The variational extremum method is further extended to give the full coverage for the inclined (tilted) grain-boundary (GB) configuration with respect to the sidewalls of a bicrystal thin solid film having strong anisotropic specific surface Gibbs free energy associated with the singular directions (faceting). A set of critical computer simulation experiments is performed on the asymmetrically disposed (inclination) bicrystal thin metallic films having four- and sixfold anisotropic specific surface Gibbs free energies to demonstrate the various GB-groove root topologies. Special computer runs are also designed using the realistic structural and physicochemical properties to simulate the thermal grooving profile of polycrystalline alumina (Lucalox (TM)), and tungsten, which undergone heat treatments for 90 and 120 min at 1650 and 1350 degrees C in air and vacuum (10(-4) Pa), respectively. The simulation profiles almost perfectly agree with the published experimental atomic force microscopy photographs after linewidth matching procedures, and the simulations produced very accurate mean surface (mass) diffusivities of alumina and tungsten given by D-Al2O3 congruent to 6.45x10(-12) m(2)/s and D-W congruent to 5.2x10(-13) m(2)/s, respectively. These findings are in good agreement with the diffusivities reported in the literature. (c) 2008 American Institute of Physics.