Multiquadric Radial Basis Function Method for Boundary Value and Free Vibration Problems

2013 ◽  
Vol 4 (2) ◽  
pp. 138 ◽  
Author(s):  
R. K. Misra ◽  
Sushil Kumar
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.


2018 ◽  
Vol 34 (3) ◽  
pp. 959-981 ◽  
Author(s):  
Nam Mai-Duy ◽  
Deepak Dalal ◽  
Thi Thuy Van Le ◽  
Duc Ngo-Cong ◽  
Thanh Tran-Cong

2020 ◽  
pp. 112067212090295 ◽  
Author(s):  
Gabor Nemeth ◽  
Laszlo Modis

Purpose: The aim was to assess the postoperative results of a biometric method using artificial intelligence (Hill–radial basis function 2.0), and data from a modern formula (Barrett Universal II) and the Sanders–Retzlaff–Kraft/Theoretical formula. Methods: Phacoemulsification and biconvex intraocular lens implantation were performed in 186 cataractous eyes. The diopters of intraocular lens were established with the Hill–radial basis function method, based on biometric data obtained using the Aladdin device. The required diopters of the intraocular lens were also calculated by the Barrett Universal II formula and with the Sanders–Retzlaff–Kraft/Theoretical formula. The differences between the manifest postoperative refractive errors and the planned refractive errors were calculated, as well as the percentage of eyes within ±0.5 D of the prediction error. The mean- and the median absolute refractive errors were also determined. Results: The mean age of the patients was 70.13 years (SD = 10.67 years), and the mean axial length was 23.47 mm (range = 20.72–28.78 mm). The percentage of eyes within a prediction error of ±0.5 D was 83.62% using the Hill–radial basis function method, 79.66% with the Barrett Universal II formula, and 74.01% in the case of the Sanders–Retzlaff–Kraft/Theoretical formula. The mean- and the median absolute refractive errors were not statistically different. Conclusion: Clinical success was the highest when using the biometric method, based on pattern recognition. The results obtained using Barrett Universal II came a close second. Both methods performed better compared to a traditionally used formula.


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