Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes

Effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method

“…The image and the contour of the PU function are illustrated in Figure B,C, respectively. Using the method in An et al, the flattop PU approximation established from a rectangular mesh is proved to be linearly independent at a global level, which is the same as that for a triangular mesh.…”

Complementarity problem arising from static growth of multiple cracks and MLS-based numerical manifold method

“…Similar to GFEM, however, it might incur the issue of linear dependency. An et al proposed an algorithm for predicting the rank deficiency of the stiffness matrix [8]. Recently, Ghasemzadeh et al developed a scheme with high order polynomials as the local approximations that has no linear dependency [9].…”

A high-order numerical manifold method with nine-node triangular meshes

“…Cai et al [18] have used a dual local approximation scheme by treating boundary and interior nodes separately. An et al [19] have discussed the origin of the LD and proposed an algorithm for predicting the rank deficiency of the global stiffness matrix. Recently, Zheng et al [20] have illustrated the application of NMM to thin plate bending problems.…”