of statistical outputs by exploiting the statistical correlation between the MSCG solution and the reduced basis approximation. The proposed method is thus well suited for both deterministic and stochastic simulations, as well as robust design of photonic crystals. We provide convergence and cost analysis of the MSCG method, as well as a simulation results for a waveguide T-splitter and a Z-bend to illustrate its advantages for stochastic simulation and robust design.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.jcpx.2019.100016
