Diffusion-accelerated solution of the 2-D S{sub n} equations with bilinear-discontinuous differencing

A new diffusion-synthetic acceleration scheme is developed for solving the 2-D S{sub n} equations in X-Y geometry with bilinear- discontinuous finite-element spatial discretization. This method differs from previous methods in that it is unconditionally efficient fore problems with isotropic or weakly anisotropic scattering. Computational results are given which demonstrate this property

The Black Box Multigrid Numerical Homogenization Algorithm

In mathematical models of flow through porous media, the coefficients typically exhibit severe variations in two or more significantly different length scales. Consequently, the numerical treatment of these problems relies on a homogenization or upscaling procedure to define an approximate coarse-scale problem that adequately captures the influence of the fine-scale structure. Inherent in such a procedure is a compromise between its computational cost and the accuracy of the resulting coarse-scale solution. Although techniques that balance the conflicting demands of accuracy and efficiency exist for a few specific classes of fine-scale structure (e.g., fine-scale periodic), this is not the case in general. In this paper we propose a new, efficient, numerical approach for the homogenization of the permeability in models of single-phase saturated flow. Our approach is motivated by the observation that multiple length scales are captured automatically by robust multilevel iterative solver..