Stochastic Galerkin methods for elliptic interface problems with random input
Journal of Computational and Applied Mathematics
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We propose a new concept of the effective properties of composites with uncertain spatial arrangements of constitutive materials and within-material properties. Rather than replacing a heterogeneous property with a constant effective parameter, we seek to preserve the internal macro structure of a composite. This general concept is used to derive the effective conductivity of composite heterogeneous media that consist of two materials whose internal geometries and conductivities are uncertain. Our analysis relies on a random domain decomposition to explicitly account for the separate effects of material and geometric uncertainties on the ensemble moments of pressure and flux. We present a general expression for the effective (apparent) conductivity of such media and analyze it in detail for one- and two-dimensional steady flows in bounded random media composed of two materials with highly contrasting conductivities.