Abstract: The mathematical mesh of numerical manifold method (NMM) does not have to accommodate to various boundaries of physical domains, and thus the mathematical coverage is always built by the regular structured mesh. However, for most problems, it is wasteful to use the mesh with the uniform density on the the whole physical region. Therefore, it is necessary to study the implementation of the local refinement on structured mesh, and a method of refining physical patches is proposed to solve the problem. For a practical problem, firstly we determine each region in which the mesh needs to be refined, and it is found that the physical patches entirely is contained by the refined mesh. Then, an interpolation on the refined mesh is constructed inside each physical patch, and the original local approximation of the physical patch is replaced by the new interpolation. Thus, the order of the local approximation is improved. Numerical results show the proposed method has good convergence. In addition, for two-dimensional analysis, the stiffness matrix obtained by the proposed method is positive definite if local approximations on all physical patches are constant.

Key words: numerical manifold method, refined physical patches, structured mesh, local refinement