An efficient localized Trefftz-based collocation scheme for heat conduction analysis in two kinds of heterogeneous materials under temperature loading

Xi, Qiang; Fu, Zhuojia; Zhang, Chuanzeng; Yin, Deshun

doi:10.1016/j.compstruc.2021.106619

Cited by 44 publications

(6 citation statements)

References 51 publications

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“…In addition, the present STRTCM scheme cannot handle the problems with heterogeneous materials because it is a nontrivial task to derive the corresponding semi-analytical basis solutions. For this, combining with the localized collocation scheme [43] and the extended multiple reciprocity method-generalized reciprocity method [44]-may be a good way. These topics are under study and will be reported in a subsequent paper.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

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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“…Indeed, the two approaches have distinct advantages. Meshless Collation Methods are suitable for large-scale computation with high computational efficiency [28][29][30]. On the other hand, spectral Collocation Methods with outstanding error properties potentially involve Fourier Series expansions [31].…”

Section: Literature Reviewmentioning

confidence: 99%

Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions

Kang¹,

Abdella²,

Pollanen³

et al. 2022

AAMM

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This paper presents the numerical solution of the time-dependent Gross-Pitaevskii Equation describing the movement of quantum mechanics particles under non-homogeneous boundary conditions. Due to their inherent non-linearity, the equation generally can not be solved analytically. Instead, a highly accurate approximation to the solutions defined in a finite domain is proposed, using the Crank-Nicolson difference method and Sinc Collocation numerical methods to discretize separately in time and space. Two Sinc numerical approaches, involving the Sinc Collocation Method (SCM) and the Sinc Derivative Collocation Method (SDCM), are easy to implement. The results demonstrate that Sinc numerical methods are highly efficient and yield accurate results. Mainly, the SDCM decays errors faster than the SCM. Future work suggests that the SDCM can be extensively applied to approximate solutions under other boundary conditions to demonstrate its broad applicability further.

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“…Liu and Fan et al [36] developed the localized Trefftz method and applied it to numerical solutions of Laplace equation and biharmonic equation. Xi and Fu et al [37] presented a localized collocation Trefftz method for heat conduction analysis in two kinds of heterogeneous materials (functionally graded materials and multi-medium materials) under temperature loading. Wang et al proposed a localized SBM and a localized Chebyshev collocation method [38,39].…”

Section: Introductionmentioning

confidence: 99%

Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material

null¹,

Wang²

2023

AAMM

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This paper documents the first attempt to apply a localized method of fundamental solutions (LMFS) to the acoustic analysis of car cavity containing soundabsorbing materials. The LMFS is a recently developed meshless approach with the merits of being mathematically simple, numerically accurate, and requiring less computer time and storage. Compared with the traditional method of fundamental solutions (MFS) with a full interpolation matrix, the LMFS can obtain a sparse banded linear algebraic system, and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains. In the LMFS, only circular or spherical fictitious boundary is involved. Based on these advantages, the method can be regarded as a competitive alternative to the standard method, especially for high-dimensional and large-scale problems. Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.

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An efficient localized Trefftz-based collocation scheme for heat conduction analysis in two kinds of heterogeneous materials under temperature loading

Cited by 44 publications

References 51 publications

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

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

Sinc Collocation Numerical Methods for Solving Two-Dimensional Gross-Pitaevskii Equations with Non-Homogeneous Dirichlet Boundary Conditions

Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material

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