TU CE GSC CE People at the Graduate School CE Alumni Christopher Spannring Research Project of -Template Student-

Reduced basis method for PDEs with random data

The incorporation of stochastic quantities in Numerics rises complexity in theory and computation. In the last two decades various numerical methods were developed to predict partial differential equations (PDEs) influenced by random input data. These influences (or parameters) can come into the equations by the differential operator, right hand side, boundary conditions or the geometry. In the context of solving such problems some quantity of interest (QOI) is predicted. It contains statistical information like mean, variance or higher moments of average temperature, maximum stress, velocity fields,... Uncertainty quantification (UQ) for these problems can be accomplished by solving a large number of uncoupled deterministic PDEs, e.g. Monte Carlo (MC) method. Solving high dimensional problems in many query situations result in high demands of computation time. It is the aspect where model order reduction (MOR) is considered. The reduced basis method (RBM) is applied, that replaces a high dimensional discretized model by a low dimensional reduced problem. The core of the project is the a posteriori error estimation of the reduced model influenced by random data.

Error estimation of reduced models

Christopher Spannring

Dipl.-Ing.

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