Solutions of Two-Dimensional Wave Equation using some Form of the Trefftz Functions
Faculty of Management and Computer Modelling, Kielce University of Technology
Al. Tysiąclecia PP 7, 25-314 Kielce, Poland
e-mail: sokala@tu.kielce.pl
Received:
Received: 14 May 2008; published online: 19 November 2008
DOI: 10.12921/cmst.2008.14.02.111-122
OAI: oai:lib.psnc.pl:649
Abstract:
The paper presents a specific technique to generate the Trefftz functions for the two-dimensional wave equation. The obtained functions are used to determine approximate solutions of some tested problems. The accuracy of the method is discussed.
Key words:
References:
[1] M. Ciałkowski, Heat functions and their application to solving heat conduction and mechanics problems (in Polish), Poznań University of Technology, Poznań, 2000.
[2] M. Ciałkowski and A. Frąckowiak, Funkcje cieplne i pokrewne w rozwiązywaniu wybranych równań mechaniki, Część I. Rozwiązywanie niektórych równań różniczkowych za pomocą operacji odwrotnych, Uniwersytet Zielonogórski. Studia i Materiały. Technika 3, s. 7-69, Zielona Góra 2003.
[3] A. Maciąg and J. Wauer, Wave polynomials for solving different types of two-dimensional wave equations, Computer Assisted Mechanics and Engineering Sciences (CAMES) 12, 363-378 (2005).
[4] A. Maciąg, B. Maciejewska and M. Sokała, 2D wave polynomials as base function in modified FEM (in preparation).
[5] E.B. Magrab, Vibrations of elastic structural members, SIJTHOFF&NOORDHOFF, Maryland USA, 1979.
[6] M.M. Smirnow, Problems of partial differential equations (in Polish), PWN, Warszawa, 1976.
[7] M. Sokała, Analytical and numerical method of solving heat conduction problems with the use of heat functions and inverse operations (in Polish), Doctoral thesis, Poznań, 2004.
The paper presents a specific technique to generate the Trefftz functions for the two-dimensional wave equation. The obtained functions are used to determine approximate solutions of some tested problems. The accuracy of the method is discussed.
Key words:
References:
[1] M. Ciałkowski, Heat functions and their application to solving heat conduction and mechanics problems (in Polish), Poznań University of Technology, Poznań, 2000.
[2] M. Ciałkowski and A. Frąckowiak, Funkcje cieplne i pokrewne w rozwiązywaniu wybranych równań mechaniki, Część I. Rozwiązywanie niektórych równań różniczkowych za pomocą operacji odwrotnych, Uniwersytet Zielonogórski. Studia i Materiały. Technika 3, s. 7-69, Zielona Góra 2003.
[3] A. Maciąg and J. Wauer, Wave polynomials for solving different types of two-dimensional wave equations, Computer Assisted Mechanics and Engineering Sciences (CAMES) 12, 363-378 (2005).
[4] A. Maciąg, B. Maciejewska and M. Sokała, 2D wave polynomials as base function in modified FEM (in preparation).
[5] E.B. Magrab, Vibrations of elastic structural members, SIJTHOFF&NOORDHOFF, Maryland USA, 1979.
[6] M.M. Smirnow, Problems of partial differential equations (in Polish), PWN, Warszawa, 1976.
[7] M. Sokała, Analytical and numerical method of solving heat conduction problems with the use of heat functions and inverse operations (in Polish), Doctoral thesis, Poznań, 2004.