Focus of our work
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Extension of the reduced basis method to nonlinear time-dependent problems and development of suitable a-posteriori estimators. |
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Geometry parametrization and RB treatment by reference mapping. |
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Treatment of more general discretization methods than FEM, in particularly covering Finite Volume or Local Discontinuous Galerkin discretizations, which may involve explicit and implicit operator contributions. |
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Application of the developed methods to linear and nonlinear transport phenomena, e.g. single- or two-phase flow, porous media and fuel-cell related processes. |
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Basis generation procedures, in particular snapshot-based approaches by suitable parameter-space-sampling schemes, e.g. adaptive grids, etc. |
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Application of reduced models in sophisticated settings such as parameter optimization. |
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Application of Reduced Basis Techniques for parametrized dynamical systems. |
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Software development for RB-methodology on both high-level MATLAB tools for interactive use and simulation, as well as efficient high-performance computing C++ implementation for the numerical programming environment DUNE. |