Abstract: High accuracy surface modeling is a new method for modeling surface by interpolation, which can model surface with high accuracy. However, its speed is a major limitation for its application in large scale data for its huge computation. To address this problem, this paper presents HASM-GA, a Graphic Processor Unit（GPU） accelerated High Accuracy Surface Modelling, to simulate surface with a significantly boost performance. This method decomposes HASM method, including discretization by finite difference and solution of huge linear system using conjugate gratitude and preconditioned, into numerous independent small tasks, so that a large scale of threads can be launched and each assigned one part of these tasks. In this way, this method accelerates HASM by fully utilizing parallel computing power of modern GPU, which has a highly parallel architecture with hundreds of multiprocessors and stream processors. The HASM-GA method through NVIDA’s Compute Unified Development Architecture（CUDA） is implemented on Quadro 2000 GPU. Both the numerical test and several real-world simulations of digital elevation model （DEM） test show that one order of magnitude speedup can be achieved compared with the traditional CPU method.

Key words: Graphic Processor Unit（GPU）, High Accuracy Surface Modelling（HASM）, surface modeling, Compute Unified Development Architecture（CUDA）

摘要： 以曲面轮为基础发展的高精度曲面建模方法（HASM）可以建立具有高精度的数字高程模型，但使用该方法需要求解偏微分方程离散产生的大规模线性方程组，计算量巨大，严重制约了对大规模数据的模拟应用；而现代GPU技术的发展使GPU越来越广泛地应用于通用计算加速。为了提高HASM方法的模拟速度，把高精度曲面模拟与GPU通用技术相结合，提出了GPU加速的高精度曲面建模方法。把HASM模拟过程中的有限差分离散、离散后的大规模线性系统求解分别使用GPU进行分解，使用共轭梯度（CG）和预处理共轭梯度方法（PCG）将求解任务分解为可以并行处理的独立的多任务，使得计算任务并行化，同时并行运行大规模线程，每个线程执行一个独立的任务，充分利用了现代GPU强大的通用计算能力，并行处理以获得加速。利用并行化加速的高精度曲面建模算法使用英伟达公司的统一计算开发架构（CUDA）编程实现，GPU采用该公司的Quadro 2000。分别应用该算法进行了数值实验和实际项目区数字高程模型（DEM）模拟实验。实验结果表明，充分利用GPU的并行处理能力加速后的HASM方法，在保证达到相同曲面模拟的精度条件下，和传统的CPU方法相比，算法可以获得超过一个数量级的加速。

关键词: 图形处理单元, 高精度曲面建模, 曲面模拟, 统一计算开发架构