A simple empirical formula of origin intensity factor in singular boundary method for two-dimensional Hausdorff derivative Laplace equations with Dirichlet boundary

Wang, Fajie; Chen, Wen; Hua, Qingsong

doi:10.1016/j.camwa.2018.05.041

Cited by 32 publications

(3 citation statements)

References 21 publications

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“…For the parameter identification problem, it is essential to first solve the direct problem. The SBM was proposed by Chen and collaborators [31][32][33][34][35] and can be viewed as an improvement in MFS [36,37] to solve some boundary value problems of partial differential equations. It can also be regarded as a modified method of BEM, as it inherited their advantages but possesses its unique innovation.…”

Section: Introductionmentioning

confidence: 99%

Thermal Conductivity Identification in Functionally Graded Materials via a Machine Learning Strategy Based on Singular Boundary Method

Xu,

Fu,

2022

Mathematics

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A machine learning strategy based on the semi-analytical singular boundary method (SBM) is presented for the thermal conductivity identification of functionally graded materials (FGMs). In this study, only the temperature or heat flux on the surface or interior of FGMs can be measured by the thermal sensors, and the SBM is used to construct the database of the relationship between the thermal conductivity and the temperature distribution of the functionally graded structure. Based on the aforementioned constructed database, the artificial neural network-based machine learning strategy was implemented to identify the thermal conductivity of FGMs. Finally, several benchmark examples are presented to verify the feasibility, robustness, and applicability of the proposed machine learning strategy.

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Section: Introductionmentioning

confidence: 99%

Thermal Conductivity Identification in Functionally Graded Materials via a Machine Learning Strategy Based on Singular Boundary Method

Xu,

Fu,

2022

Mathematics

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“…Recently, a fractal derivative diffusion model was developed as a powerful tool to characterize anomalous diffusion in complex systems [14][15][16][17][18][19][20][21]. As shown in [15,16], the definition of fractal derivative was improved and employed to model water diffusion transport in unsaturated porous media.…”

Section: Introductionmentioning

confidence: 99%

Simulating chloride penetration in fly ash concrete by a fractal derivative model

Liu

Băleanu

2019

THERM SCI

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In the real engineering field, the chloride ions behave abnormal diffusion phenomena in concrete caused by different compositions of the concrete which lead to the complex physical and chemical properties. This paper utilizes a fractal derivative model and a fractional derivative model to describe the diffusion phenomena. Furthermore, according to actual experimental data in the field, the fractional and fractal model can simulate the diffusion behavior of chloride ions in concrete. In comparison to the fractional derivative model, the fractal derivative model gives a simpler mathematical expression and lower calculation costs. In addition, the linear regression analysis method is used to establish an effective relationship between the internal composition of concrete and the parameters of fractal model such as fractal order, α, and diffusion coefficient, D. As a result, the fractal model with the parameters estimated by previous relationship can predict the diffusion behavior of chloride ions.

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“…Another effective method, finite element methods, is also widely used for the numerical solution, see [24,25]. Another popular method for the direct and inverse heat conduction problems is the singular boundary method, we can see [26][27][28][29][30] for further reading.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

et al. 2019

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In this paper, we give an effective numerical method for the heat conduction problem connected with the Laplace equation. Through the use of a single-layer potential approach to the solution, we get the boundary integral equation about the density function. In order to deal with the weakly singular kernel of the integral equation, we give the projection method to deal with this part, i.e., using the Lagrange trigonometric polynomials basis to give an approximation of the density function. Although the problems under investigation are well-posed, herein the Tikhonov regularization method is not used to regularize the aforementioned direct problem with noisy data, but to filter out the noise in the corresponding perturbed data. Finally, the effectiveness of the proposed method is demonstrated using a few examples, including a boundary condition with a jump discontinuity and a boundary condition with a corner. Whilst a comparative study with the method of fundamental solutions (MFS) is also given.

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A simple empirical formula of origin intensity factor in singular boundary method for two-dimensional Hausdorff derivative Laplace equations with Dirichlet boundary

Cited by 32 publications

References 21 publications

Thermal Conductivity Identification in Functionally Graded Materials via a Machine Learning Strategy Based on Singular Boundary Method

Thermal Conductivity Identification in Functionally Graded Materials via a Machine Learning Strategy Based on Singular Boundary Method

Simulating chloride penetration in fly ash concrete by a fractal derivative model

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

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