CreateReducedBasis¶
This post process creates a reduced basis approximation of a given simulation setup. Currently it is only working for timeharmonic electromagnetic scattering problems.
Introduction
A number of optical applications require simulation of a basic system setup in a large number of different configurations. Examples are scatterometry, where a number of geometrical or material parameters are varied and reconstructed from optical measurements, source mask optimization in lithography, or general optimizations of nano optical systems such as light sources, outcoupling structures, or solar cells.
Such systems have a given setup, which is described by a finite number of variable parameters which are allowed to vary in a given range.
Performing a large number of simulations for fixed parameter set values are often numerically very costly and even prohibit a number of applications. E.g. in scatterometry large libraries are precomputed to enable realtime reconstruction of parameters in a measurement. But even construction of such libraries itself can be prohibitively expensive from a practical point of view.
Basic idea
The reduced basis method is a very efficient technique to simulate parametrized systems for a large number of realizations. The basic idea is a onlineoffline decomposition of the parametrized systems. In the offline phase, the parametrized system is simulated for a number of different configurations. In the online phase these solutions are used to obtain results for arbitrary parameters within specified parameter intervals. The more solutions, so called “snapshots” are computed in the offline phase and included into the reduced basis representation of the system, the more accurate the results of the online phase are. Usually the reduced basis method converges much faster than interpolation techniques, because of a number of reasons. First, the parameter realizations chosen in the offline phase are based on error estimation techniques, which guarantee that a maximum of new information about the parametrized system is included into the basis. Second, in the offline phase all snapshots computed in the offline phase contribute to the solution. In interpolatory methods, often e.g. only nearest neighbours are used to construct an unknown solution of the parameter space.
Bibliography
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