Approximation Methods to Solve Stochastic Problems in Computational Electromagnetics
Chapitre d'ouvrage scientifique
To account for uncertainties on model parameters, the stochastic approach can be used. The model parameters as well as the outputs are then random fields or variables. Several methods are available in the literature to solve stochastic models like sampling methods, perturbation methods or approximation methods. In this paper, we propose an overview on the solution of stochastic problems in computational electromagnetics using approximation methods. Some applications will be presented in order to illustrate the possibilities offered by the approximation methods but also their current limitations due to the curse of dimensionality. Finally, recent numerical techniques proposed in the literature to face the curse of dimensionality are presented for non-intrusive and intrusive approaches.
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Article dans une revue avec comité de lecturePIERQUIN, Antoine; HENNERON, Thomas; CLENET, Stéphane; BRISSET, Stephane (Wydawnictwo Czasopism i Ksia̜żek Technicznych Sigma, 2015)The modelling of a multirate system -composed of components with heterogeneous time constants- can be done using fixed-point method. This method allows a time-discretization of each subsystem with respect to its own time ...
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