Natural boundary integral method and related numerical methods

Engineering Analysis with Boundary Elements

Volumn 28, Issue 8, 2004, Pages 937-944

  Yu, Dehao ^a   Zhao, Longhua ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Artificial boundary condition; Boundary element method; Domain decomposition; Exterior problem; Natural boundary reduction

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; VISCOSITY;

ARTIFICIAL BOUNDARY CONDITION; DOMAIN DECOMPOSITION; EXTERIOR PROBLEM; NATURAL BOUNDARY REDUCTION;

BOUNDARY VALUE PROBLEMS;

EID: 2942579367     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0955-7997(03)00120-6     Document Type: Article

References (25)

1. Babuška I., Strouboulis T. The finite element method and its reliability. 2001;Oxford University Press, Oxford.
2. Du Q., Yu D. Dirichlet-Neumann alternating algorithm based on the natural boundary reduction for time-dependent problems over an unbounded domain. Appl Numer Math. 44:2003;471-486.
3. Feng K. Differential versus integral equation and finite versus infinite Element. Math Numer Sinica. 2:(1):1980;100-105.
4. Feng K., Yu D.H. Canonical integral equations of elliptic boundary value problems and their numerical solutions. Proceedings of the China-France Symposium on FEM (1982, Beijing). 1983;211-252.
5. Feng K. Finite element method and natural boundary reduction. Proceedings of the International Congress of Mathematicians, Warszawa. 1983;1439-1453.
6. Feng K. Asymptotic radiation conditions for reduced wave equation. J Comput Math. 2:(2):1984;130-138.
7. Han H., Wu X. Approximation of infinite boundary condition and its application to finite element methods. J Comput Math. 3:(3):1985;179-192.
8. Hsiao G.C., Wendland W.L. A finite element method for some integral equations of the first kind. J Math Anal Appl. 58:(3):1997;449-481.
9. Hu Q., Yu D. Solving singularity problems in unbounded domains by coupling of natural BEM and composite grid FEM. Appl Numer Math. 37:2001;127-143.
10. Keller J.B., Givoli D. Exact non-reflecting boundary conditions. J Comput Phys. 82:1989;172-192.
11. Shigeta T. Numerical methods for magnetostatic unbounded domain/inverse problems using the mixed finite element method. Doctoral Thesis. Ibaraki University; 2000.
12. Shi Z.-C., Ushijima T. Proceedings of the First China-Japan Joint Seminar on Numerical Mathematics Beijing, China, August 24-29, 1992. 1993;World Scientific, Singapore.
13. Wu J., Yu D. The Overlapping DDM for biharmonic equation over exterior 3-d domain. J Comput Math. 18:(1):2000;83-94.
14. Ying L.-A. Infinite element methods. 1989;Peking University Press, Beijing. in Chinese.
15. Yu D.-H. Numerical solutions of harmonic and biharmonic canonical integral equations in interior or exterior circular. J Comput Math. 1:(1):1983;52-62.
16. Yu D.-H. Approximation of boundary conditions at infinity for harmonic problem over cracked domain. J Comput Math. 3:(3):1985;219-227.
17. Yu D.-H. Mathematical theory of natural boundary element method. 1993;Science Press, Beijing. in Chinese.
18. Yu D. A domain decomposition method based on the natural boundary reduction over unbounded domain. Math Numer Sinica. 16:(4):1994;448-459 Yu D. Chin J Numer Math Appl. 17:(1):1995;95-105.
19. Yu D. A domain decomposition method based on the natural boundary reduction over unbounded domain. Math Numer Sinica. 16:(4):1994;448-459 Yu D. Chin J Numer Math Appl. 17:(1):1995;95-105.
20. Yu D. Discretization of non-overlapping DDM for unbounded domains and its convergence. Math Numer Sinica. 18:(3):1996;328-436 Yu D. Chin J Numer Math Appl. 18:(4):1996;93-102.
21. Yu D. Discretization of non-overlapping DDM for unbounded domains and its convergence. Math Numer Sinica. 18:(3):1996;328-436 Yu D. Chin J Numer Math Appl. 18:(4):1996;93-102.
22. Yu D.-H. Natural boundary integral method and its applications. 2002;Kluwer, Dordrecht.
23. Yu D., Jia Z. Natural integral operator on elliptic boundary and the coupling method for an anisotropic problem. Math Numer Sinica. 24:(3):2002;375-384 Yu D., Jia Z. Chin J Numer Math Appl. 24:(4):2002;95-107.
24. Yu D., Jia Z. Natural integral operator on elliptic boundary and the coupling method for an anisotropic problem. Math Numer Sinica. 24:(3):2002;375-384 Yu D., Jia Z. Chin J Numer Math Appl. 24:(4):2002;95-107.
25. Zheng Q. Domain decomposition method for elliptic boundary value problems over unbounded domains (in Chinese). PhD Dissertation. ISMSEC, Academia Sinica; 1997.