English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Reduced basis methods (RBMs) are recommended to reduce the computational cost of solving parameter-dependent PDEs in scenarios where many choices of parameters need to be considered, for example, in uncertainty quantification (UQ). A reduced basis is constructed during a computationally demanding offline (or set-up) stage that allows the user to obtain cheap approximations for parameter choices of interest, online. In this paper we consider RBMs for parameter-dependent saddle point problems, in particular the one that arises in the mixed formulation of the Darcy flow problem in groundwater flow modeling. We apply a discrete empirical interpolation method (DEIM) to approximate the inverse of the diffusion coefficient, which depends nonaffinely on the system parameters. We develop an efficient RBM that exploits the DEIM approximation and combine it with a sparse grid stochastic collocation mixed finite element method (SCMFEM) to construct a surrogate solution, which then allows for efficient forward UQ. Thr...

Efficient Reduced Basis Methods for Saddle Point Problems with Applications in Groundwater Flow