New integral equation approach to solution of diffusion equation

• Autorzy: Sladek V. , Sladek J. , Keer van R.
• Konferencja: 8th International Conference on Numerical Methods in Continuum Mechanics (September 19-24, 2000 ; Liptovsky Ján, Low Tatras ; Slovakia)
• Języki publikacji: EN

Abstrakty

EN

The paper concerns the theoretical derivation of a new formulation for solution of the initial-boundary value problems for the diffusion equation. The global and local integral equations are derived by using the fundamental solution for the Laplace differential operator. Assuming certain approximations with respect to spatial variable, we obtain a set of the ordinary differential equations (ODE) with continuous time variable. Standard methods for the time integration can be applied to these ODEs. Besides a review of the one step theta-method we propose a new integral equation method for solution of a set of linear ODEs. The paper deals also with the numerical implementation of the global and local integral equations yielding the ODEs.

Słowa kluczowe

EN

integral equation; diffusion equation

PL

równanie całkowe; równanie dyfuzji

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2002
• Tom: Vol. 9, No. 4
• Strony: 556--572
• Opis fizyczny: Bibliogr. 7 poz., tab.

Twórcy

autor

Sladek V.

• Institute of Construction and Architecture, Slovak Academy of Sciences, 842 20 Bratislava, Slovak Republic

autor

Sladek J.

• Institute of Construction and Architecture, Slovak Academy of Sciences, 842 20 Bratislava, Slovak Republic

autor

Keer van R.

• Dept. Mathematical Analysis, University of Gent, Galglaan2, B-9000, Gent, Belgium

Bibliografia

• [1] J. Balas, J. Sladek, V. Sladek. Stress Analysis by Boundary Element Method. Elsevier, Amsterdam, 1989.
• [2] T. Belytschko, Y.Y. Lu, L. Gu. Element-free Galerkin methods. Int. J. Num. Meth. Eng., 37: 229-256, 1994.
• [3] C.A. Brebbia, J.C.F. Telles, L.C. Wrobel. Boundary Element Techniques. Theory and Applications. Springer-Verlag, Berlin, 1984.
• [4] T.J.R. Hughes. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Prentice Hall, Englewood Clifs, New Jersey, 1987.
• [5] V. Sladek, J. Sladek, eds. Singular Integrals in Boundary Element Methods. CMP, Southampton, 1998.
• [6] V. Sladek, J. Sladek, S.N. Atluri, R. Van Keer. Numerical integration of singularities in meshless implementation of local boundary integral equations. Computational Mechanics, 25: 394-403, 2000.
• [7] M. Tanaka, V. Sladek, J. Sladek. Regularization techniques applied to boundary element methods. Applied. Mechanics Reviews, 47: 457-499, 1994.