Trefftz-Herrera Method

  • Ismael Herrera Instituto de Investigación en Matemáticas

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.

Keywords

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.
Published
Jun 19, 2023
How to Cite
HERRERA, Ismael. Trefftz-Herrera Method. Computer Assisted Methods in Engineering and Science, [S.l.], v. 4, n. 3-4, p. 369-382, june 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1379>. Date accessed: 23 dec. 2024.
Section
Articles