|
|
- 2017
基于RASM的紧支撑径向基函数自适应并行地形插值方法
|
Abstract:
快速、准确地对地形进行重建以生成数字高程模型是地理信息表达的重要研究内容，径向基函数（radial basis function，RBF）作为一种插值性能较优的空间插值方法，特别适合于重建复杂的地形模型，但随着已知地形采样点数量的增加，RBF插值模型求解速度变慢，同时插值矩阵过于庞大而导致插值模型求解困难甚至求解失败。针对这个问题，本文基于区域分解和施瓦兹并行原理进行地形插值，以紧支撑径向基函数（compact support RBF，CSRBF）构建基于所有地形采样数据的全局插值矩阵，并自适应求解子区域CSRBF插值节点紧支撑半径，基于限制性加性施瓦兹方法（restricted additive Schwarz method，RASM）采用多核并行架构对各局部子区域的插值矩阵进行求解。以某地区数字高程模型（DEM）数据进行插值实验，结果表明，本文方法能够对大规模地形数据进行准确重建，并且具有较高的求解效率
| [1] | Liu Po, Gong Jianhua. Parallel Construction of Global Pyramid for Large Remote Sensing Images[J].<em>Geomatics and Information Science of Wuhan University</em>, 2016, 41(1):117-122(刘坡, 龚建华. 大规模遥感影像全球金字塔并行构建方法[J]. 武汉大学学报·信息科学版, 2016, 41(1):117-122) |
| [2] | Franke R. Scattered Data Interpolation:Tests of Some Methods[J]. <em>Mathematics of Computation</em>, 1982, 38(157):181-200 |
| [3] | Saad Y. A Flexible Inner-outer Preconditioned GMRES Algorithm[J]. SIAM Journal on Scientific Computing, 1993, 14(2):461-469 |
| [4] | Li Zhilin, Zhu Qing. Digital Elevation Model[M]. Wuhan, China:Wuhan University Press, 2001:125-139(李志林, 朱庆. 数字高程模型[M]. 武汉:武汉大学出版社, 2001:125-139) |
| [5] | Tang Guoan, Yang Xin. ArcGIS Spatial Analysis Experiment Tutorial[M]. Beijing, China:Science Press, 2006:363-422(汤国安, 杨昕. ArcGIS空间分析实验教程[M]. 北京:科学出版社, 2006, 363-422) |
| [6] | Yokota R, Barba L A, Knepley M G. PetRBF-A Parallel O(<em>N</em>) Algorithm for Radial Basis Function Interpolation with Gaussians[J]. <em>Computer Methods in Applied Mechanics and Engineering</em>, 2010, 199(25):1793-1804 |
| [7] | Fasshauer G E. Meshfree Approximation Methods with MATLAB[M]. Singapore:World Scientific, 2007 |
| [8] | Duan Ping, Sheng Yehua, Zhang Siyang, et al. A 3D Local RBF Spatial Interpolation Considering Anisotropy[J]. <em>Geomatics and Information Science of Wuhan University</em>, 2015, 40(5):632-637(段平, 盛业华, 张思阳, 等. 顾及异向性的局部径向基函数三维空间插值[J]. 武汉大学学报·信息科学版, 2015, 40(5):632-637) |
| [9] | Lv Haiyang, Sheng Yehua, Duan Ping, et al.A Hierarchical RBF Interpolation Method Based on Local Optimal Shape Parameters[J]. <em>Journal of Geo-information Science</em>, 2015, 17(3):260-267(吕海洋, 盛业华, 段平, 等. 局部最优形态参数的RBF分块地形插值方法与实验[J]. 地球信息科学学报, 2015, 17(3):260-267) |
| [10] | Carr J C,Beatson R K, Cherrie J B, et al. Reconstruction and Representation of 3D Objects with Radial Basis Functions[C]. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques. New York, USA, 2001 |
| [11] | Beatson RK, Light W A, Billings S. Fast Solution of the Radial Basis Function Interpolation Equations:Domain Decomposition Methods[J]. <em>SIAM Journal on Scientific Computing</em>, 2001, 22(5):1717-1740 |
| [12] | Wang Q, Pan Z, Bu J, et al. Parallel RBF-based Reconstruction from Contour Dataset[C]. Computer Aided Design and Computer Graphics, 200710th IEEE International Conference, Piscataway, USA, 2007 |
| [13] | Cai X C, Sarkis M. A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems[J]. <em>SIAM Journal on Scientific Computing</em>, 1999, 21(2):792-797 |
| [14] | Hardy R L.Theory and Applications of the Multiquadric-biharmonic Method 20 Years of Discovery 1968-1988[J]. <em>Computers & Mathematics with Applications</em>, 1990, 19(8):163-208 |
| [15] | Beatson R K, Cherrie J B, Mouat C T. FastFitting of Radial Basis Functions:Methods Based on Preconditioned GMRES Iteration[J]. <em>Advances in Computational Mathematics</em>, 1999, 11(2-3):253-270 |
| [16] | WendlandH. Fast Evaluation of Radial Basis Functions:Methods Based on Partition of Unity[M]//Approximation Theory X:Wavelets, Splines, and Applications. Nashville, Tennessee, USA:Vanderbilt University Press, 2002 |
