摘要：Radial basis function (RBF) is a basis function suitable for scattered data interpolation and high dimensional function interpolation, wherein the independent shape parameters have a direct impact on the accuracy of calculation results. Research in this field is mostly concerned with the shape parameter selection strategy based on the premise of global distribution or block regional distribution. In this paper, a shape parameter selection strategy is proposed, which is used for the local RBF collocation method (LRBF) for solving partial differential equations. It overcomes many limitations of the traditional methods applied to LRBF. In this strategy, a set of twin matrices similar to the interpolation matrix are constructed to evaluate the error of the model. In addition, the penalty term contained in the twin matrix is used to relax the influence of the far end region on the target node. Since the objective problem is nonlinear, a particle swarm optimization algorithm (PSO) is employed to minimize the training objective and adjust the shape parameters of the basis function at each iteration. Extensive numerical results showed the effectiveness of the error estimation strategy, by providing a good shape parameter and better solution accuracy. At the end of the paper, the generality of the shape parameter optimization framework based on this strategy is discussed through three examples. ? 2022 Elsevier Inc.

ISSN号：0096-3003

卷、期、页： 卷440

发表日期：2023-03-01

期刊分区（SCI为中科院分区）：二区

收录情况：SCI（科学引文索引印刷版）,EI（工程索引）,SCIE（科学引文索引网络版）

发表期刊名称：Applied Mathematics and Computation

通讯作者：李洋,尹哲旭,陈韵,孟晋

第一作者：刘得军

论文类型：期刊论文

论文概要：李洋,刘得军,尹哲旭,陈韵,孟晋，Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations，Applied Mathematics and Computation，2023， 卷440

论文题目：Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations