A meshless singular boundary method for transient heat conduction problems in layered materials

Qiu, Lin; Wang, Fajie; Lin, Ji

doi:10.1016/j.camwa.2019.05.027

Cited by 54 publications

(7 citation statements)

References 43 publications

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“…In order to get rid of the complexity of mesh generation and reduce the time of preprocessing, various meshless methods have devoted considerable attention. These approaches include the elementfree Galerkin method [8][9][10][11], the reproducing kernel particle method [12][13][14][15], the meshless local Petrov-Galerkin method [16,17], the radial basis function collocation method (RBFCM) [18,19], the generalized finite difference method (GFDM) [20][21][22][23], the singular boundary method (SBM) [24,25], the method of fundamental solutions (MFS) [26,27] and the boundary knot method (BKM) [28,29], etc. The successful application of these meshless methods fully demonstrates their development prospect.…”

Section: Introductionmentioning

confidence: 99%

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

Zhang¹,

Wang²,

Chen³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two-and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

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Section: Introductionmentioning

confidence: 99%

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

Zhang¹,

Wang²,

Chen³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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“…In SBM, the source points and the collocation points are the same set of points, and the interpolating basis function is the fundamental solution, but the SBM introduced the original intensity factors (OIFs) to eliminate the singularity of the fundamental solution, which appears when the source point and the collocation point coincide. Prior to this study, the SBM has been successfully used to solve various physical problems such as potential problems [38], heat conduction problems [39,40], wave equations [41,42] and elastic problems [43,44].…”

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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“…The developed meshless approaches can be classified into collocation-based and Galerkin-based methods. Compared with the latter, the meshless collocation methods have the advantages of no numerical quadrature and mesh generation, and some of these are the localized method of fundamental solutions (LMFS) [20][21][22], the generalized finite difference method (GFDM) [23][24][25][26][27][28][29][30][31][32][33], the localized Chebyshev collocation method [34], the singular boundary method (SBM) [35][36][37][38][39][40][41][42][43], and the localized knot method (LKM) [44].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Wang

Kim

2022

Mathematics

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In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method.

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A meshless singular boundary method for transient heat conduction problems in layered materials

Cited by 54 publications

References 43 publications

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

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

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

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