The nominal electric field calculation of HVDC transmission lines is the basis of its electromagnetic environment analysis.Considering the effect of uneven terrain under the transmission line

an adaptive boundary element method with rapidly filling matrix entries is proposed

which estimates the posteriori error based on the calculated results to adaptively mesh the boundary elements.In order to avoid repeatedly calculatingthe matrix elements in the process of adaptive iterations

this paper uses the adaptive cross-product approximation method to accelerate filling matrix elements

which can reduce the requirements of computational storage.Meanwhile

a pre-conditioning technique is utilized to improve the compu tational efficiency of the iterative solver.Numerical examples prove the correctness and validity of the method proposed in this paper.This method can establish a foundation for analyzing the electromagnetic environment of HVDC transmission lines with complex terrain siutations.