Stochastic boundary elements for two-dimensional potential flow in non-homogeneous media (Q1913238)

A stochastic boundary element formulation is presented for the treatment of two-dimensional problems of steady-state potential flow in non-homogeneous media that involve a random operator in the governing differential equation. The randomness is introduced through the material parameter of the domain which is described as a non-homogeneous random field. The random field is discretized into a set of correlated random variables, and a perturbation is applied to the differential equation of the problem. This leads to differential equations for the unknown potential and its first- and second-order derivatives. The equations are solved using the boundary element method to obtain the unknown boundary values of the potentials and their respective first- and second-order derivatives which are then used to compute the desired response statistics. Quadratic, conforming boundary elements are used in the boundary integration, and four-node quadrilateral cells are used in the domain integration.