A boundary collocation method for anomalous heat conduction analysis in functionally graded materials

Fu, Zhuojia; Yang, Li-Wen; Xi, Qiang; Liu, Chein‐Shan

doi:10.1016/j.camwa.2020.02.023

Cited by 58 publications

(13 citation statements)

References 58 publications

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“…Here we introduce one of the well-established numerical inverse Laplace transformation algorithms, the fixed Talbot algorithm (FTA) [7], [8], to regain the time-dependent solution ( , ) u t x in the time-domain from the Laplace-space solutions   ( )…”

Section: Numerical Inverse Laplace Transformationmentioning

confidence: 99%

Localized Collocation Trefftz Method in Conjunction With the Generalized Reciprocity Method for Transient Heat Conduction Analysis in Heterogeneous Materials

Yang

et al. 2021

WIT Transactions on Engineering Sciences

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This paper presents a novel localized collocation Trefftz method (LCTM) in conjunction with Laplace transformation for transient heat conduction analysis in heterogeneous materials under temperature loading. In contrast to the conventional CTM, the proposed LCTM divides the whole domain into many stencil support domains consisting of several discretization nodes. Inspired by the dual reciprocity method (DRM) and multiple reciprocity method (MRM), an efficient technique, the generalized reciprocity method (GRM), is proposed to derive the problem-dependent T-complete functions for approximating the particular solution of the nonhomogeneous heat conduction equations in the local subdomains. Based on the moving least square technique and T-complete functions, the LCTM numerical differentiation formulation at a certain node can be derived by using a linear combination of the T-complete functions at its adjacent discretization nodes in the related stencil support domain. It inherits the semi-analytical property from the conventional CTM and avoids the ill-conditioned dense matrix problem, which is present particularly in large-scale heat conduction analysis. Some numerical examples of heat conduction problems in heterogeneous materials are presented, and the numerical results demonstrate the accuracy and efficiency of the proposed LCTM in comparison with the known analytical solutions.

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Section: Numerical Inverse Laplace Transformationmentioning

confidence: 99%

Localized Collocation Trefftz Method in Conjunction With the Generalized Reciprocity Method for Transient Heat Conduction Analysis in Heterogeneous Materials

Yang

et al. 2021

WIT Transactions on Engineering Sciences

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“…Prior to this study, the SBM has been successfully applied to simulate the thermal behavior of FGMs [45] and the thermal conductivity identification based on traditional gradients and heuristic optimization algorithms [14,15]. To overcome the drawbacks of the traditional optimization algorithms above-mentioned, the more superior data-driven ANN model is introduced to identify the unknown thermal conductivity of FGMs.…”

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 weak-form boundary meshless methods mainly include the local boundary integral equation method [16], boundary node method [17], hybrid boundary node method [18], boundary face method [19], null-field boundary integral equation method [20], and so on. The strong-form boundary meshless methods mainly include the wave superposition method [21,22], method of fundamental solutions (MFS) [23,24], regularized meshless method [25], boundary distributed source method [26], singular boundary method (SBM) [27][28][29][30][31], collocation Trefftz method (CTM) [32,33], and so on. Due to their simpler form, integral-free and easy-to-use merits, this study focused on the strong-form boundary meshless methods based on the semi-analytical basis functions.…”

Section: Introductionmentioning

confidence: 99%

A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation

Chen

2022

Mathematics

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In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations. Unlike the traditional time discretization strategies, the proposed numerical scheme introduces the spatial–temporal radial Trefftz functions (STRTFs) as the basis functions for the spatial and temporal discretization of the transient wave equations. The STRTFs are constructed in the spatial–temporal domain, which is a combination of 3D Euclidean space and time into a 4D manifold. Moreover, since the initial and boundary conditions are imposed on the spatial–temporal domain boundaries, the original transient wave propagation problem can be converted to an inverse boundary value problem. To deal with the specified time-dependent sound source excitations, the composite multiple reciprocity technique is extended from the spatial domain to the spatial–temporal domain, which transforms the original problem with a source term into a high-order problem without a source term. By deriving the related STRTFs for the considered high-order problem, the proposed scheme only requires the node discretization on the spatial–temporal domain boundaries. The efficiency of the proposed method is numerically verified by four benchmark examples under 3D transient wave equations with specified time-dependent sound source excitation.

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A boundary collocation method for anomalous heat conduction analysis in functionally graded materials

Cited by 58 publications

References 58 publications

Localized Collocation Trefftz Method in Conjunction With the Generalized Reciprocity Method for Transient Heat Conduction Analysis in Heterogeneous Materials

Localized Collocation Trefftz Method in Conjunction With the Generalized Reciprocity Method for Transient Heat Conduction Analysis in Heterogeneous Materials

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

A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation

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