Banach space projections and Petrov-Galerkin estimates [PDF]
Numerische Mathematik, 2015 We sharpen the classic a priori error estimate of Babuska for Petrov-Galerkin methods on a Banach space. In particular, we do so by (i) introducing a new constant, called the Banach-Mazur constant, to describe the geometry of a normed vector space; (ii ...
Stern, Ari
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Physics-driven proper orthogonal decomposition: A simulation methodology for partial differential equations [PDF]
MethodsX, 2023 A simulation methodology derived from a learning algorithm based on Proper Orthogonal Decomposition (POD) is presented to solve partial differential equations (PDEs) for physical problems of interest.
Alessandro Pulimeno +6 more
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Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction [PDF]
Journal of Computational Physics, 2017 Submitted to Journal of Computational ...
Carlberg, Kevin +2 more
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POD-Galerkin FSI Analysis for Flapping Motion [PDF]
Biomimetics, 2023 FSI simulations of flapping motions have been widely investigated to develop a flapping-wing micro air vehicle. Because an intensive parametric study is important for the product design, a computationally efficient model is required.
Shigeki Kaneko, Shinobu Yoshimura
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Journal of Computational Physics, 2017 The present paper deals with the numerical solution of the incompressible Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods for discretization in space.
Fehn, Niklas +2 more
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Conservative interpolation between volume meshes by local Galerkin projection
Computer Methods in Applied Mechanics and Engineering, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farrell, P, Maddison, J
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Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction
SIAM Journal on Scientific Computing, 2019 Accepted to the SIAM Journal on Scientific ...
Choi, Youngsoo, Carlberg, Kevin
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Reduced order models based on local POD plus Galerkin projection [PDF]
Journal of Computational Physics, 2010 A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained via POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estimate of the error of the Galerkin ...
Rapun Banzo, Maria Luisa +1 more
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EXPLORING TRANSIENT, NEUTRONIC, REDUCED-ORDER MODELS USING DMD/POD-GALERKIN AND DATA-DRIVEN DMD [PDF]
EPJ Web of Conferences, 2021 There is growing interest in the development of transient, multiphysics models for nuclear reactors and analysis of uncertainties in those models. Reduced-order models (ROMs) provide a computationally cheaper alternative to compute uncertainties. However,
Elzohery Rabab, Roberts Jeremy
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Chaotic systems learning with hybrid echo state network/proper orthogonal decomposition based model
Data-Centric Engineering, 2021 We explore the possibility of combining a knowledge-based reduced order model (ROM) with a reservoir computing approach to learn and predict the dynamics of chaotic systems.
Mathias Lesjak, Nguyen Anh Khoa Doan
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