数值流形法的数学网格不需要适应求解域内各种不连续界面和边界，因此，总可以用规则的结构化网格建立数学覆盖。但对于大多数问题，在整个求解域上布置统一密度的网格显得浪费。因此，需要研究在结构化网格上实施局部加密，建立了加密物理片的方法用以解决这一问题。具体的实施过程中，确定了需要加密的区域后，先在这些区域布置规则的精细网格，然后找到这些区域中包含的原始网格中的物理片，用精细网格上建立的插值代替被加密物理片上的局部近似，从而提高了局部近似的阶次。数值算例结果表明，该方法收敛性良好。另外，如果所有物理片上的局部近似都采用0阶多项式(常数)，那么将会得到正定的刚度矩阵。

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.