Steady state diffusion problems on non-trivial domains: Support operator method integrated with direct optimized grid generation

This paper incorporates variational, geometry and solution adaptive, grid-generation technology, with a new class of finite-volume methods to solve modeling problems with non-homogeneous and non-isotropic material properties. Current grid generation technology provides a powerful tool for adapting grids to complex geometries, discontinuities in the material properties, and discontinuities in the problem solution. The support-operators finite-volume methods have been proven to be effective in solving problems with discontinuous coefficients on general grids. The main goal of this research is to combine these two technologies to produce algorithms for fast and accurate solutions of difficult modeling problems.