A Multiscale Model Reduction Method for Partial Differential Equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013115 ◽

2014 ◽

Vol 48 (2) ◽

pp. 449-474 ◽

Author(s):

Maolin Ci ◽

Thomas Y. Hou ◽

Zuoqiang Shi

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Reduction Method ◽

Multiscale Model ◽

Partial Differential

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A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22856 ◽

2021 ◽

Author(s):

Guannan Zhang ◽

Lin Mu

Keyword(s):

Steady State ◽

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Model Reduction ◽

Reduction Method ◽

Random Coefficients ◽

Partial Differential ◽

Decomposition Model

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Local–global model reduction method for stochastic optimal control problems constrained by partial differential equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2018.05.012 ◽

2018 ◽

Vol 339 ◽

pp. 514-541 ◽

Author(s):

Lingling Ma ◽

Qiuqi Li ◽

Lijian Jiang

Keyword(s):

Optimal Control ◽

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Stochastic Optimal Control ◽

Reduction Method ◽

Optimal Control Problems ◽

Global Model ◽

Control Problems ◽

Partial Differential

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Reinforcement Learning-based Model Reduction for Partial Differential Equations

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.1515 ◽

2020 ◽

Vol 53 (2) ◽

pp. 7704-7709

Author(s):

Mouhacine Benosman ◽

Ankush Chakrabarty ◽

Jeff Borggaard

Keyword(s):

Reinforcement Learning ◽

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Partial Differential

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Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs

Journal of Computational Physics ◽

10.1016/j.jcp.2020.109326 ◽

2020 ◽

Vol 409 ◽

pp. 109326

Author(s):

Kejun Tang ◽

Qifeng Liao

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

High Dimensional ◽

Partial Differential ◽

Random Inputs ◽

Tensor Recovery

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Symmetry multi-reduction method for partial differential equations with conservation laws

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2020.105349 ◽

2020 ◽

Vol 91 ◽

pp. 105349

Author(s):

Stephen C. Anco ◽

M.L. Gandarias

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Conservation Laws ◽

Reduction Method ◽

Partial Differential

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A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

Journal of Computational Physics ◽

10.1016/j.jcp.2015.05.041 ◽

2015 ◽

Vol 297 ◽

pp. 700-720 ◽

Author(s):

F. Vidal-Codina ◽

N.C. Nguyen ◽

M.B. Giles ◽

J. Peraire

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Variance Reduction ◽

Reduction Method ◽

Elliptic Partial Differential Equations ◽

Partial Differential

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A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2010.01.009 ◽

2010 ◽

Vol 199 (23-24) ◽

pp. 1603-1626 ◽

Author(s):

Anthony Nouy

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

A Priori ◽

Time Dependent ◽

Proper Generalized Decomposition ◽

Partial Differential

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Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2021.114206 ◽

2022 ◽

Vol 388 ◽

pp. 114206

Author(s):

Michael K. Sleeman ◽

Masayuki Yano

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Nonlinear Partial Differential Equations ◽

Time Dependent ◽

Partial Differential

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Goal‐oriented model reduction of parametrized nonlinear partial differential equations: Application to aerodynamics

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6395 ◽

2020 ◽

Vol 121 (23) ◽

pp. 5200-5226

Author(s):

Masayuki Yano

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Nonlinear Partial Differential Equations ◽

Partial Differential

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Optimal actuator placement and model reduction for a class of parabolic partial differential equations using spatial H/sub 2/ norm

Proceedings of the 2005, American Control Conference, 2005. ◽

10.1109/acc.2005.1470716 ◽

2005 ◽

Author(s):

M.A. Demetriou ◽

A. Armaou

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Model Reduction ◽

Parabolic Partial Differential Equations ◽

Partial Differential ◽

Actuator Placement

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