Adaptive selection strategy of shape parameters for RPIM for solving partial differential equations (A SP logging simulation case)

Citation Author(s):
Yang
Li
Submitted by:
Yang Li
Last updated:
Mon, 07/08/2024 - 15:58
DOI:
10.21227/zrwm-wn29
Data Format:
Research Article Link:
Links:
License:
55 Views
Categories:
Keywords:
0
0 ratings - Please login to submit your rating.

Abstract 

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.

Instructions: 

This is a typical case of SP simulation problem. It has been made into an installation package by us, or it can be run directly in the matlab2021a environment.

Funding Agency: 
National Natural Science Foundation of China
Grant Number: 
42074124