### Abstract

Variational modelling is the use of a variational structure of a problem to simplify the model or to find approximations of the solutions in a consistent way. In both cases the consistent use of the variational structure consists in restricting the relevant functionals to smaller sets and consider the Euler-Lagrange equation on the restricted set instead of on the original set. One type of restriction may be to specialise the set of phenomena. To find approximate solutions, parameterized manifolds of functions are used to restrict the functional; either low-dimensional manifolds of appropriate 'trial'-functions, or high-dimensional linear subspaces for numerical discretizations. In these notes another type of restriction will be discussed. We describe how typical problems for all-optical devices in integrated optics have to be considered on unbounded domains. The variational structure is then exploited to confine the problem to a finite domain by restriction to functions that satisfy, or approximate, the equations on the exterior domain. For a typical reflection problem this leads to boundary conditions that are 'transparent' for a-priorily unknown radiation and transmittance, but allow a prescribed influx of light into the structure.

Original language | English |
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Title of host publication | Proceedings 4th IMACS-symposium on Mathematical Modelling |

Place of Publication | Vienna |

Publisher | Vienna University of Technology |

Pages | 76-82 |

ISBN (Print) | 3-91608-24-9 |

Publication status | Published - 5 Feb 2003 |

Event | 4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003 - Vienna University of Technology, Vienna, Austria Duration: 5 Feb 2003 → 7 Feb 2003 Conference number: 4 |

### Publication series

Name | |
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Publisher | TU Vienna |

### Conference

Conference | 4th IMCAS Symposium on Mathematical Modelling, MATHMOD 2003 |
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Abbreviated title | MATHMOD |

Country | Austria |

City | Vienna |

Period | 5/02/03 → 7/02/03 |

### Keywords

- METIS-213145
- IR-45735

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## Cite this

van Groesen, E. W. C. (2003). Variational modelling for integrated optical devices. In

*Proceedings 4th IMACS-symposium on Mathematical Modelling*(pp. 76-82). Vienna: Vienna University of Technology.