The Trefftz method for solving eigenvalue problems

Engineering Analysis with Boundary Elements

Volumn 30, Issue 4, 2006, Pages 292-308

  Li, Zi Cai ^a,b   Lu, Tzon Tzer ^a,b   Tsai, Heng Shuing ^a,b   Cheng, Alexander H D ^c  

^a NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

^b National Center for Theoretical Science   (Taiwan)

^c The University of Mississippi   (United States)

Author keywords

Helmholtz equation; Interfaces; Laplace eigenvalue problems; Non linear solutions; The cracked beam; The Trefftz method

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ITERATIVE METHODS; NUMERICAL ANALYSIS; PIECEWISE LINEAR TECHNIQUES;

BOUNDARY APPROXIMATION METHOD; DIRICHLET CONDITION; HELMHOLTZ EQUATION; NON-LINEAR SOLUTIONS; NUMERICAL TESTING; ROOTFINDING; THE CRACKED BEAM; TREFFTZ METHOD; UNIT SQUARE;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 33644906675     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.10.006     Document Type: Article

References (25)

1. Abramowitz M, Stegun IA, editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: Dover; 1972. p. 361.
2. K.E. Atkinson An introduction to numerical analysis 2nd ed 1989 Wiley New York
3. I. Babuska, and J. Osborn Eigenvalue problems P.G. Ciarlet J.L. Lions Handbook of numerical analysis Finite element methods (part I) vol. II 1991 North Holland Amsterdam 641 787
4. S. Bergman Integral operators in the theory of linear partial differential equations 1969 Springer Berlin
5. G. Birkhoff, and R.E. Lynch Numerical solution of elliptic problems 1984 SIAM Philadelphia, PA
6. R. Courant, and D. Hilbert Methods of mathematical physics vol. I 1953 Wiley-InterScience New York
7. S.C. Eisenstat On the rate of convergence of the Bergman-Vekua methods for the numerical solution of elliptic boundary-value problems SIAM J Numer Anal 11 1974 654 680
8. L. Fox, P. Henrici, and C. Molor Approximations and bounds for eigenvalues of elliptic operators SIAM J Numer Anal 4 1967 89 102
9. G.H. Golub, and C.F. van Loan Matrix computation 2nd ed 1989 John Hopkins University Press Baltimore, MD
10. J.R. Kuttler, and V.G. Sigilloto Eigenvalues of the Laplacian in two dimensions SIAM Rev 26 1984 163 193
11. Z.C. Li Combined methods for elliptic equations with singularities, interfaces and infinities 1998 Kluwer Academic Publishers Dordrecht
12. Li ZC. Error analysis of the Trefftz method for solving eigenvalue problems, technical report. Department of Applied Mathmatrics, National Sun Yet-sen University, Taiwan; 2004
13. also submitted for J Comp Appl Math.
14. Z.C. Li, T.T. Lu, H.Y. Hu, and A.H.D. Cheng Particular solutions of Laplace's equations on polygons and new models involving mild singularities Eng Anal Bound Elem 29 2005 59 75
15. Z.C. Li, and R. Mathon Boundary approximation methods for solving elliptic problems on unbounded domains J Comput Phys 89 1990 414 431
16. Z.C. Li, and R. Mathon Error and stability analysis of boundary methods for elliptic problems with interfaces Math Comput 54 1990 41 61
17. Z.C. Li, R. Mathon, and P. Sermer Boundary methods for solving elliptic problems with singularities and interfaces SIAM J Numer Anal 24 1987 487 498
18. T.T. Lu, H.Y. Hu, and Z.C. Li Highly accurate solutions of Motz's and the cracked beam problems Eng Anal Bound Elem 28 2004 1387 1403
19. R. Mathon, and P. Sermer Numerical solution of the Helmholtz equation Congressus Numerantium 34 1982 313 330
20. M. Ortega Numerical analysis, a second course 1990 SIAM Philadelphia, PA
21. B.N. Parlett The symmetric eigenvalue problems 1998 SIAM Philadelphia, PA
22. G. Strang, and G.J. Fix An analysis of finite element methods 1973 Prentice-Hall Englewood Cliffs, NJ
23. Trefftz E. Ein gegenstuck zum ritz'schen verfahren. Proceedings of the second international congress on applied mechanics, Zurich; 1926. p. 131-7.
24. I.N. Vekua New method for solving elliptic equations 1967 North-Holland Amsterdam
25. J.H. Wilkinson The algebraic eigenvalue problem 1965 Oxford University Press Oxford