Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods

By Marcus Meyer, Hermann G. Matthies. 2003

178 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/36ccbf2ada6a718a40c191de493ebdd16f29e432

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Citations in the corpus

An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations (2008, methodology): “Our approach is based on past and recent development of the reduced-basis approaches [1, 2, 3, 4, 5, 6, 7] and reduced-order modeling techniques [8, 9, 10, 11, 12, 13, 14].”
Certified Real-Time Solution of Parametrized Partial Differential Equations (2005, unknown): “time-domain model reduction procedures [19, 25, 36].”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, background): “ics [191]–[194], combustion [195]–[197], cosmology [198]– [200], electrodynamics [201]–[204], meteorology [205]–[208], fluid mechanics [209]–[215], heat transfer [216]–[218] and various other multiphysics processes [219]–[225], as well as systems and control theories [226]–[231] in order to provide ”
Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations (2007, background): “The Proper Orthogonal Decomposition (POD) or Karhunen-Loève (KL) [72, 80] approach to sampling [75, 77, 97, 142] is immensely popular in a variety of contexts — turbulent flows [85], fluid-structure interaction [46], non-linear structural mechanics [73], turbo-machinery flows [156] — most notably in”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, background): “RB-like “snapshot” ideas are also found in some of the many Reduced Order Model (ROM) approaches in the temporal domain [14,38,39, 89 ,116,130,145,155,156]: POD sampling procedures are often invoked, and more recently greedy sampling approaches have also been considered [21].”
A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation (2008, methodology): “Meyer and Matthies (2003) used adjoint modeling to improve the efficiency of the POD approach to model reduction when targeting a scalar aspect of the model dynamics.”
Sparse-grid, reduced-basis Bayesian inversion (2015, methodology): “dual problem with the density Θ(y), and construct a so-called dual-weighted-residual (DWR) [38] as an a posteriori error estimate.”
Nonlinear Model Reduction via Discrete Empirical Interpolation (2010, background): “In [58], the authors applied the dual-weighted-residual”
Reduced-order optimal control of water flooding using proper orthogonal decomposition (2006, methodology): “Reduced-order modelling and reduced-order control may provide an alternative to this [5,9, 10 ,19].”
Model Reduction via Proper Orthogonal Decomposition (2008, background): “New approaches exploiting the relation between POD and balanced truncation [21, 34, 37] or dual techniques [24, 25] yield a way out of this problem.”
Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation (2007, methodology): “Adjoint model information may be taken into account using a dual-weighted procedure [44].”