Abstract: The scope of a numerical manifold method (NMM) based on partially overlapping covers is narrowed to a special case based on independent covers. Convergence of the new method is discussed from two aspects: completeness and coordination. The convergence of the method is due to the convergence of each independent cover. Results show that the size of the strips between independent covers should be small. Moreover, the cover meshes have three excellent features: arbitrary shape, arbitrary connection, and arbitrary refinement. Finally, some illustrations are given to verify these “arbitrary” features, and the method can be used to greatly simplify the pre-processing of numerical analysis.

Key words: numerical manifold method (NMM), partially overlapping covers, independent covers, convergence, mesh features