Reduced basis method and greedy algorithms for non-coercive problems

Abstract:

In applications arising in control, optimization and design, one often needs to compute a given output obtained through the solution of the harmonic Maxwell’s equations for many different parameter configurations. To solve this problem, we propose a discontinuous Galerkin approximation of the underlying equations (called the truth approximation) combined with the reduced basis method (a model order reduction method). The main features of this procedure are: i) rapid convergence on the entire representative parameter set, ii) a rigorous a posteriori error estimator for the reduced basis output with respect to the truth approximation counterpart, iii) under an affine parameter dependence of the operators involved on the PDE (affine assumption), the computations can be divided into a parameter independent off-line phase and a computationally very efficient on-line phase. When this assumption is violated, we replace the non-affine operators by an affine approximation obtained with the empirical interpolation method. This approach will be applied to the radar cross section computation of a scatterer in 2D considering the wave number, the angle of incidence and the angle of measurement as the set of parameters. It allows to considerably reduce the computational cost compared to the truth approximation computations obtaining a similar accuracy.

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Ana M. Alonso Rodriguez