Sparse Non-negative Stencils for Anisotropic Diffusion
We introduce a new discretization scheme for Anisotropic Diffusion, AD-LBR, on two and three dimensional Cartesian grids. The main features of this scheme is that it is non-negative and has sparse stencils, of cardinality bounded by 6 in 2D, by 12 in 3D, despite allowing diffusion tensors of arbitrary anisotropy. The radius of these stencils is not a-priori bounded however, and can be quite large for pronounced anisotropies. Our scheme also has good spectral properties, which permits larger time steps and avoids e.g. chessboard artifacts.
anisotropic diffusion non-negative numerical scheme lattice basis reduction