Results 21 to 30 of about 702,196 (224)

Equivalence Between DFR Method and DG Method for Solving Parabolic Equation and Convection-diffusion Equation

Journal of Harbin University of Science and Technology, 2022
The equivalence between direct flux reconstruction method and discontinuous Galerkin method for solving parabolic equation and convection-diffusion equation is studied.
BI Hui, LIU Lei
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The convergence of Galerkin–Petrov methods for Dirichlet projections

Annals of Functional Analysis, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li He, Yifang Li, Yiyuan Zhang
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Interpolation, Projection and Hierarchical Bases in Discontinuous Galerkin Methods [PDF]

Numerical Mathematics: Theory, Methods and Applications, 2015
AbstractThe paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based on hierarchical bases, and on inverse inequalities.
Angermann, Lutz, Henke, Christian
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Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems [PDF]

SIAM/ASA Journal on Uncertainty Quantification, 2019
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal basis of the random space, e.g., the polynomial chaos expansions.
Pulch, Roland, Augustin, Florian
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A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Fluids, 2018
We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes.
Sk. Mashfiqur Rahman, Omer San, Adil Rasheed   +2 more
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Galerkin projected residual method applied to diffusion–reaction problems [PDF]

Computer Methods in Applied Mechanics and Engineering, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dutra do Carmo, Eduardo Gomes, Alvarez, Gustavo Benitez, Rochinha, Fernando Alves, Loula, Abimael Fernando Dourado   +3 more
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POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations

Advanced Modeling and Simulation in Engineering Sciences, 2023
We present a Reduced Order Model (ROM) which exploits recent developments in Physics Informed Neural Networks (PINNs) for solving inverse problems for the Navier–Stokes equations (NSE).
Saddam Hijazi, Melina Freitag, Niels Landwehr   +2 more
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Uncertainty Analysis of Neutron Diffusion Eigenvalue Problem Based on Reduced-order Model

Yuanzineng kexue jishu, 2023
In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics, the proper orthogonal decomposition (POD) and Galerkin projection method were combined to study the application feasibility of reduced-order model ...
In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics, the proper orthogonal decomposition (POD) and Galerkin projection method were combined to study the application feasibility of reduced-order model based on POD-Galerkin method in core physical uncertainty analysis. The two-dimensional two group TWIGL benchmark question was taken as the research object, the key variation characteristics of the core flux distribution were extracted under the finite perturbation of the group constants of each material region, and the full-order neutron diffusion problem was projected on the variation characteristics to establish a reduced-order neutron diffusion model. The reduced-order model was used to replace the full-order model to carry out the uncertainty analysis of the group constants of the material region. The results show that the bias of the mathematical expectation of keff calculated by reduced-order and full-order models is close to 1 pcm. In addition, compared with the calculation time required for uncertainty analysis of full-order model, the analysis time of reduced-order model (including the calculation time of the full-order model required for the construction of reduced-order model) is only 11.48%, which greatly improves the efficiency of uncertainty analysis. The biases of mathematical expectation of keff calculated by reduced-order and full-order models based on Latin hypercube sampling and simple random sampling are less than 8 pcm, and under the same sample size, the bias from the Latin hypercube sampling result is smaller. From the TWIGL benchmark test results, under the same sample size, Latin hypercube sampling method is more recommended for POD-Galerkin reduced-order model.
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L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Journal of Inequalities and Applications, 2010
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Hyun Young Lee, Mi Ray Ohm, Jun Yong Shin   +2 more
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Convergence of the Galerkin method in the problem of electromagnetic wave diffraction on a system of solids and curvilinear screens

Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2023
Background. The purpose of this study is to prove the convergence of the projection method in the problem of diffraction of electromagnetic waves by scatterers of a complex shape. Material and methods.
Aleksey A. Tsupak
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