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Reduced basis method for Maxwell's equations with resonance phenomena

Please always quote using this URN: urn:nbn:de:0297-zib-55687
  • Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field.

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Author:Martin Hammerschmidt, Sven Herrmann, Jan Pomplun, Lin Zschiedrich, Sven BurgerORCiD, Frank Schmidt
Document Type:ZIB-Report
Parent Title (English):Proc. SPIE
Volume:9630
First Page:96300R
Tag:finite element method; maxwell equation; nano-photonics; photonic crystal; reduced basis method
MSC-Classification:65-XX NUMERICAL ANALYSIS
78-XX OPTICS, ELECTROMAGNETIC THEORY (For quantum optics, see 81V80)
PACS-Classification:40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS
Publishing Institution:Zuse Institute Berlin (ZIB)
Date of first Publication:2015/08/10
Series (Serial Number):ZIB-Report (15-37)
ISSN:1438-0064
Published in:Proc. SPIE 9630, 96300R (2015)
DOI:https://doi.org/10.1117/12.2190425
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