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.