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Proposing Institution

Frauenhofer ITWM Competence Center for High Performance Computing
Project Manager

Prof. Dr. Oleg Iliev
Fraunhofer-Platz 1
67633 Kaiserslautern
Abstract
Stochastic PDEs attract recently a great attention, in particular due to their practical importance in modeling and simulation of variety of environmental and industrial processes. In this project, we consider the classical example for evaluation of the mean flux for a single phase flow in random heterogeneous porous media. Uncertainty Quantification (UQ) for such problems, due to the randomness , leads to extremely high dimensional problems. A popular approach for solving such problems is the Multilevel Monte Carlo (MLMC) method. Well known fact is that standard Monte Carlo method converges very slowly (i.e., a large number of deterministic PDE problems have to be solved for different realizations of the permeability field). The idea of the MLMC is to combine in a proper way fewer expensive computations with a plenty of cheap computations, so that the targeted expected value is computed at significantly lower costs compared to the standard Monte Carlo algorithm. Key components of MLMC is the selection of the coarser levels and independent sampling. MLMC is not only efficient algorithm for solving UQ problems, but it also provides opportunities for coarse grain parallelization. Our developments are a part of the SPPEXA program of DFG, specifically, they are part of Exa-DUNE project, https://www.researchgate.net/project/EXA-DUNE-Flexible-PDE-Solvers-Numerical-Methods-and-Applications. A number of different approaches for building coarse spaces have been considered earlier. We have investigated cases when MsFEM and renormalization are used to build the coarse levels. Parallel implementations have been developed and tested on Beehive cluster at Fraunhofer ITWM. The next step is to exploit the coarse grain potential of the MLMC and to test the parallel algorithms on massively parallel computer.

Impressum, Conny Wendler