The selection of shape parameter and fictitious radius for RBF collocation method using the modified Franke formula and effective condition number

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY Engineering Analysis with Boundary Elements Pub Date : 2025-02-18 DOI:10.1016/j.enganabound.2025.106159

Xinxiang Li , Han Liu

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引用次数: 0

Abstract

The shape parameter

c

and the fictitious radius

R

are important parameters that affect the performance of the polynomial-augmented RBF collocation method (RBFCM) with fictitious centers. It is known that the RBFCM can reduce the accuracy dependency on shape parameter by using extra polynomial constraints. Moreover, we find that calculation inaccuracies exhibit a strong association with the effective condition numbers for various fictitious radii. While there have been some methods for selecting the shape parameter, an approach that allows for the simultaneous selection of

c

and

R

has not yet been widely researched. In this paper, we propose a systematic method to choose parameters for the polynomial-augmented RBFCM with fictitious centers. The method utilizes the effective condition number to find an appropriate fictitious radius

R

and the modified Franke formula to select a good shape parameter

c

. Five examples of second and fourth order PDEs in 2D and 3D are presented to demonstrate the effectiveness of the proposed method.

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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.