Trefftz spectral method for elliptic equations of general type

• Autorzy: Reutskiy S. , Tirozzi B.
• Języki publikacji: EN

Abstrakty

EN

A new numerical method for 2D linear elliptic partial differential equations in an arbitrary geometry is presented. The special feature of the method presented is that the trial functions, which are used to approximate a solution, satisfy the PDE only approximately. This reduction of the requirement to the trial functions extends the field of application of the Trefftz method. The method is tested on several one- and two-dimensional problems.

Słowa kluczowe

EN

Trefftz method; elliptic equation

PL

metoda Trefftza; równanie eliptyczne

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2001
• Tom: Vol. 8, No. 4
• Strony: 629--644
• Opis fizyczny: Bibliogr. 15 poz., tab.

Twórcy

autor

Reutskiy S.

• Magnetohydrodynamics Laboratory, P. O. Box 136, Moskovski av., 199, 310037, Kharkov, Ukraine

autor

Tirozzi B.

• Physics Department, University of Rome "La Sapienza", P.le A. Moro 2, 00185 Rome, Italy

Bibliografia

• [1] G.H. Hardy. Divergent Series , Oxford, 1949.
• [2] I. Herrera, Trefftz Method. In: C.A. Brebbia, ed., Progress in Boundary Element Methods, v.3, Wiley, New York, 1983.
• [3] J. Jirousek, A. Wróblewski. T-elements: State of the Art and Future Trends, Archive of Computational Methods in Engineering, 3/4: 323.434, 1996.
• [4] C. Lanczos. Applied Analysis , Prentice Hall Inc., New York, 1956.
• [5] S.A. Lifits, S.Yu. Reutskiy, B. Tirozzi. A New Tre¤tz.typeMethod for Solving Bound- ary Value Problems, ARI , 50: 85.95, 1997.
• [6] S.A. Lifits, S.Yu. Reutskiy, B. Tirozzi. Trefftz Spectral Method for Initial-Boundary Problems, Comp. Ass. Mech. and Eng. Sci., 4: 549.565, 1997.
• [7] S.A. Lifits, S.Yu. Reutskiy, B. Tirozzi. A Quasi Trefftz.type Spectral Method for Solving Initial Value Problems with Moving Boundaries, Math. Models Meth. in App. Sci. , 7: 385.404, 1997.
• [8] G. Pontrelli, S. Lifits, S. Reutskiy, B. Tirozzi. Quasi Trefftz Spectral method for Stokes Problem, Math. Models Meth. in App. Sci. , 7: 1187.2012, 1997.
• [9] S.Yu. Reutskiy. The Method of Equivalent Charges in Calculations of MHD-Flow in a Complex Geometry, Magnetohydrodynamics, N 2, 66.74, 1990.
• [10] S. Reutskiy, B. Tirozzi, Quasi Trefftz Spectral Method for Separable Linear Elliptic Equations, Comp. Math. with Appl. , 37, 47.74, 1999.
• [11] V. Smelov, Sturm-Liouville Operators and Their Non-Classic Applications, Nauka, Novosibirsk, 1992.
• [12] B. Szybiński, A.P. Zieliński. Alternative T.Complete Systems of Sharpe Functions Applied in Analitical Trefftz Finite Elements. Num. Meth. Part. Diff. Eq., 11: 375.388, 1995.
• [13] A.P. Zieliński, O.C. Zienkiewicz. Generalized Finite Element Analysis with T-complete Boundary Solution Functions. Int. J. Numer. Meth. Eng., 21: 509.528, 1985.
• [14] A.P. Zieliński. On Trial Functions Applied in the Generalized Trefftz Method. Advances in Engineering Software, 24: 147.155, 1995.
• [15] A.P. Zieliński, I. Herrera. Trefftz Method: Fitting Boundary Conditions. Int. J. Num. Meth. Eng., 24: 871.891, 1987.