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Discontinuous Galerkin methods in nanophotonics
Author(s) -
Busch K.,
König M.,
Niegemann J.
Publication year - 2011
Publication title -
laser and photonics reviews
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.778
H-Index - 116
eISSN - 1863-8899
pISSN - 1863-8880
DOI - 10.1002/lpor.201000045
Subject(s) - discontinuous galerkin method , discretization , nanophotonics , galerkin method , finite element method , computer science , domain (mathematical analysis) , physics , mathematics , mathematical analysis , optics , thermodynamics
This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. We describe in detail the underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures. In addition, formulations for both time‐ and frequency‐domain solvers are provided and specific advantages and limitations of the technique are discussed. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems.