Optimal shape parameters of RPIM for resolving point source two-dimensional variational problem
LI Jun-Jie1, YAN Jia-Bin2
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
Radial point interpolation method (RPIM) is a kind of high precision meshfree method. As its shape function is constructed by interpolation method in combination with radial basis function, the boundary conditions can be directly loaded. This paper utilizes RPIM to the calculation of point source two-dimensional electric field. Firstly, the approximate principle of RPIM is introduced in detail and the discrete system matrix expression is deduced corresponding to point source two-dimensional variational problem. Secondly, background grid integral technology is briefly introduced and the influence of different number of gauss points on calculation accuracy of RPIM is discussed. Lastly, the optimal range of support domain dimensionless size and the shape parameter optimal value of RPIM are obtained through numerical experiments. Studies show that RPIM has robustness for solving point source two-dimensional variational problem, and the optimal α range is 1.0 to 1.2.
李俊杰, 严家斌. RPIM求解点源二维变分问题的最优形状参数[J]. 物探与化探, 2015, 39(6): 1233-1237.
LI Jun-Jie, YAN Jia-Bin. Optimal shape parameters of RPIM for resolving point source two-dimensional variational problem. Geophysical and Geochemical Exploration, 2015, 39(6): 1233-1237.
