Numerical analysis of a two-level preconditioner for the diffusion equation with an anisotropic diffusion tensor

We develop and analyze a new two-level preconditioner for algebraic systems arising from finite volume discretization of 3D anisotropic diffusion problems on prismatic meshes. The preconditioner is based on partitioning of the mesh in the (x,y)-plane into non-overlapping subdomains and on a special coarsening algorithm. The condition number of the preconditioned matrix does not depend on the coefficients in the diffusion operator. Numerical experiments confirm the theoretical results and reveal the competitiveness of the new preconditioner with respect to the algebraic multigrid preconditioner.