Details
| Original language | English |
|---|---|
| Article number | 103519 |
| Journal | Probabilistic Engineering Mechanics |
| Volume | 74 |
| Early online date | 30 Aug 2023 |
| Publication status | Published - Oct 2023 |
Abstract
This paper explores the accuracy and the efficiency of analytical solution of Fredholm integral equation to represent a random field on complex geometry. Because no analytical solution is available for arbitrary domains, it is proposed to use the analytical solution on simple bounding domains that enclose complex two- or three-dimensional geometries. It is a simple, accurate and robust approach for discretising a random field. The effect of the size of the bounding box on the resulting random field variance is investigated carefully and compared with the numerical solution given by the finite element method. The error variance is particularly localised near to the support domain boundary. Therefore, it is suggested to expand the bounding domain. This paper proposes a calibration of the correlation length to the ratio of the domain to maintain the convergence rate and the variance accuracy of the KLE without enlarging the stochastic dimension.
Keywords
- Analytical solution, Axis-aligned bounding box, Bounding box approach, Integral eigenvalue problem, Karhunen-Loève expansion, Random field discretisation, Stochastic finite element method
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Engineering(all)
- Civil and Structural Engineering
- Energy(all)
- Nuclear Energy and Engineering
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Aerospace Engineering
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
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In: Probabilistic Engineering Mechanics, Vol. 74, 103519, 10.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Karhunen-Loève expansion based on an analytical solution over a bounding box domain
AU - Basmaji, A. A.
AU - Dannert, M. M.
AU - Bensel, F.
AU - Fleury, R. M.N.
AU - Fau, A.
AU - Nackenhorst, U.
N1 - Funding Information: The support of the German Research Foundation (DFG) through the International Research Training Group IRTG 2657 (DFG-grant 433082294 ) as well as the priority program SPP 1886 (NA330/12-1) is gratefully acknowledged. The support of the French-German University is also sincerely acknowledged under the French-German doctoral college grant DFDK 04-19 .
PY - 2023/10
Y1 - 2023/10
N2 - This paper explores the accuracy and the efficiency of analytical solution of Fredholm integral equation to represent a random field on complex geometry. Because no analytical solution is available for arbitrary domains, it is proposed to use the analytical solution on simple bounding domains that enclose complex two- or three-dimensional geometries. It is a simple, accurate and robust approach for discretising a random field. The effect of the size of the bounding box on the resulting random field variance is investigated carefully and compared with the numerical solution given by the finite element method. The error variance is particularly localised near to the support domain boundary. Therefore, it is suggested to expand the bounding domain. This paper proposes a calibration of the correlation length to the ratio of the domain to maintain the convergence rate and the variance accuracy of the KLE without enlarging the stochastic dimension.
AB - This paper explores the accuracy and the efficiency of analytical solution of Fredholm integral equation to represent a random field on complex geometry. Because no analytical solution is available for arbitrary domains, it is proposed to use the analytical solution on simple bounding domains that enclose complex two- or three-dimensional geometries. It is a simple, accurate and robust approach for discretising a random field. The effect of the size of the bounding box on the resulting random field variance is investigated carefully and compared with the numerical solution given by the finite element method. The error variance is particularly localised near to the support domain boundary. Therefore, it is suggested to expand the bounding domain. This paper proposes a calibration of the correlation length to the ratio of the domain to maintain the convergence rate and the variance accuracy of the KLE without enlarging the stochastic dimension.
KW - Analytical solution
KW - Axis-aligned bounding box
KW - Bounding box approach
KW - Integral eigenvalue problem
KW - Karhunen-Loève expansion
KW - Random field discretisation
KW - Stochastic finite element method
UR - http://www.scopus.com/inward/record.url?scp=85169884675&partnerID=8YFLogxK
U2 - 10.1016/j.probengmech.2023.103519
DO - 10.1016/j.probengmech.2023.103519
M3 - Article
AN - SCOPUS:85169884675
VL - 74
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
M1 - 103519
ER -