This paper addresses the scheduling problem of coflows in identical parallel networks, which is a well-known $NP$-hard problem. Coflow is a relatively new network abstraction used to characterize communication patterns in data centers. We consider both flow-level scheduling and coflow-level scheduling problems. In the flow-level scheduling problem, flows within a coflow can be transmitted through different network cores. However, in the coflow-level scheduling problem, flows within a coflow must be transmitted through the same network core. The key difference between these two problems lies in their scheduling granularity. Previous approaches relied on linear programming to solve the scheduling order. In this paper, we enhance the efficiency of solving by utilizing the primal-dual method. For the flow-level scheduling problem, we propose a $(6-\frac{2}{m})$-approximation algorithm with arbitrary release times and a $(5-\frac{2}{m})$-approximation algorithm without release time, where $m$ represents the number of network cores. Additionally, for the coflow-level scheduling problem, we introduce a $(4m+1)$-approximation algorithm with arbitrary release times and a $(4m)$-approximation algorithm without release time. To validate the effectiveness of our proposed algorithms, we conduct simulations using both synthetic and real traffic traces. The results demonstrate the superior performance of our algorithms compared to previous approach, emphasizing their practical utility.