Abstract: Numerical manifold method with partially overlapping covers is an analysis mode mainly concerning independent covers. To automatically select independent cover regions in a mathematical mesh with general element size, the elements of the mathematical mesh are partitioned into a number of independent sets by graph colouring. Based on this, the elements for defining independent covers (i.e. the covers of all nodes of an element are merged into single one) are selected according to the principle of as many regions with independent covers as possible, and the rest of elements is defined as the overlapping cover regions for keeping the continuity, and the nodes which do not belong to the independent cover elements are defined as general nodal covers. Examples reveal that the linear dependencies between the overlapping covers exist only in the nodal covers on the mathematical mesh boundary, and cover merging could reduce the nullity of stiffness matrix or even avoid the linear dependencies.

Key words: numerical manifold method, generalized finite element method, independent covers, automatic selection, graph colouring, linear dependencies