The artificial boundary method for a nonlinear interface problem on unbounded domain

CMES - Computer Modeling in Engineering and Sciences

Volumn 35, Issue 3, 2008, Pages 227-252

  Yu, De Hao ^a   Huang, Hong Ying ^b  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b ZHEJIANG OCEAN UNIVERSITY   (China)

Author keywords

Artificial boundary method; Dirichlet to Neumann mapping; Finite element method; Natural integral operator; Nonlinear interface problem

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONFORMAL MAPPING; FINITE ELEMENT METHOD; THREE DIMENSIONAL;

ARTIFICIAL BOUNDARY CONDITIONS; ARTIFICIAL BOUNDARY METHOD; BOUNDED DOMAINS; DIRICHLET TO NEUMANN MAPPING; ELLIPSOIDAL SURFACES; ERROR ESTIMATES; INFINITE SERIES; MESH SIZES; NATURAL INTEGRAL OPERATOR; NONLINEAR INTERFACE PROBLEM; NUMERICAL EXAMPLES; ORIGINAL PROBLEMS; UNBOUNDED DOMAINS; WEAK FORMULATIONS;

BOUNDARY ELEMENT METHOD;

EID: 58149526315     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. Brezzi, F.; Johnson C. (1979): On the coupling of boundary integral and finite element methods. Calcolo, vol. 76, pp. 189-201.
2. Johnson C.; Nedelec J. C. (1980): On the coupling of boundary integral and finite element methods. Math. Comp., vol. 35, pp. 1063-1079.
3. Wendland W. L. (1986): On asymptotic error estimates for combined BEM and FEM. In R. P. Shaw et al.(ed), Innovative Numerical Methods in Engrg., Springer, Berlin, Heidelberg, New York, pp. 55-70.
4. Costabel M. (1987): Symmetric methods for the coupling of finite elements and boundary elements. In C.A. Brebbia et al.(ed), Boundary Elements IX, volume 1, Springer-Verlag, pp. 411-420.
5. Feng K.(1983): Finite element method and natural boundary reduction. In Proc. of the International Congress of Mathematicians, Warszawa, pp. 1439-1453.
6. Han Hou De(1990): A new class of variational formulations for the coupling of finite and boundary element methods. J.Comput. Math., vol. 8, pp. 223-232.
7. Hsiao G. C.; Porter J. F.(1986): A hybrid method for an exterior boundary value problem based on asympototic expansion, boundary integral equation and finite element approximations. In C. A. Brebbia et al.(ed), Innovative Numerical Methods in Engineering, Springer, Berlin, Heidelberg, New York, pp. 83-88.
8. MacCamy R. C.; Marin S. P.(1980): A finite element method for exterior interface problems. Int. J. Math. Math. Sci., vol. 3, pp. 311-350.
9. Yu D. H.(1983): Coupling canonical boundary element method with FEM to solve harmonic problem over cracked domain. J. Comp. Math., vol. 1(3), pp. 195-202.
10. Feng K.; Yu D. H.(1983): Canonical integral equations of elliptic boundary value problems and their numerical solutions. Proceedings of China-France Symposium on the Finite Element Method (Feng, K. and Lions, J. L. ed.), Science Press and Gordon Breach, Beijing, New York, pp. 211-252.
11. Keller Joseph B.; Givoli Dan(1989): An exact non-reflection boundary conditions. Journal of Computational Physics, vol. 82, pp. 172-192.
12. Grote M. J.; Keller Joseph B.(1995): On non-reflecting boundary conditions. Journal of Computational Physics, vol. 122, pp. 231-243.
13. Yu De Hao(2002): Natural Boundary Integral Method and Its Applications. Klumer Academic Publishers, Reading, Massachusetts.
14. Wu J. M.; Yu D. H.(2000): The natural boundary element method for exterior elliptic domain. Chinese J. Numer. Math. & Appl., vol. 22(4), pp. 91-104.
15. Wu J. M.(1999): Natural Boundary Element Method and Domain Decomposition Algorithm for Three Dimensional Problems. PhD thesis, The Institute of Computational Mathematics and Scientific/ Engineering Computing of the Chinese Academy of Sciences, in Chinese.
16. Huang H. Y.(2007): An artificial boundary method for three-dimensional problems over unbounded domain with an ellipsoidal artificial boundary. PhD thesis, Academy of Mathematics and System Sciences of the Chinese Academy of Sciences, in Chinese.
17. Yu D. H.(1985): Approximation of boundary conditions at infinity for a harmonic equation. J. Comp. Math., vol. 3(3), pp. 219-227.
18. Du Q. K.; Yu D. H.(2000): The coupled method based on natural boundary reduction for parabolic equation. Computational Physics, vol. 17(6), pp. 593-601, in Chinese.
19. Du Q. K.; Yu D. H.(2001): On the natural integral equation for initial boundary value problems of two dimensional hyperbolic equation. Acta Mathematicae Applicatae Sinica, vol. 24(1), pp. 17-26.
20. Liu Y.(2007): Solution of Some Electromagnetic Problems Based on Natural Boundary Elements and Domain Decomposition Method. PhD thesis, Academy of Mathematics and System Sciences of the Chinese Academy of Sciences, in Chinese.
21. Hu Q. Y.; Yu D. H.(2001): A solution method for a certain nonlinear interface problem in unbounded domains. Computing, vol. 67, pp. 119-140.
22. Huang H. Y.; Yu D. H.(2006): Natural boundary element method for three dimensional exterior harmonic problem with an inner prolate spheriod boundary. J. Comput. Math., vol. 24(2), pp. 193-208.
23. Feistauer M.(1985): Mathematical and numerical study of nonlinear problems in fluid mechanics. In M. Zlámal J. Vosmanshẏ(ed), Proc. Conf. Equadiff 6, Springer, pp. 3-16.
24. Feistauer M.(1987): On the finite element approximation of a cascade flow problem. Numer. Math., vol. 50, pp. 655-684.
25. Carstensen Carsten; Gwinner Joachim(1997): FEM and BEM coupling for a nonlinear transmission problem with Signorini contact. SIAM J.Numer.Anal., vol. 34, pp. 1845-1864.
26. Costabel M. M.; Stephan E. P.(1990): Coupling of finite and boundary element methods for an elastoplastic interface problem. SIAM J. Numer. Anal., vol. 27(5), pp. 1212-1226.
27. Stephan E. P.(1992): Coupling of finite elements and boundary elements for some nonlinear interface problems. Comput. Methods Appl. Mech. Engrg., vol. 101, pp. 61-72.
28. Lions J. L.; Magenes E.(1972): Non-Homogeneous Boundary Value Problems and Applications, volume I. Springer-Verlag, New York.
29. Ciarlet P. G.(1978): The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, New York.
30. Ying L. A.(2006): Numerical Methods for Exterior Problems. World Scientific, New Jersey.
31. Yang S. S.; Chen J. T.; Liang M. T.(1995): Dual boundary integral equations for exterior problems. Engrg. Anal. with Boundary Elements, vol. 16, pp. 333-340.
32. Chen C. T.; Chen J. T.; Chen K. H.(2002): Adaptive boundary element method of time-harmonic exterior acoustics in two dimensions. Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 3331-3345.
33. Chen P. Y.; Chen I. L.; Chen J. T.; Chen C. T.(2007): A semi-analytical approach for radiation and scattering problems with circular boundaries. Computer Methods in Applied Mechanics and Engineering, vol. 196, pp. 2751-2764.
34. Liu Chein-Shan(2007): A meshless regularized integral equation method for laplace equation in arbitrary interior or exterior plane domains. CMES: Computer Modeling in Engineering & Sceinces, vol. 19(1), pp. 99-109.
35. Jr. Soares Delfim(2008): A time-domain fem-bem iterative coupling algorithm to numerically model the propagation of electromagnetic waves. CMES: Computer Modeling in Engineering & Sceinces, vol. 32(2), pp. 57-68.
36. Novati G.; Springhetti R.; Margonari M.(2006): Weak coupling of the symmetric galerkin bem with fem for potential and elastostatic problems. CMES: Computer Modeling in Engineering & Sceinces, vol. 13(1), pp. 67-80.