Martin Drohmann

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We present a new approach to treat nonlinear operators in reduced basis approximations of parametrized evolution equations. Our approach is based on empirical interpolation of nonlinear differential operators and their Frechet derivatives. Efficient offline/online decomposition is obtained for discrete operators that allow an efficient evaluation for a(More)
Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis methods is a suitable means to reduce computational time. In this proceedings, we show the(More)
In this paper we discuss parametrized partial differential equations (P2DEs) for parameters that describe the geometry of the underlying problem. One can think of applications in control theory and optimization which depend on time-consuming parameter-studies of such problems. Therefore, we want to reduce the order of complexity of the numerical simulations(More)
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive ‘error indicators’ to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic)(More)
Many applications, e.g. in control theory and optimization depend on time– consuming parameter studies of parametrized evolution equations. Reduced basis methods are an approach to reduce the computation time of numerical simulations for these problems. The methods have gained popularity for model reduction of different numerical schemes with remarkable(More)
Many applications from science and engineering are based on parametrized evolution equations and depend on time-consuming parameter studies or need to ensure critical constraints on the simulation time. For both settings, model order reduction by the reduced basis approach is a suitable means to reduce computational time. The method is based on a projection(More)
This thesis deals with extensions to the reduced basis method for general non linear parametrized evolution problems. So far necessary assumptions on the underlying non linearities or the a ne separation of parameters and spatial variables are overcome by a generalization of the empirical interpolation method for discrete operators. Next to the development(More)
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