TY - JOUR

T1 - Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations

AU - Shalimova, Irina A.

AU - Sabelfeld, Karl K.

AU - Dulzon, Olga V.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - A probabilistic collocation based polynomial chaos expansion method is developed to solve stochastic boundary value problems with random coefficients and randomly distributed initial data. In this paper we deal with two different boundary value problems with random data: the Darcy equation with random lognormally distributed hydraulic conductivity, and a diffusion equation with absorption, with random distribution of the initial concentration under periodic boundary conditions. Special attention is paid to the extension of the probabilistic collocation method to input data with arbitrary correlation functions defined both analytically and through measurements. We construct the relevant Karhunen-Loève expansion from a special randomized singular value decomposition of the correlation matrix, which makes possible to treat problems of high dimension. We show that the unknown statistical characteristics of the random input data can be recovered from the correlation analysis of the solution field.

AB - A probabilistic collocation based polynomial chaos expansion method is developed to solve stochastic boundary value problems with random coefficients and randomly distributed initial data. In this paper we deal with two different boundary value problems with random data: the Darcy equation with random lognormally distributed hydraulic conductivity, and a diffusion equation with absorption, with random distribution of the initial concentration under periodic boundary conditions. Special attention is paid to the extension of the probabilistic collocation method to input data with arbitrary correlation functions defined both analytically and through measurements. We construct the relevant Karhunen-Loève expansion from a special randomized singular value decomposition of the correlation matrix, which makes possible to treat problems of high dimension. We show that the unknown statistical characteristics of the random input data can be recovered from the correlation analysis of the solution field.

KW - Darcy equation

KW - Monte Carlo direct simulation

KW - polynomial chaos

KW - probabilistic collocation

KW - Uncertainty quantification

KW - TRANSPORT

KW - APPROXIMATIONS

KW - KINETICS

KW - MEDIA

KW - ALGORITHMS

KW - SIMULATION

KW - COLLOCATION

UR - http://www.scopus.com/inward/record.url?scp=85020434261&partnerID=8YFLogxK

U2 - 10.1515/jiip-2016-0037

DO - 10.1515/jiip-2016-0037

M3 - Article

AN - SCOPUS:85020434261

VL - 25

SP - 733

EP - 745

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 6

ER -