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

DOI10.1515/9783110671490-001OpenAlexW2989659967MaRDI QIDQ4992987

Giovanni Stabile, Gianluigi Rozza, Marco Tezzele, Francesco Ballarin, Martin W. Hess

Publication date: 15 June 2021

Published in: Snapshot-Based Methods and Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.08954

zbMATH Keywords

reduced basis methodempirical interpolation methodradial basis function interpolationactive subspacesshape morphing techniques

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical interpolation (65D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Finite volume methods for boundary value problems involving PDEs (65N08) Numerical radial basis function approximation (65D12)

Related Items (6)

Registration-based model reduction of parameterized two-dimensional conservation laws ⋮ A training set subsampling strategy for the reduced basis method ⋮ Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots ⋮ Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximation ⋮ A discretize-then-map approach for the treatment of parameterized geometries in model order reduction ⋮ A Supervised Learning Approach Involving Active Subspaces for an Efficient Genetic Algorithm in High-Dimensional Optimization Problems

This page was built for publication: 1 Basic ideas and tools for projection-based model reduction of parametric partial differential equations