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Subject: Karhunen-Loève expansion ×

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    Stokes flows under random boundary velocity excitations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Sabelfeld, Karl
    A viscous Stokes flow over a disc under random fluctuations of the velocity on the boundary is studied. We give exact Karhunen-Loève (K-L) expansions for the velocity components, pressure, stress, and vorticity, and the series representations for the corresponding correlation tensors. Both the white noise fluctuations, and general homogeneous random excitations of the velocities prescribed on the boundary are studied. We analyze the decay of correlation functions in angular and radial directions, both for exterior and interior Stokes problems. Numerical experiments show the fast convergence of the K-L expansions. The results indicate that ignoring the boundary condition uncertainty dramatically underestimates the variance of the velocity and pressure in the interior/exterior of the domain.
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    Stochastic analysis of an elastic 3D half-space respond to random boundary displacements : exact results and Karhunen-Loéve expansion
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Shalimova, Irina A.; Sabelfeld, Karl K.
    A stochastic response of an elastic 3D half-space to random displacement excitations on the boundary plane is studied. We derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary. Solutions to this elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction. This enables us to construct explicitly the Karhunen-Loève (K-L) series expansion by solving the eigen-value problem for the correlation operator. Simulation results are presented and compared with the exact representations derived for the displacement correlation tensor. This paper is a complete 3D generalization of the 2D case study we presented in J. Stat. Physics, v.132 (2008), N6, 1071-1095.