Rovas, D; (2000) An overview of blackbox reduced-basis output bound methods for elliptic partial differential equations. In: Deville, Michel and Owens, Robert, (eds.) Proceedings of 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation - 2000. IMACS: Lausanne, Switzerland.

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Abstract

We present a two-stage off-line/on-line blackbox reduced-basis output bound method for the prediction of outputs of interest of elliptic partial differential equations with affine parameter dependence. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator. The method is both efficient and certain: thanks to rigorous a posteriori error bounds, we may retain only the minimal number of modes necessary to achieve the prescribed accuracy in the output of interest. The technique is particularly appropriate for applications such as design, optimization, and control, in which repeated and rapid evaluation of the output is required. In this paper three versions of this method are presented: (i) for coercive equilibrium problems, (ii) for symmetric eigenvalue problems, and (iii) for non-coercive equilibrium problems.

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