New investigations into the BKM for inverse problems of Helmholtz equation

References

• Banoczi, J. M., N. C. Chiu, G. E. Cho, and I. C. F. Ipsen. 1998. “The Lack of Influence of the Right-hand Side on the Accuracy of Linear System Solution.” SIAM Journal on Scientific Computing 20 (1): 203–227. doi: 10.1137/S106482759630526X.
   Web of Science ®Google Scholar
• Chen, J. T., M. H. Chang, K. H. Chen, and I. L. Chen. 2002. “Boundary Collocation Method for Acoustic Eigenanalysis of Three Dimensional Cavities Using Radial Basis Function.” Computational Mechanics 29 (4–5): 392–408. doi: 10.1007/s00466-002-0350-y.
   Web of Science ®Google Scholar
• Chen, J. T., M. H. Chang, K. H. Chen, and S. R. Lin. 2002. “The Boundary Collocation Method with Meshless Concept for Acoustic Eigen Analysis of Two-dimensional Cavities Using Radial Basis Function.” Journal of Sound and Vibration 257 (4): 667–711. doi: 10.1006/jsvi.2002.5038.
   Web of Science ®Google Scholar
• Chen, J. T., M. H. Chang, I. L. Chung, and Y. C. Cheng. 2002. “Comments on Eigenmode Analysis of Arbitrarily Shaped Two-dimensional Cavities by the Method of Point Matching.” Journal of the Acoustical Society of America 111 (1): 33–36. doi: 10.1121/1.1410966.
   PubMed Web of Science ®Google Scholar
• Chen, J. T., and K. H. Chen. 1998. “Analytical Study and Numerical Experiments for Laplace Equation with Overspecified Boundary Conditions.” Applied Mathematical Modelling 22 (9): 703–725. doi: 10.1016/S0307-904X(98)10054-9.
   Web of Science ®Google Scholar
• Chen, J. T., I. L. Chen, K. H. Chen, and Y. T. Lee. 2003. “Comments on Free Vibration Analysis of Arbitrarily Shaped Plates with Clamped Edges Using Wave-type Functions.” Journal of Sound and Vibration 262 (2): 370–378. doi: 10.1016/S0022-460X(02)01414-1.
   Web of Science ®Google Scholar
• Chen, J. T., I. L. Chen, K. H. Chen, Y. T. Lee, and Y. T. Yeh. 2004. “A Meshless Method for Free Vibration Analysis of Circular and Rectangular Clamped Plates Using Radial Basis Function.” Engineering Analysis with Boundary Elements 28 (5): 535–545. doi: 10.1016/S0955-7997(03)00106-1.
   Web of Science ®Google Scholar
• Chen, W., and Y. C. Hon. 2003. “Numerical Investigation on Convergence of Boundary Knot Method in the Analysis of Homogeneous Helmholtz, Modified Helmholtz and Convection-Diffusion Problems.” Computer Methods in Applied Mechanics and Engineering 192 (15): 1859–1875. doi: 10.1016/S0045-7825(03)00216-0.
   Web of Science ®Google Scholar
• Chen, J. T., S. Y. Lin, I. L. Chen, and Y. T. Lee. 2006. “Mathematical Analysis and Numerical Study of True and Spurious Eigenequations for Free Vibration of Plates Using Imaginary-part BEM.” Journal of Sound and Vibration 293: 380–408. doi: 10.1007/s00466-004-0562-4.
   Web of Science ®Google Scholar
• Chen, W., and M. Tanaka. 2002. “A Meshless, Integration-free, and Boundary-Only RBF Technique.” Computers and Mathematics with Applications 43 (3–5): 379–391. doi: 10.1016/S0898-1221(01)00293-0.
   Web of Science ®Google Scholar
• Chen, W., and F. Z. Wang. 2010. “A Method of Fundamental Solutions without Fictitious Boundary.” Engineering Analysis with Boundary Elements 34 (5): 530–532. doi: 10.1016/j.enganabound.2009.12.002.
   Web of Science ®Google Scholar
• Cheng, Y. M., and M. J. Peng. 2005. “Boundary Element-free Method for Elastodynamics.” Science in China G: Physics and Astronomy 48 (6): 641–657. doi: 10.1360/142004-25.
   Web of Science ®Google Scholar
• Christiansen, S., and P. C. Hansen. 1994. “The Effective Condition Number Applied to Error Analysis of Certain Boundary Collocation Methods.” Journal of Computational and Applied Mathematics 54 (1): 15–36. doi: 10.1016/0377-0427(94)90391-3.
   Web of Science ®Google Scholar
• Drombosky, T. W., A. L. Meyer, and L. Ling. 2009. “Applicability of the Method of Fundamental Solutions.” Enginnering Analysis with Boundary Elements 33 (5): 637–643. doi: 10.1016/j.enganabound.2008.10.007.
   Web of Science ®Google Scholar
• Hon, Y. C., and W. Chen. 2003. “Boundary Knot Method for 2D and 3D Helmholtz and Convection-diffusion Problems under Complicated Geometry.” International Journal for Numerical Methods in Engineering 56 (13): 1931–1948. doi: 10.1002/nme.642.
   Web of Science ®Google Scholar
• Jin, B. T., and W. Chen. 2006. “Boundary Knot Method Based on Geodesic Distance for Anisotropic Problems.” Journal of Computational Physics 215 (2): 614–629. doi: 10.1016/j.jcp.2005.11.032.
   Web of Science ®Google Scholar
• Jin, B. T., and Y. Zheng. 2005a. “Boundary Knot Method for Some Inverse Problems Associated with the Helmholtz Equation.” International Journal for Numerical Methods in Engineering 62 (12): 1636–1651. doi: 10.1002/nme.1240.
   Web of Science ®Google Scholar
• Jin, B. T., and Y. Zheng. 2005b. “Boundary Knot Method for the Cauchy Problem Associated with the Inhomogeneous Helmholtz Equation.” Engineering Analysis with Boundary Elements 29 (10): 925–935. doi: 10.1016/j.enganabound.2005.05.005.
   Web of Science ®Google Scholar
• Kang, S. W., J. M. Lee, and Y. J. Kang. 1999. “Vibration Analysis of Arbitrarily Shaped Membranes Using Non-Dimensional Dynamic Influence Function.” Journal of Sound and Vibration 221 (1): 117–132. doi: 10.1006/jsvi.1998.2009.
   Web of Science ®Google Scholar
• Li, Z. C., H. T. Huang, J. T. Chen, and Y. M. Wei. 2010. “Effective Condition Number and Its Applications.” Computing 89 (1–2): 87–112. doi: 10.1007/s00607-010-0098-8.
   Web of Science ®Google Scholar
• Liu, C. S. 2008. “Improving the Ill-conditioning of the Method of Fundamental Solutions for 2D Laplace Equation.” CMES: Computer Modeling in Engineering & Sciences 28 (2): 77–94. doi: 10.3970/cmes.2008.028.077.
   Web of Science ®Google Scholar
• Liu, C. S. 2009. “A Fictitious Time Integration Method for Solving Delay Ordinary Differential Equations.” CMC: Computers, Materials, Continua 10 (1): 97–116. doi: 10.3970/cmc.2009.010.097.
   Web of Science ®Google Scholar
• Liu, C. S., and S. N. Atluri. 2013. “Numerical Solution of the Laplacian Cauchy Problem by Using a Better Postconditioning Collocation Trefftz Method.” Engineering Analysis with Boundary Elements 37 (1): 74–83. doi: 10.1016/j.enganabound.2012.08.008.
   Web of Science ®Google Scholar
• Mukherjee, Y. X., and S. Mukherjee. 1997. “The Boundary Node Method for Potential Problems.” International Journal for Numerical Methods in Engineering 40 (5): 797–815. doi: 10.1002/(SICI)1097-0207(19970315)40:5<nan:AIDNME89>3.0.CO;2-#.
   Web of Science ®Google Scholar
• Wang, F. Z., W. Chen, and X. R. Jiang. 2010. “Investigation of Regularized Techniques for Boundary Knot Method.” International Journal for Numerical Methods in Biomedical Engineering 26 (12): 1868–1877. doi: 10.1002/cnm.1275.
   Web of Science ®Google Scholar
• Wang, F. Z., L. Ling, and W. Chen. 2009. “Effective Condition Number for Boundary Knot Method.” CMC: Computers, Materials, Continua 12 (1): 57–70. doi: 10.3970/cmc.2009.012.057.
   Web of Science ®Google Scholar
• Wang, F. Z., and J. Zhang. 2015. “Numerical Simulation of Acoustic Problems with High Wavenumbers.” Applied Mathematics & Information Sciences 9 (2): 1011–1014. doi: 10.12785/amis/090252 This article will be published in 2016.
   Google Scholar
• Wang, F. Z., and K. H. Zheng. 2014. “Analysis of the Boundary Knot Method for 3D Helmholtz-Type Problems.” Mathematical Problems in Engineering 2014: 1–9. doi: 10.1155/2014/853252.
   Web of Science ®Google Scholar
• Wang, F. Z., and K. H. Zheng. 2015. “The Method of Fundamental Solutions for Steady-State Groundwater Flow Problems.” Journal of the Chinese Institute of Engineers (Accepted). doi: 10.1080/02533839.2015.1082936.
   Google Scholar
• Young, D. L., K. H. Chen, and C. W. Lee. 2005. “Novel Meshless Method for Solving the Potential Problems with Arbitrary Domains.” Journal of Computational Physics 209 (1): 290–321. doi: 10.1016/j.jcp.2005.03.007.
   Web of Science ®Google Scholar