Multigrid methods for diffusion equations with highly discontinuous coefficients

The subject of this paper is the numerical solution by multigrid methods of -{nabla}{center dot}D(x){nabla}U(x) + {sigma}(x)U(x) = F(x) , x{element of}{Omega} and v(x){center dot}D(x){nabla}U(x) + {gamma}(x)U(x) = 0 , x {element of}{partial derivative}{Omega} , where {Omega} is a bounded region in R{sup 2} or R{sup 3} with boundary {partial derivative}{Omega}, D{sup i} is positive, {sigma} and {gamma} are nonnegative, and D{sup i}, {sigma}, and F are allowed to be discontinuous across internal boundaries {Gamma} of {Omega}.