A Matrix Decomposition MFS Algorithm For Helmholtz Problems

• Autorzy: Karageorghis A. , Smyrlis Y. S.
• Konferencja: Symposium Vibrations in Physical Systems (XXI ; 26-29.05.2004 ; Poznań-Kierz, Polska)
• Języki publikacji: EN

Abstrakty

EN

The Method of Fundamental Solutions (MFS) is a boundary-type method for the solution of certain elliptic boundary value problems. In this work, we develop an efficient matrix decomposition MFS algorithm for solution of exterior Helmholtz problems in domains surrounding circular domains in two dimensions. These ideas are extended for the solution of exterior Helmholtz problems in domains surrounding axisymmetric domains.

Słowa kluczowe

EN

method of fundamental solutions; MFS; Helmholtz equation; matrix decomposition

PL

metoda rozwiązań podstawowych; MFS; równanie Helmholtza; rozkład macierzy

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2004
• Tom: Vol. 21
• Strony: 47--54
• Opis fizyczny: Bibliogr. 16 poz., wz.

Twórcy

autor

Karageorghis A.

• Departament of Mathematics and Statistics, University of Cyprus, P. O. Box 20537, 1678 Nicosia

autor

Smyrlis Y. S.

• Departament of Mathematics and Statistics, University of Cyprus, P. O. Box 20537, 1678 Nicosia

Bibliografia

• 1. M. ABRAMOWITZ I. A. and STEGUN, Handbook of Mathematical Functions, Verlag Harri Deutsch, Thun 1984.
• 2. B. BIAŁECKI and G. FAIRWEATHER, Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions, J. Comp. Appl. Math., 46, 369-386, 1993.
• 3. P. J. Davis, Circulant Matrices, John Wiley and Sons, New York, 1979.
• 4. A. DOICU, Yu. EREMIN and T. WRIEDT. Acoustic and Electromagnetic Sources, Analysis using Discrete Sources, Academic Press, New York, 2000.
• 5. G. FAIRWEATHER and A. KARAGEORGHIS, The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math., 9, 69-95. 1998.
• 6. G. FAIRWEATHER and A. KARAGEORGHIS, AND P. A. MARTIN, The method of fundamental solutions for scattering and radiation problems, Engng. Analysis with Boundary Elements, 27, 759-769, 2003.
• 7. G. FAIRWEATHER and A. KARAGEORGHIS AND Y.S. SMYRLIS, A matrix decomposition MFS algorithm for asymmetric biharmonic problems, Adv. Comput. Math., to appear.
• 8. M. A. GOLBERG and C.S. CHEN, Discrete Projection Methods for Integral Equations, Computational Mechanics Publications, Southampton, 1996.
• 9. Numerical Algorithms Group Library Mark 20, NAG Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK, 2001.
• 10. Y. S. SMYRLIS and A. KARAGEORGHIS, Some aspects of the method of fundamental solutions for certain harmonic problems, J. Sci. Comp., 16, 341-371, 2001.
• 11. Y. S. SMYRLIS and A. KARAGEORGHIS, Some aspects of the method of fundamental solutions for certain harmonic problems, Computer Modelling in Engineering & Sciences, 4, 535-550, 2003.
• 12. Y. S. SMYRLIS and A. KARAGEORGHIS, A matrix decomposition MFS algorithm for asymmetric potential problems, Enging. Analysis with Boundary Elements, to appear.
• 13. T. USHIJIMA and F. CHIBA, Error estimates for fundamental solutions method applied to reduced wave problems in a domain exterior to a disc, J. Comput. Appl. Math. 159, 137-148, 2003.
• 14. O. VON ESTORFF (ED), Boundary Elements in Acoustics, WIT Press, Southampton, 2000.
• 15. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd Edition, Cambridge University Press, Cambridge, 1966.
• 16. T. W. WU (ED), Boundary Element Acoustics: Fundamentals and Computer Codes, WIT Press, Southampton, 2000.

Uwagi

Brak numeracji w dołączonym pliku. Podany zakres stron odnosi się do drukowanej wersji tekstu.