Computational heat transfer with spectral graph theory: Quantitative verification

Kevin D. Cole, M. Reza Yavari, Prahalada K. Rao

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The objective of this paper is to quantify the precision of a novel approach for computational heat transfer modeling based on spectral graph theory. Two benchmark heat transfer problems with planar boundaries, for which exact analytical solutions are available, are used to determine the precision of temperature predictions obtained from spectral graph, finite difference (one-dimensional), and finite element (three-dimensional) methods. These studies show that the spectral graph approach captures the temperature trends in the benchmark case studies with error in the range of 2% to 10% depending on the location in the body. These verification studies also provide an approach to calibrate the numerical parameters in the new method. The spectral graph approach is applied for predicting the thermal history of a complex three-dimensional additive manufactured (3D printed) part. The temperature trends in a 50-layer part are computed 2.3 times faster than a commercial finite-element software package, and the results differ by less than 7.5%. Further improvements in the computational speed of the spectral graph approach are expected through code optimization and parallelization. This work has far-reaching practical implications for predicting thermal-induced defects in a variety of manufacturing processes including casting and additive manufacturing.

Original languageEnglish (US)
Article number106383
JournalInternational Journal of Thermal Sciences
StatePublished - Jul 2020


  • Additive manufacturing
  • Diffusion equation
  • Discrete Laplacian matrix
  • Finite element analysis
  • Green's function
  • Heat conduction

ASJC Scopus subject areas

  • Condensed Matter Physics
  • General Engineering


Dive into the research topics of 'Computational heat transfer with spectral graph theory: Quantitative verification'. Together they form a unique fingerprint.

Cite this