Unified theory of Trefftz methods and numerical implications

• Autorzy: Herrera I.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

In the 1st International Workshop, devoted to Trefftz Method, the author presented an indirect approach to Trefftz Method (Trefftz-Herrera Method), while in the Second one some of the basic ideas of how to integrate different approaches to Trefftz method were introduced. The present Plenary Lecture, corresponding to the 3rd International Workshop of this series, is devoted to show that Trefftz Method, when formulated in an suitable framework, is a very broad concept capable of incorporating and unifying many numerical methods for partial differential equations. In this manner, the unified theory of Trefftz Method that was announced in the second publication of this series, has been developed. It includes Direct Trefftz Methods (Trefftz-Jirousek) and Indirect Trefftz Methods (Trefftz-Herrera). At present, the unified theory is fully developed and an overview is given here, as well as a brief description of its numerical implications.

Słowa kluczowe

EN

numerical implications; Trefftz methods

PL

metoda Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 495--514
• Opis fizyczny: Bibliogr. 27 poz., rys., tab., wykr.

Twórcy

autor

Herrera I.

• Instituto de Geofisica, Universidad Nacional Autonoma de Mexico (UNAM0, Apartado Postal 22-582, 14000, Mexico, D.F.

Bibliografia

• [1] I. Herrera. Trefftz method: A general theory. Numer M eths for PDE, 16(6): 561-580, 2000.
• [2] I. Herrera. A unified theory of domain decomposition methods. In: 14th Int. Conf. on DDM , Cocoyoc, Mex., 2002.
• [3] I. Herrera. Trefftz-Herrera Method. GAMES, 4: 369-382, 1997.
• [4] I. Herrera. Trefftz-Herrera domain decomposition. Advances in Engineering Software, 24: 43-56, 1995. Special Volume on Trefftz Method: 70 Years Anniversary.
• [5] I. Herrera. On Jirousek method and its generalizations. GAMES, 8: 325-342, 2001.
• [6] I. Herrera, R. Yates, and M. Diaz. General theory of domain decomposition: Indirect methods. Numer Meths for PDE, 18(3): 296-322, 2002.
• [7] I. Herrera. The indirect approach to domain decomposition. In: 14th Int. Conf. on DDM, Cocoyoc, Mex., 2002. Plenary Talk.
• [8] I. Herrera. Una teoria general de métodos de descomposición de dominio. In: E. 0nate, F. Zarate, G . Ayala, S. Botello, and M.A. Moreles, editors, Memorias del II Congreso Internacional de Métodos Numéricos en Ingeniería y Ciencias Aplicadas, pages 55-70, Guanajuato, Mex., 2002. Electronic publication (Plenary Talk).
• [9] M. Diaz, I. Herrera, and R. Yates. Aplicación del método indirecto de colocación trefftz-herrera a problemas elipticos en 2d. In: E. 0nate, F. Zarate, G. Ayala, S. Botello, and M.A. Moreles, editors, Memorias del II Congreso Internacional de Métodos Numéricos en Ingeniería y Ciencias Aplicadas, pages 201-214, Guanajuato, Mex., 2002. Electronic publication (Plenary Talk).
• [10] I. Herrera and Yates R. General theory of domain decomposition: Beyond schwarz methods. Numer Meths forPDE, 17(5): 495-517, 2001.
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• [23] Proceedings of 14th conferences on domain decomposition methods. International Scientific Committee for Domain Decomposition.
• [24] R. Berlanga and I. Herrera. The Gauss theorem for domain decompositions in Sobolev spaces. Applicable Analysis , 76: 67-81, 2000.
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• [26] M. Celia and I. Herrera. Solution of general differential equations using the algebraic theory approach. Numer Meths for PDE, pages 117-129, 1987.
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