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 -