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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Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

Journal of Computational Physics ◽

10.1016/j.jcp.2017.08.067 ◽

2017 ◽

Vol 351 ◽

pp. 203-215 ◽

Author(s):

R. Tipireddy ◽

P. Stinis ◽

A.M. Tartakovsky

Keyword(s):

Steady State ◽

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Random Coefficients ◽

Partial Differential

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Stochastic Basis Adaptation and Spatial Domain Decomposition for Partial Differential Equations with Random Coefficients

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/16m1097134 ◽

2018 ◽

Vol 6 (1) ◽

pp. 273-301 ◽

Author(s):

R. Tipireddy ◽

P. Stinis ◽

A. M. Tartakovsky

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Spatial Domain ◽

Random Coefficients ◽

Partial Differential ◽

Stochastic Basis

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A Domain Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients

SIAM Journal on Scientific Computing ◽

10.1137/18m1170601 ◽

2019 ◽

Vol 41 (3) ◽

pp. A1984-A2011 ◽

Author(s):

Lin Mu ◽

Guannan Zhang

Keyword(s):

Domain Decomposition ◽

Model Reduction ◽

Reduction Method ◽

Random Coefficients ◽

Diffusion Equations ◽

Convection Diffusion ◽

Decomposition Model

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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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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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A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations

Concurrency and Computation Practice and Experience ◽

10.1002/cpe.569 ◽

2001 ◽

Vol 13 (5) ◽

pp. 327-350 ◽

Author(s):

Randolph E. Bank ◽

Peter K. Jimack

Keyword(s):

Finite Element ◽

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Elliptic Partial Differential Equations ◽

Adaptive Finite Element ◽

Element Solution ◽

Partial Differential

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Asymptotic solutions of linear partial differential equations of first order having random coefficients

Random Operators and Stochastic Equations ◽

10.1515/rose.1994.2.1.61 ◽

1994 ◽

Vol 2 (1) ◽

Author(s):

F. HOPPENSTEADT ◽

R. KHASMINSKII ◽

H. SALEHI

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Random Coefficients ◽

Asymptotic Solutions ◽

Partial Differential ◽

First Order ◽

Linear Partial Differential Equations

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Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2021.114129 ◽

2021 ◽

Vol 387 ◽

pp. 114129

Author(s):

Suchuan Dong ◽

Zongwei Li

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Nonlinear Partial Differential Equations ◽

Extreme Learning Machines ◽

Partial Differential ◽

Learning Machines ◽

Linear And Nonlinear ◽

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A domain decomposition method for optimization problems for partial differential equations

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(00)00152-8 ◽

2000 ◽

Vol 40 (2-3) ◽

pp. 177-192 ◽

Author(s):

M.D. Gunzburger ◽

Jeehyun Lee

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Decomposition Method ◽

Optimization Problems ◽

Domain Decomposition Method ◽

Partial Differential

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