00506nas a2200109   4500008004100000245009600041210006900137100002100206700002100227700002100248856012700269       2022                        eng d00aData-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics0 aDataDriven Enhanced Model Reduction for Bifurcating Models in Co1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/data-driven-enhanced-model-reduction-bifurcating-models-computational-fluid-dynamics00572nas a2200109   4500008004100000245016300041210006900204100002100273700002100294700002100315856012600336       2022                        eng d00aA Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation0 aDataDriven Surrogate Modeling Approach for TimeDependent Incompr1 aHess, Martin, W.1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/data-driven-surrogate-modeling-approach-time-dependent-incompressible-navier-stokes01780nas a2200169   4500008004100000020002200041245009500063210006900158260005200227520110800279100001601387700002101403700002101424700002301445700001901468856012301487       2021                        eng d  a978-3-030-55874-100aDiscontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation0 aDiscontinuous Galerkin Model Order Reduction of Geometrically Pa  aChambSpringer International Publishingc2021//3 a<p>The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time.</p>1 aShah, Nirav1 aHess, Martin, W.1 aRozza, Gianluigi1 aVermolen, Fred, J.1 aVuik, Cornelis  uhttps://www.math.sissa.it/publication/discontinuous-galerkin-model-order-reduction-geometrically-parametrized-stokes-0