中文摘要：

以曲面论为理论基础建立的高精度曲面模型（High Accuracy Surface Modelling,HASM）其插值精度较传统方法提高了多倍,为CAD和GIS系统提供了更有效的曲面模拟工具。但由于HASM需要对研究区域用相同的网格分辨率模拟,且对研究区域内每个网格点建立偏微分方程,因此,计算量和存储量问题严重制约其推广使用。适应法网格精化技术,可以根据模拟区域的地形复杂度或者精度要求调整网格分辨率,即在地形平坦区域用粗网格模拟,在复杂区域用细网格模拟。基于此理论,我们建立了适应算法的HASM。对甘肃省董志塬进行的DEM模拟表明,HASM适应算法能在保证模拟精度的同时,极大地减少了计算时间和降低存储量,从而有效解决了HASM推广使用的计算量和存储量瓶颈问题。

英文摘要：

High Accuracy Surface Modelling（HASM） constructed on the base of fundamental theory of surfaces is more accurate than the classical methods for surface modelling. However, the traditional solving method for HASM is to employ an invariable resolution to simulate the whole computational domain, which causes a huge computa- tion cost and an enormous amount of data. In general, under the same amount of sampling points, the accuracy of HASM depends on mesh spacing. The finer the finite-difference mesh, the more accurate the solution is. Unfortunately, due to limitations in computational resources, it is often impossible to use a single uniform mesh to solve a given problem to the desired accuracy. On the other hand, it is often the case that the finest resolution is only required in regions which only make up a small fraction of the computational domain. Computing an unnecessarily fine solution outside these regions represents a waste of computational resources. Adaptive mesh refinement method can select the simulation resolution adaptively with the terrain complexity or accuracy requirement, which places more grid points in regions where the terrain is complex, while using fewer grid points in flat regions. Based on the adaptive mesh refinement theory, we constructed the adaptive algorithm of HASM. Dongzhi tableland was selected for validating the effectiveness of HASM. The results show that the adaptive algorithm of HASM reduces much computation cost and data volume under the same accuracy of traditional HASM.