Hydraulic fracture modeling is a multi-scale and multi-physics problem. It should capture various effects including those of in-situ stresses, poroelasticity, and reservoir heterogeneities at different length scales. A peridynamics-based hydraulic fracturing simulator has been demonstrated to reproduce this physics accurately. However, accounting for such details leads to a reduction in computational speed. In this paper, we present a novel coupling of the peridynamics-based simulator with computationally efficient classical methods to achieve a significant improvement in computational performance. Unlike classical methods such as Finite Element (FE) and Finite Volume (FV) that solve differential equations, peridynamics (PD) utilizes an integral formulation to circumvent the undefined spatial derivatives at crack tips. We implemented three coupling schemes of our PD-based simulator with the classical methods - static PD region scheme, dynamic PD region scheme, and adaptive mesh refinement scheme. PD equations are solved using a refined mesh close to the fracture, whereas FE/FV equations are solved using a progressively coarser mesh away from the fracture. As the fracture grows, a dynamic conversion of FE/FV cells to PD nodes and adaptive mesh refinement are incorporated. The coupling schemes are verified against the KGD fracture propagation problem. No spurious behavior is observed near the transition between PD and FE/FV regions. In the three coupling schemes, the computational runtime for single fracture propagation is reduced by 10, 20 and 50 times respectively compared to a pure PD model. Laboratory experiments on the interaction of a hydraulic fracture with a natural fracture are revisited. The model captures complex fracture behavior such as turning in the case of low stress contrast and low angle of interaction, kinking for higher stress contrast or higher angle of interaction, and fracture crossing for near-orthogonal natural fractures. Moreover, several previously reported phenomena, including fracture propagation at an angle to the principal stress directions, competing fracture growth from multiple closely spaced clusters, and interaction with layers of varying mechanical properties are successfully modeled. In addition, it is shown that by coupling peridynamics with FEM and FVM an efficient fracturing simulator is obtained that can reproduce complex fracture interactions in an arbitrarily heterogeneous reservoir.