“…Many models in early stages, such as the PK model [7], PKN model [8], KGD mode [9], pseudo-3D models, and planar-3D models [10,11], can only be used in simulating the propagation of fractures with highly idealized geometries. Some traditional methods, such as the finite difference method [12], finite element method [13], extended finite element method [14][15][16], discrete element method [17], have been used in the simulation of fracture network in recent years, but are computationally demanding and are ill-conditioned [17] for the fluid-rock coupling process of hydraulic fracturing. Different from these traditional methods, meshless methods [18][19][20] are free from meshing and with capability to deal with moving boundary conditions.…”