Boundary particle method for inverse cauchy problems of inhomogeneous helmholtz equations

Journal of Marine Science and Technology

Volumn 17, Issue 3, 2009, Pages 157-163

  Chen, Wen ^a   Fu, Zhuojia ^a  

^a HOHAI UNIVERSITY   (China)

Author keywords

Boundary particle method; Inhomogeneous helmholtz equations; Inverse problem; Truncated singular value decomposition

Indexed keywords

BOUNDARY PARTICLE METHOD; BOUNDARY PARTICLE METHODS; CAUCHY PROBLEMS; COMPUTATIONALLY EFFICIENT; DISCRETIZATION METHOD; HIGHER ORDER; INHOMOGENEOUS HELMHOLTZ EQUATIONS; INHOMOGENEOUS PROBLEMS; MESHLESS; NUMERICAL EXPERIMENTS; PARTICULAR SOLUTION; REGULARIZATION TECHNIQUE; TRUNCATED SINGULAR VALUE DECOMPOSITION;

DIFFERENTIAL EQUATIONS; DISCRETE EVENT SIMULATION; HELMHOLTZ EQUATION; INVERSE PROBLEMS; SINGULAR VALUE DECOMPOSITION;

PROBLEM SOLVING;

EID: 70350148229     PISSN: 10232796     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Bai, M. R., "Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries," Journal of the Acoustical Society of America, Vol.92, pp. 533-549 (1992).
2. Beatson, R. K., Cherrie, J. B., and Mouat, C. T., "Fast fitting of radial basis functions: methods based on preconditioned GMRES iteration," Advances in Computational Mathematics, Vol.11, pp. 253-270 (1999).
3. Bogaert, I., Pissoort, D., and Olyslager, F., "A normalized plane wave method for 2d Helmholtz problems," Microwave and Optical Technology Letters, Vol.48, No.2, pp. 237-243 (2006).
4. Chen, C. S., Cho, H. A., and Golberg, M. A., "Some comments on the ill-conditioning of the method of fundamental solutions," Engineering Analysis with Boundary Elements, Vol.30, pp. 405-410 (2006).
5. Chen, K. H., Chen, J. T., and Kao, J. H., "Regularized meshless method for antiplane shear problems with multiple inclusions," International Journal for Numerical Methods in Engineering, Vol.73, pp. 1251-1273 (2007).
6. Chen, W., "Meshfree boundary particle method applied to Helmholtz problems," Engineering Analysis with Boundary Elements, Vol.26, pp. 577-581 (2002).
7. Chen, W., "Distance function wavelets - Part III: "Exotic" transforms and series. Research report of Simula Research Laboratory," CoRR preprint, http://arxiv.org/abs/cs.CE/0206016.2002.
8. Chen, W. and Jin, B. T, "A truly boundary-only meshfree method for inhomogeneous problems," Proceeding of The 2nd ICCES Special Symposium on Meshless Methods (2006).
9. Chen, W., Shen, Z. J., and Yuan, G W., "General solutions and fundamental solutions of varied orders to the vibrational thin, the Berger, and the Winkler plates," Engineering Analysis with Boundary Elements, Vol.29, pp. 699-702 (2005).
10. Chen, W. and Tanaka, M., "A meshless, exponential convergence, integration-free, and boundary-only RBF technique," Computers and Mathematics with Applications, Vol.43, pp. 379-391 (2002).
11. Fairweather, G and Karageorghis, A., "The method of fundamental solutions for elliptic boundary value problems," Advances in Computational Mathematics, Vol.9, pp. 69-95 (1998). (Pubitemid 128403959)
12. Hansen, P. C, "The truncated SVD as a method for regularization," BIT Numerical Mathematics, Vol.27, No.4, pp. 534-553 (1987).
13. Hansen, P. G, "Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems," Numerical Algorithms, Vol.6, pp. 1-35(1994).
14. Hon, Y. C. and Wu, Z., "A numerical computation for inverse determination problem," Engineering Analysis with Boundary Elements, Vol.24, pp. 599-606 (2000).
15. Itagaki, M., "Higher order three-dimensional fundamental solutions to the Helmholtz and the modified Helmholtz equations," Engineering Analysis with Boundary Elements, Vol.15, pp. 289-293 (1995).
16. Jin, B. T. and Marin, L., "The plane wave method for inverse problems associated with Helmholtz-type equations," Engineering Analysis with Boundary Elements, Vol.32, No.3, pp. 223-240 (2008).
17. Jin, B. T. and Zheng, Y., "Boundary knot method for some inverse problems associated with Helmholtz equation," International Journal for Numerical Methods in Engineering, Vol.62, No.12, pp. 1636-1651 (2005). (Pubitemid 40427190)
18. Jin, B. T. and Zheng, Y., "Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation," Engineering Analysis with Boundary Elements, Vol.29, No.10, pp. 925-935 (2005). (Pubitemid 41455091)
19. Kim, B. K. and Ih, J. G, "On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method," Journal of the Acoustical Society of America, Vol.100, pp. 3003-3016(1996).
20. Ling, L. and Kansa, E. J., "Preconditioning for radial basis functionswith domain decomposition methods," International Workshop on Meshfree Methods, Portugual, Instituto Superior Technico Lisbon, 2003.
21. Liu, C. S., "A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length," Computer Modeling in Engineering & Sciences, Vol.21, pp. 53-65 (2007).
22. Liu, C. S., "Improving the ill-conditioning of the method of fundamental solutions for 2D Laplace equation," Computer Modeling in Engineering & Sciences, Vol.28, pp. 77-93 (2008).
23. Liu, C. S., "A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation," Engineering Analysis with Boundary Elements, Vol.32, pp. 778-785 (2008).
24. Marin, L., Elliott, L., Heggs, P. J., Ingham, D. B., Lesnic, D., and Wen, X., "An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation," Computer Methods in Applied Mechanics and Engineering, Vol.192, pp. 709-722 (2003).
25. Marin, L., Elliott, L., Heggs, P. J., Ingham, D. B., Lesnic, D., and Wen, X., "Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation," International Journal for Numerical Methods in Engineering, Vol.60, No.11, pp. 1933-1947 (2004).
26. Marin, L. and Lesnic, D., "The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations," Computers & Structures, Vol.83, pp. 267-278 (2005). (Pubitemid 40072215)
27. Nowak, A. J. and Partridge, P. W., "Comparison of the dual reciprocity and the multiple reciprocity methods," Engineering Analysis with Boundary Elements, Vol.10, pp. 155-160 (1992).
28. Patridge, P. W., Brebbia, C. A., and Wrobel, L. W., The Dual Reciprocity Boundary Element Method, Computational Mechanics Publication, Southampton, 1992.
29. Pinkus, A., "Approximating by ridge functions," In: Le Mehaute, A., Rabut, C, and Schumaker, L. L., (eds.), Surface Fittin and Multiresolution Methods, Nashville, TN: Vanderbilt University Press, pp. 279-292 (1997).
30. Wei, T, Hon, Y. C, and Ling, L., "Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators," Engineering Analysis with Boundary Elements, Vol.31, No.4, pp. 373-385 (2007).
31. Wu, S. R. and Yu, J., "Application of BEM-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries," Journal of the Acoustical Society of America, Vol.104, pp. 2054-2060 (1998).
32. Young, D. L., Chen, K. H., and Lee, C. W., "Novel meshfree method for solving the potential problems with arbitrary domain," Journal of Computational Physics, Vol.209, pp. 290-321 (2005).
33. Young, D. L., Tsai, C. C, Fan, C. M., and Chen, C. W., "The method of fundamental solutions and condition number analysis for inverse problem of Laplace equation," Computers and Mathematics with Applications, Vol.55, pp. 1189-1200 (2008).