Time integration and the Trefftz Method Part I - First-order and parabolic problems

  • João A. Teixeira de Freitas Technical University of Lisbon

Abstract

The finite element method is applied in the time domain to establish formulations for the integration of first-order and parabolic (transient) problems. The modal decomposition concept is applied using two distinct approaches. The first is based on modal decomposition in the space domain to recover the well-established method for uncoupling the parabolic system of equations. To overcome the limitations of this approach in the implementation of large-scale, non-linear problems, the second approach that is reported consists in inducing uncoupling through modal decomposition in the time domain without using the periodic approximation that characterise analyses in the frequency domain. The methods of modal decomposition are related with the implementation of the Trefftz concept in both time and space.

Keywords

Time integration, first-order problems, parabolic problems, Trefftz method,

References

[1] A.P. Zielinski. Trefftz Method. CAMES, 4(3/4), 1997.
[2] J. A. T. Freitas and J. P. M. Almeida. Trefftz method. CAMES, 8(2/3), 2001.
[3] K. K. Tamma, X. Zhou, and D. Sha. The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications. Archives of Computational Methods in Engineering, 7(2): 67-290, 2000.
[4] J. A. T. Freitas. Mixed finite element formulation for the solution of parabolic problems. Computer Methods in Applied Mechanics and Engineering, 191: 3425-3457, 2002.
[5] J. Jirousek and Q. H. Qin. Application of hybrid-Trefftz element approach to transient heat conduction analysis. Computers and Structures, 58(1): 195-201, 1996.
Published
Jan 26, 2023
How to Cite
FREITAS, João A. Teixeira de. Time integration and the Trefftz Method Part I - First-order and parabolic problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 10, n. 4, p. 453-463, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1057>. Date accessed: 23 nov. 2024.
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Articles