Abstract: In practice, a sampled vector field is viewed as a piecewise linear field, which simplifies the interpolation of curve integration, and this assumption is widely adopted in most visualization algorithms. However, existing works omit the local coherent nature of this simplification, which could be leveraged to improve the efficiency of computation. In this paper, we reformulate the scheme of linear interpolation and integration for the simplicial mesh grid with homogeneous coordinates, and find that we can benefit significantly by simultaneously integrating multiple curves passing through a single cell. Based on this observation, we revise the 4th-order Runge–Kutta method and propose an efficient cell-wise and step-wise batch advection scheme for both 2D and 3D datasets, which is useful in the multiple particle tracing for the integral curves, e.g. streamline, pathline, timeline and streakline. We apply our method to some applications for a series of datasets, and the results show that our batch advection method can significantly speed up the curve integration while comparing with the traditional 4th-order Runge–Kutta.