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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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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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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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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Implicit Space-Time Domain Decomposition Methods for Stochastic Parabolic Partial Differential Equations

SIAM Journal on Scientific Computing ◽

10.1137/12090410x ◽

2014 ◽

Vol 36 (1) ◽

pp. C1-C24 ◽

Author(s):

Cui Cong ◽

Xiao-Chuan Cai ◽

Karl Gustafson

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Time Domain ◽

Decomposition Methods ◽

Parabolic Partial Differential Equations ◽

Domain Decomposition Methods ◽

Partial Differential

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A Kernel-Based Collocation Method for Elliptic Partial Differential Equations With Random Coefficients

Monte Carlo and Quasi-Monte Carlo Methods 2012 - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-642-41095-6_14 ◽

2013 ◽

pp. 331-347 ◽

Author(s):

Gregory E. Fasshauer ◽

Qi Ye

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Collocation Method ◽

Elliptic Partial Differential Equations ◽

Random Coefficients ◽

Partial Differential

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Domain Decomposition Methods for Partial Differential Equations

ICASE/LaRC Interdisciplinary Series in Science and Engineering - Parallel Numerical Algorithms ◽

10.1007/978-94-011-5412-3_8 ◽

1997 ◽

pp. 225-243 ◽

Author(s):

Barry F. Smith

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Decomposition Methods ◽

Domain Decomposition Methods ◽

Partial Differential

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NUMERICAL EXPERIMENTS FOR A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

Numerical Analysis ◽

10.1142/9789812812872_0007 ◽

1996 ◽

pp. 85-97 ◽

Author(s):

JIM DOUGLAS ◽

DAOQI YANG

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Domain Decomposition ◽

Numerical Experiments ◽

Decomposition Method ◽

Domain Decomposition Method ◽

Nonoverlapping Domain ◽

Partial Differential ◽

Nonoverlapping Domain Decomposition

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