A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques

Ahmadvand, M.; Esmaeilbeigi, Mohsen; Kamandi, Ahmad; Yaghoobi, Farajollah Mohammadi

doi:10.1007/s10589-018-0051-x

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…Augarde and Deeks pointed out this fact in [25]; see also [29]. In fact, the displacements given in (19) are not an exact solution of the plane stress equations only if the load is distributed parabolically (the third equation in (20)) and if the essential boundary conditions are applied at x � 0 according to (19). To fairly compare the numerical errors computed by different solution methods, Simonenko et al suggested using Dirichlet boundary conditions given by (1) in all boundaries of the beam and comparing the numerical solutions with the exact solution for displacements (19) and stresses (20) [29].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the same paper, Rippa also proposed a very interesting algorithm, called the Leave-One-Out Cross Validation (LOOCV) algorithm, to select a good value of the shape parameter. Recently, some improvements of the LOOCV algorithm have been deeply studied; see [16][17][18][19][20] and references therein. Other techniques for finding the optimal shape parameter include the energy-based method [7,9], the sample solution approach [10], the interval method [21], and so on.…”

Section: Introductionmentioning

confidence: 99%

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A Coupled RBF Method for the Solution of Elastostatic Problems

Chen

Cao

2021

Mathematical Problems in Engineering

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Radial basis function (RBF) has been widely used in many scientific computing and engineering applications, for instance, multidimensional scattered data interpolation and solving partial differential equations. However, the accuracy and stability of the RBF methods often strongly depend on the shape parameter. A coupled RBF (CRBF) method was proposed recently and successfully applied to solve the Poisson equation and the heat transfer equation (Appl. Math. Lett., 2019, 97: 93–98). Numerical results show that the CRBF method completely overcomes the troublesome issue of the optimal shape parameter that is a formidable obstacle to global schemes. In this paper, we further extend the CRBF method to solve the elastostatic problems. Discretization schemes are present in detail. With two elastostatic numerical examples, it is found that both numerical solutions of the CRBF method and the condition numbers of the discretized matrices are almost independent of the shape parameter. In addition, even if the traditional RBF methods take the optimal shape parameter, the CRBF method achieves better accuracy.

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