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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| Vydáno v: | Computers & structures Ročník 249; s. 106513 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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New York
Elsevier Ltd
01.06.2021
Elsevier BV |
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| ISSN: | 0045-7949, 1879-2243 |
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| Abstract | •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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| AbstractList | •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. 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. |
| ArticleNumber | 106513 |
| Author | Nie, C.B. Gao, Q. |
| Author_xml | – sequence: 1 givenname: Q. surname: Gao fullname: Gao, Q. email: qgao@dlut.edu.cn – sequence: 2 givenname: C.B. surname: Nie fullname: Nie, C.B. email: ncbchina@mail.dlut.edu.cn |
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| Keywords | Chebyshev expansion method Transient heat conduction Matrix exponential Crank-Nicholson method Large-scale problems |
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| Snippet | •An efficient method is proposed for large-scale heat conduction problems.•The matrix exponential is approximated with Chebyshev matrix polynomials.•The... In this paper, an efficient and accurate Chebyshev expansion method is presented for solving large-scale transient heat conduction problems. Based on the... |
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| SubjectTerms | 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 |
| Title | An accurate and efficient Chebyshev expansion method for large-scale transient heat conduction problems |
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