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BY-NC-ND 4.0 license Open Access Published by De Gruyter 2021

1 Basic ideas and tools for projection-based model reduction of parametric partial differential equations

From the book Volume 2 Snapshot-Based Methods and Algorithms

  • Gianluigi Rozza , Martin Hess , Giovanni Stabile , Marco Tezzele and Francesco Ballarin


We provide first the functional analysis background required for reducedorder modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition, and error estimation are introduced. Several tools for geometry parameterizations such as free form deformation, radial basis function interpolation, and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with nonaffine parameter dependency and nonlinear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspace properties are discussed to reduce high-dimensional parameter spaces as a preprocessing step. Several examples illustrate the methodologies.

© 2020 Walter de Gruyter GmbH, Berlin/Munich/Boston
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