An efficient boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials under heat source load

  • Qiang Xi
  • Zhuo-Jia FuEmail author
  • Timon Rabczuk
Original Paper


This paper presents a boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials (FGMs) with heat source load. In the proposed scheme, Laplace transformation and the numerical inverse Laplace transformation (NILT) are implemented to avoid the troublesome time-stepping effect on numerical efficiency. The collocation Trefftz method (CTM) coupled with composite multiple reciprocity method is used to obtain the high accurate results in the solution of nonhomogeneous problems in Laplace-space domain. The extended precision arithmetic is introduced to overcome the ill-posed issues generated from the CTM simulation, the NILT process and the large-size-ratio FGM. Heuristic error analysis and numerical investigation are presented to demonstrate the effectiveness of the proposed scheme for transient thermal analysis. Several benchmark examples are considered under large-size-ratio FGMs with some specific spatial variations (quadratic, exponential and trigonometric functions). The proposed scheme is validated in comparison with known analytical solutions and COMSOL simulation.


Collocation Trefftz scheme Numerical inverse Laplace transformation Extended precision arithmetic Transient thermal analysis Large size ratio 



The authors thank the anonymous reviewers of this article for their very helpful comments and suggestions to significantly improve the academic quality of this article. The work described in this paper was supported by the National Science Funds of China (Grant No. 11772119), the Fundamental Research Funds for the Central Universities (Grant No. 2016B06214), the Foundation for Open Project of State Key Laboratory of Structural Analysis for Industrial Equipment (Grant No. GZ1707), Qing Lan Project.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Coastal Disaster and Defence, Ministry of EducationHohai UniversityNanjingChina
  2. 2.Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and MaterialsHohai UniversityNanjingChina
  3. 3.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  4. 4.Institute of Structural MechanicsBauhaus-University WeimarWeimarGermany

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