A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals
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 incorporat...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier BV
2020
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| Online Access: | https://hdl.handle.net/1721.1/126109 |
| _version_ | 1826194026207903744 |
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| author | Vidal-Codina, Ferran Saà-Seoane, J. Nguyen, N.-C. Peraire, Jaime |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Vidal-Codina, Ferran Saà-Seoane, J. Nguyen, N.-C. Peraire, Jaime |
| author_sort | Vidal-Codina, Ferran |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:49:22Z |
| format | Article |
| id | mit-1721.1/126109 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:49:22Z |
| publishDate | 2020 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1261092022-09-26T13:57:44Z A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals Vidal-Codina, Ferran Saà-Seoane, J. Nguyen, N.-C. Peraire, Jaime Massachusetts Institute of Technology. Department of Aeronautics and Astronautics 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. Air Force Office of Scientific Research (Grant FA9550-15-1-0276) 2020-07-08T20:59:50Z 2020-07-08T20:59:50Z 2019-03 2018-11 2019-10-30T17:44:43Z Article http://purl.org/eprint/type/JournalArticle 2590-0552 https://hdl.handle.net/1721.1/126109 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) en http://dx.doi.org/10.1016/j.jcpx.2019.100016 Journal of Computational Physics: X Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV Elsevier |
| spellingShingle | Vidal-Codina, Ferran Saà-Seoane, J. Nguyen, N.-C. Peraire, Jaime A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title | A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title_full | A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title_fullStr | A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title_full_unstemmed | A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title_short | A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals |
| title_sort | multiscale continuous galerkin method for stochastic simulation and robust design of photonic crystals |
| url | https://hdl.handle.net/1721.1/126109 |
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