An efficient ensemble algorithm for numerical approximation of stochastic Stokes–Darcy equations

We propose and analyze an efficient ensemble algorithm for fast computation of multiple realizations of the stochastic Stokes–Darcy model with a random hydraulic conductivity tensor. The algorithm results in a common coefficient matrix for all realizations at each time step making solving the linear...

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Vydané v:Computer methods in applied mechanics and engineering Ročník 343; s. 249 - 275
Hlavní autori: Jiang, Nan, Qiu, Changxin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.01.2019
Elsevier BV
Predmet:
Algorithms
Approximation
Convergence
Efficiency
Ensemble algorithm
Finite element method
Linear systems
Mathematical models
Matrix methods
Parallel processing
Partitioned method
Stochastic models
Stokes–Darcy equations
Tensors
Uncertainty quantification
Finite element method
Uncertainty quantification
Ensemble algorithm
Partitioned method
Stokes–Darcy equations
ISSN:0045-7825, 1879-2138
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Popis
Shrnutí:We propose and analyze an efficient ensemble algorithm for fast computation of multiple realizations of the stochastic Stokes–Darcy model with a random hydraulic conductivity tensor. The algorithm results in a common coefficient matrix for all realizations at each time step making solving the linear systems much less expensive while maintaining comparable accuracy to traditional methods that compute each realization separately. Moreover, it decouples the Stokes–Darcy system into two smaller sub-physics problems, which reduces the size of the linear systems and allows parallel computation of the two sub-physics problems. We prove the ensemble method is long time stable and first-order in time convergent under a time-step condition and two parameter conditions. Numerical examples are presented to support the theoretical results and illustrate the application of the algorithm.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2018.08.020