An accurate and efficient Chebyshev expansion method for large-scale transient heat conduction problems

•An efficient method is proposed for large-scale heat conduction problems.•The matrix exponential is approximated with Chebyshev matrix polynomials.•The computational cost of the proposed method decreases with time step increases.•The proposed method is proved to be unconditionally stable. In this p...

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Bibliographic Details
Published in:Computers & structures Vol. 249; p. 106513
Main Authors: Gao, Q., Nie, C.B.
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.06.2021
Elsevier BV
Subjects:
Boundary conditions
Chebyshev approximation
Chebyshev expansion method
Computational efficiency
Computing costs
Conduction heating
Conductive heat transfer
Crank-Nicholson method
Heat sources
Large-scale problems
Mathematical analysis
Matrix algebra
Matrix exponential
Matrix methods
Polynomials
Sparse matrices
Stability analysis
Thermal analysis
Transient heat conduction
Chebyshev expansion method
Transient heat conduction
Matrix exponential
Crank-Nicholson method
Large-scale problems
ISSN:0045-7949, 1879-2243
Online Access:Get full text
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Summary:•An efficient method is proposed for large-scale heat conduction problems.•The matrix exponential is approximated with Chebyshev matrix polynomials.•The computational cost of the proposed method decreases with time step increases.•The proposed method is proved to be unconditionally stable. In this paper, an efficient and accurate Chebyshev expansion method is presented for solving large-scale transient heat conduction problems. Based on the Chebyshev expansion method, the matrix exponential is approximated with a series of Chebyshev matrix polynomials. Furthermore, according to the characteristics of practical thermal loads, an efficient method is developed to decrease the computational cost of temperature response induced by heat sources and nonhomogeneous boundary conditions. A theoretical method is developed to investigate the relationship of the computational cost of the proposed method and the time step, and the results indicate that under the given truncation criterion, the computational cost decreases with the increasing of the time step. Since the computational cost is sparse matrix–vector multiplications and only a few of vectors are stored in the computer memory, the proposed method has great advantages both in computational cost and storage requirement for large-scale transient heat conduction problems. In addition, a stability analysis is developed and the results show that the proposed method is unconditionally stable. Numerical examples exhibit that the proposed method has excellent efficiency and accuracy.
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2021.106513