Fig 1. Matrix structure of diffusion problem with different meshing approaches in finite volume discretization.

(A) The tetrahedral mesh matrix has a large bandwidth with no apparent block structure. In FEV discretization of unstructured domains, unknown nodal values typically occur in dozens of balance equations which augments matrix bandwidth thus substantially hampering the solvability of the underlying transport problem. (B) The structured Cartesian (cuboid) mesh covering the same domain with similar characteristic edge length has a much narrower bandwidth and has block structure which is ideally suited for block diagonalization preconditioning. Tetrahedral meshes also require almost ten times (in our example 9.2 times) more grid cells (nz) than the analogue cuboid mesh.