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We consider parametric partial differential equations (PPDEs) with stochastic influences e.g. in terms of random coefficients. Using standard discretizations such as finite elements, this often amounts to high-dimensional problems. In a multi-query context, the PPDE has to be solved for various instances of the deterministic parameter as well as the… (More)
We present a new approach to solve nonlinear parametric partial differential equations (PPDEs) with stochastic coefficients, which is based on the Reduced Basis (RB) method. It is imposed that the problem formulation allows for an affine decomposition in the (deterministic) parameter. The uncertainties in the coefficients are modeled using Karhunen-Lò eve… (More)
We consider parameter dependent spatial stochastic processes in the context of partial differential equations (PDEs) and model order reduction. For a given parameter, a random sample of such a process specifies a sample coefficient function of a PDE, e.g. characteristics of porous media such as Li-ion batteries or random influences in biomechanical systems.… (More)
Die in diesem Diskussionsbeitrag vertretenen Standpunkte liegen ausschließlich in der Verantwortung der Verfasser bzw. des Verfassers und decken sich nicht zwingend mit denen der Herausgeber. Standpoints expressed in this discussion paper are within the responsibility of the author(s) and do not necessarily reflect those of the editors.
The key condition for the application of the Reduced Basis Method (RBM) to Parametrized Partial Differential Equations (PPDEs) is the availability of affine decompositions of the systems in parameter and space. The efficiency of the RBM depends on both the number of reduced basis functions and the number of affine terms. A possible way to reduce the costs… (More)
The specific objectives of TIPP are: 1. to provide a comprehensive and in-depth picture of institutional constraints to implementing transport policy throughout Europe; 2. to develop an approach for studying institutional implementation issues by combining elements from the positive theories of regulation, public choice and federalism with the standard… (More)