Variational modelling for integrated optical devices
Groesen, E. (Brenny) van (2003) Variational modelling for integrated optical devices. In: 4th IMACSsymposium on Mathematical Modelling, MATHMOD 2003, February 57, 2003, Vienna, Austria (pp. pp. 7682).

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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 EulerLagrange 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 lowdimensional manifolds of appropriate 'trial'functions, or highdimensional linear subspaces for numerical discretizations. In these notes another type of restriction will be discussed. We describe how typical problems for alloptical 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 apriorily unknown radiation and transmittance, but allow a prescribed influx of light into the structure. 
Item Type:  Conference or Workshop Item 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/45735 
Official URL:  http://wwwhome.math.utwente.nl/~groesenewc/LCN/SeminarMP2002_Optics2.pdf 
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