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Coarse H(div)- and L2-conforming Spaces by Spectral AMGe for Upscaling Mixed Finite Element Discretizations

Delyan Kalchev

Applied Mathematics,Ìý

Date and time:Ìý

Tuesday, September 1, 2015 - 11:00am

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GRVW 105

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The main goal in numerical upscaling is to reduce the fine-scale discrete model to an accurate coarse-scale model which requires less memory to store and less time to solve. Thus, the cost of a simulation can be reduced significantly and also some practically unfeasible fine-scale simulations can be accomplished by executing corresponding coarse-scale simulations, while maintaining good accuracy. Moreover, we are interested in developing flexible methods that allow for unstructured fine meshes and high-order finite elements. In this particular instance, ideas from spectral element agglomeration algebraic multigrid are applied to constructing coarse instances of the H(div)-L2 portion of the de Rham sequence which resemble finite element spaces defined on irregularly shaped coarse elements (agglomerates of fine-grid elements). The resulting coarse spaces have desired properties providing stability (in terms of inf-sup compatibility) of certain mixed finite element methods for second order elliptic equations. Furthermore, the coarse elements have well-defined topology similar to the fine elements allowing for recursively building multilevel hierarchies and using techniques like hybridization for solving the saddle-point problems resulting from coarse-scale discretizations.