Dual boundary integral equations for helmholtz equation at a corner using contour approach around singularity

Journal of Marine Science and Technology

Volumn 9, Issue 1, 2001, Pages 53-63

  Chen, I Lin ^a   Liang, Ming Te ^b   Kuo, Shyh Rong ^b   Chen, Jeng Tzong ^b  

^a NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

^b NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

Author keywords

Corner; Dual boundary element method; Limiting process; Regularized method

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; EQUATIONS OF MOTION; INTEGRATION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL METHODS; TENSORS; VECTORS; VELOCITY;

HELMHOLTZ EQUATIONS; LIMITING PROCESS; REGULARIZED METHOD;

INTEGRAL EQUATIONS;

EID: 1642492271     PISSN: 10232796     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Chen, J. T., "On Hadamard Principal Value and Boundary Integral Formulation of Fracture Mechanics," Master Thesis, under the supervision of Professor Hong-Ki Hong, Institute of Applied Mechanics, National Taiwan University, (1986).
2. Hong, H.-K. and Chen, J. T., "Derivation of Integral Equations in Elasticity," J. Eng. Mech. Div., ASCE, Vol. 114, No. 6, Em5, pp. 1028-1044 (1988).
3. Chen, J. T. and Hong H.-K., "On the Dual Integral Representation of Boundary Value Problem in Laplace Equation," Boundary Elements Abstracts, Vol. 4, No. 3, pp. 114-116 (1993).
4. Chen, J. T., Hong, H.-K. and Chyuan, S. W., "Boundary Element Analysis and Design in Seepage Flow Problems with Sheetpiles," Finite Elements in Analysis and Design, Vol. 17, pp. 1-20 (1994).
5. Chen, J. T. and Hong, H.-K., "Review of Dual Integral Representations with Emphasis on Hypersingularity and Divergent Series," Applied Mechanics Review, ASME, Vol. 52, No. 1, pp. 17-33 (1999).
6. Portela, A., Aliabadi, M. H. and Rooke, D. P., "The Dual Boundary Element Method: Effective Implementation for Crack Problems," Int. J. Num. Meth. Engng., Vol. 33, pp. 1269-1287 (1992).
7. Banerjee, P. K. and Butterfield, R., Boundary Element Methods in Engineering Science, McGraw-Hill, London, (1981).
8. Alarcon, E., Martin A. and Paris F., "Boundary Elements in Potential and Elasticity Theory," Computers and Structures, Vol. 10, pp. 351-362 (1979).
9. Walker, S. P. and Fenner, R. T., "Treatment of Corners in BIE Analysis of Potential Problems," Int. J. Num. Meth. Engng., Vol. 28, pp. 2569-2581 (1989).
10. Gray, L. J. and Manne, L. L., "Hypersingular Integrals at a Corner," Engineering Analysis with Boundary Elements, Vol. 11, pp. 327-334 (1993).
11. Gray, L. J. and Lutz, E., "On the treatment of Corners in the Boundary Element Method," J. Comp. Appl. Math., Vol. 32, pp. 369-386 (1990).
12. Lutz, E., Gray L. J. and Ingraffea, A. R., "An Overview of Integration Methods for Hypersingular Boundary Integrals," Proc. BEM13 Conference, Comp. Mech. Publ., Southampton, (1991).
13. Chen, J. T. and Hong, H.-K., Boundary Element Method, 2nd Ed., New World Press, Taipei, Taiwan, (1992) (in Chinese).
14. Mansur, W. J., Fleury, P. and Azevedo, J. P. S., "A Vector Approach to the Hyper-singular BEM Formulation for Laplace Equation in 2D," The International Journal of BEM Communications, Vol. 8, pp. 239-250 (1997).
15. Chen, J. T. and Hong, H.-K., "Dual boundary integral equations at a corner using contour approach around singularity," Advance in Engineering Software, Vol. 21, pp. 167-178 (1994).
16. Chen, J. T. and Chen, K. H., "Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary," Engineering Analysis with Boundary Elements, Vol. 21, pp. 105-116 (1998).
17. Aliabadi, M. H., Hall, W. S. and Phemister, T. G., "Taylor Expansions in the Boundary Element Methods for Neumann Problems," Boundary Elements VII, edited by C. A. Brebbia and G. Maier, Computational Mechanics Publication, pp. 12.31-12.39 (1985).
18. Aliabadi, M. H., Hall, W. S. and Phemister, T. G., "Taylor Expansions for Singular Kernels in the Boundary Element Method," Int. J. Num. Meth. Engng., Vol. 21, pp. 2221-2236 (1985).
19. Tuck, E. O., Application and Solution of Cauchy Singular Integral Equations, in The Application and Numerical Solution of Integral Equations, ed. R. S. Anderson et al., Sijthoff and Noordhoff, (1980).
20. Günter N. M., Potential Theory and Its Applications to Basic Problems of Mathematical Physics, Frederick Ungar Publishing, Co., N.Y., (1967).
21. Koo, B. -U, Lee, B. -C. and Ih, J. -G, "A Non-singular Boundary Integral Equation for Acoustic Problem," J. Sound Vib. Vol. 192, pp. 263-279 (1996).
22. Chen, G. and Zhou, J., Boundary Element Method, Computational Mathematics and Application, Academic Press, London, (1992).
23. Chen, J. T., "On Fictitious Frequencies Using Dual Series Representation," Mech. Res., Vol. 25, No. 5, pp. 529-534 (1998).
24. Lamb, H., Hydrodynamics, Dover Publications, New York, (1945).