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

Abstract 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...
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Autor*in:	Shalimova, Irina A. [verfasserIn] Sabelfeld, Karl K. Dulzon, Olga V.

Format:	Artikel

Erschienen:	2017

Anmerkung:	© 2017 Walter de Gruyter GmbH, Berlin/Boston

Übergeordnetes Werk:	Enthalten in: Journal of inverse and ill-posed problems - De Gruyter, 1993, 25(2017), 6 vom: 16. März, Seite 733-745
Übergeordnetes Werk:	volume:25 ; year:2017 ; number:6 ; day:16 ; month:03 ; pages:733-745

Links:	Volltext

DOI / URN:	10.1515/jiip-2016-0037

Katalog-ID:	OLC2139371178

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520			\|a Abstract 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.
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allfields	10.1515/jiip-2016-0037 doi (DE-627)OLC2139371178 (DE-B1597)jiip-2016-0037-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Shalimova, Irina A. verfasserin aut Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2017 Walter de Gruyter GmbH, Berlin/Boston Abstract 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. Sabelfeld, Karl K. aut Dulzon, Olga V. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 25(2017), 6 vom: 16. März, Seite 733-745 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:25 year:2017 number:6 day:16 month:03 pages:733-745 https://doi.org/10.1515/jiip-2016-0037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 25 2017 6 16 03 733-745
spelling	10.1515/jiip-2016-0037 doi (DE-627)OLC2139371178 (DE-B1597)jiip-2016-0037-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Shalimova, Irina A. verfasserin aut Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2017 Walter de Gruyter GmbH, Berlin/Boston Abstract 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. Sabelfeld, Karl K. aut Dulzon, Olga V. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 25(2017), 6 vom: 16. März, Seite 733-745 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:25 year:2017 number:6 day:16 month:03 pages:733-745 https://doi.org/10.1515/jiip-2016-0037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 25 2017 6 16 03 733-745
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allfieldsGer	10.1515/jiip-2016-0037 doi (DE-627)OLC2139371178 (DE-B1597)jiip-2016-0037-p DE-627 ger DE-627 rakwb 510 VZ 510 VZ 11 ssgn Shalimova, Irina A. verfasserin aut Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © 2017 Walter de Gruyter GmbH, Berlin/Boston Abstract 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. Sabelfeld, Karl K. aut Dulzon, Olga V. aut Enthalten in Journal of inverse and ill-posed problems De Gruyter, 1993 25(2017), 6 vom: 16. März, Seite 733-745 (DE-627)165676728 (DE-600)1160989-8 (DE-576)04851134X 0928-0219 nnns volume:25 year:2017 number:6 day:16 month:03 pages:733-745 https://doi.org/10.1515/jiip-2016-0037 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_134 GBV_ILN_267 GBV_ILN_4277 AR 25 2017 6 16 03 733-745
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author	Shalimova, Irina A.
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title	Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations
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title_sort	uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in darcy and diffusion equations
title_auth	Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations
abstract	Abstract 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. © 2017 Walter de Gruyter GmbH, Berlin/Boston
abstractGer	Abstract 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. © 2017 Walter de Gruyter GmbH, Berlin/Boston
abstract_unstemmed	Abstract 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. © 2017 Walter de Gruyter GmbH, Berlin/Boston
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title_short	Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations
url	https://doi.org/10.1515/jiip-2016-0037
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up_date	2024-07-03T19:50:46.563Z
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Uncertainty quantification and stochastic polynomial chaos expansion for recovering random data in Darcy and Diffusion equations

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