(1. 浙江省水利水電勘測設計院，杭州 310002；
2. 中南大學 地球科學與信息物理學院 有色資源與地質(zhì)災害探查湖南省重點實驗室，長沙 410083)
摘 要: 徑向基點插值法(RPIM)作為一種插值型無網(wǎng)格方法，為改善無網(wǎng)格點插值法(PIM)在形函數(shù)構(gòu)造過程中可能出現(xiàn)的矩陣奇異性問題而提出的一種方法，該算法支持域無量綱尺寸的選擇區(qū)間大，能更好地處理各類工程與科學計算問題。介紹了RPIM的近似原理，給出了徑向基函數(shù)形狀參數(shù)的推薦值；從大地電磁二維變分問題出發(fā)利用Galerkin法結(jié)合高斯積分公式推導出相應的系統(tǒng)矩陣離散表達式；為提高RPIM的計算效率，將RPIM與有限元法(FEM)耦合，提出了有限元－徑向基點插值法(FE-RPIM)，多個模型的數(shù)值計算驗證了RPIM精度高、處理復雜模型便利及耦合法計算復雜模型高效的特點。
關鍵字: 徑向基點插值法；有限元；無網(wǎng)格方法；大地電磁
（1. Zhejiang Design Institute of Water Conservancy and Hydroelectric Power, Hangzhou 310002, China;
2. Key Laboratory of Nonferrous Resources and Geological Hazard Detection,
School of Geosciences and Info-Physics, Central South University, Changsha 410083, China）
Abstract:Polynomial basis interpolation method (RPIM), as a kind of typical interpolation meshfree method, was proposed to overcome the defects of point interpolation method (PIM) that the construction process of the shape function involves the matrix inverse operation. This method overcomes the matrix inverse problem, and supports the wider domain dimensionless size interval to better deal with all kinds of engineering and scientific computing problems. The approximate principle of RPIM was introduced in detail, and the discrete system matrix expression corresponding to the magnetotelluric two-dimensional variational problem by combining the Galerkin method and the gauss integral formula was deduced. In order to overcome the defects of low computational efficiency of RPIM, the finite element-radial point interpolation method (FE-RPIM) based on coupling the FEM and RPIM was proposed. The conclusions were verified by the numerical calculation of several models. The results show that RPIM has the advantage of high precision and convenience to calculate complex models, and FE-RPIM has the characteristics of high calculation efficiency for complex models.
Key words: radial point interpolation method; finite element; meshfree method; magnetotelluric
