Despite advances in recent years, scientific computation technologies still do not allow us to efficiently simulate many physical systems. In many cases, the main stumbling block is due to the multi-scale variation of material properties, such as the permeabilities in porous-media flow. Many existing upscaling techniques rely on the numerical solution of artificially localized fine-scale problems. More efficient techniques can be based on robust multigrid methods, which give natural ways to coarsen fine-scale material properties to scales suitable for computation with less expense. In doing this, however, we must ask about the physical relevance of the coarse grid operators generated. We show that these coarse grid operators can be represented by a coarse-scale diffusion (or Darcy flow) term plus a regularization term. The effect of this regularization term on the upscaling derived from Dendy's robust BoxMG algorithm is the primary subject of our current research. Additionally, we have developed a package of C-wrappers to make the BoxMG family of Multigrid solvers more accessible. These wrappers benefit from a simplified interface and from the ability to dynamically allocate memory in C.

This research was performed under the auspices of the U.S. Department of Energy and is to be referenced as LA-UR-02-6659. The Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.