Trefftz-Herrera Method
Abstract
The author's algebraic theory of boundary value problems has permitted systematizing Trefftz method and expanding its scope. The concept of TH-completeness has played a key role for such developments. This paper is devoted to revise the present state of these matters. Starting from the basic concepts of the algebraic theory, Green- Herrera formulas are presented and Localized Adjoint Method (LAM) derived. Then the classical Trefftz method is shown to be a particular case of LAM. This leads to a natural generalization of Trefftz method and a special class of domain decomposition methods: Trefftz- Herrera domain decomposition.
References
[1] O.C. Zienkiewicz. The Finite Element Method in Engineering Science. McGraw-Hill, New York, 1977.
[2] O.C. Zienkiewicz, D.W. Kelly, P. Bettess. The coupling of the finite element method and boundary solution procedures. Int. J. Num. Math. Eng., 11: 355- 375, 1977.
[3] E. Trefftz. Ein Gregenstück zum Ritz'schen Verfahren. In: Proc. Second Int. Congress Appl. Mech. , Zurich, 1926.
[4] I. Herrera. Boundary methods. An algebraic theory. Pitman Advanced Publishing Program, Boston- LondonMelbourne, 1984.
[5] I. Herrera. Trefftz Method. In: C.A. Brebbia, ed., Topics in Boundary Element Research, Vol.l: Basic Principles and Applications, Springer- Verlag, Chapter 10, 225- 253, 1984.
[2] O.C. Zienkiewicz, D.W. Kelly, P. Bettess. The coupling of the finite element method and boundary solution procedures. Int. J. Num. Math. Eng., 11: 355- 375, 1977.
[3] E. Trefftz. Ein Gregenstück zum Ritz'schen Verfahren. In: Proc. Second Int. Congress Appl. Mech. , Zurich, 1926.
[4] I. Herrera. Boundary methods. An algebraic theory. Pitman Advanced Publishing Program, Boston- LondonMelbourne, 1984.
[5] I. Herrera. Trefftz Method. In: C.A. Brebbia, ed., Topics in Boundary Element Research, Vol.l: Basic Principles and Applications, Springer- Verlag, Chapter 10, 225- 253, 1984.
Published
2023-06-19
Issue
pp. 369-382
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Herrera, I. (2023). Trefftz-Herrera Method. Computer Assisted Methods in Engineering and Science, 4(3-4), 369-382. https://cames3.ippt.pan.pl/index.php/cames/article/view/1379
