Solution of a stochastic Darcy equation by polynomial chaos expansion
This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomi...
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| Veröffentlicht in: | Numerical analysis and applications 2017-07, Vol.10 (3), p.259-271 |
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| container_title | Numerical analysis and applications |
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| creator | Shalimova, I. A. Sabelfeld, K. K. |
| description | This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm. |
| doi_str_mv | 10.1134/S1995423917030077 |
| format | Article |
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A. ; Sabelfeld, K. K.</creator><creatorcontrib>Shalimova, I. A. ; Sabelfeld, K. K.</creatorcontrib><description>This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. 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A.</creatorcontrib><creatorcontrib>Sabelfeld, K. K.</creatorcontrib><title>Solution of a stochastic Darcy equation by polynomial chaos expansion</title><title>Numerical analysis and applications</title><addtitle>Numer. Analys. Appl</addtitle><description>This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. 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| ispartof | Numerical analysis and applications, 2017-07, Vol.10 (3), p.259-271 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Boundary value problems Collocation methods Mathematical analysis Mathematics Mathematics and Statistics Monte Carlo simulation Numerical Analysis Polynomials Probabilistic methods Probability theory Simulation Thermal expansion |
| title | Solution of a stochastic Darcy equation by polynomial chaos expansion |
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