The method of fundamental solutions for steady-state groundwater flow problems

References

• Chen, C. S., H. A. Cho, and M. A. Golberg. 2006. “Some Comments on the Ill-conditioning of the Method of Fundamental Solutions.” Engineering Analysis with Boundary Elements 30 (5): 405–410. doi: 10.1016/j.enganabound.2006.01.001.
   Web of Science ®Google Scholar
• Chen, C. S., A. Karageorghis, and Y. S. Smyrlis. 2008. The Method of Fundamental Solutions – A Meshless Method. Atlanta, GA: Dynamic Publishers.
   Google Scholar
• Chen, J. T., Y. T. Lee, I. L. Chen, and K. H. Chen. 2004. “Mathematical Analysis and Treatment for the True and Spurious Eigenequations of Circular Plates by the Meshless Method using Radial Basis Function.” Journal of the Chinese Institute of Engineers 27 (4): 547–561. doi: 10.1080/02533839.2004.9670903.
   Web of Science ®Google Scholar
• Chen, C. S., S. W. Lee, and C.-S. Huang. 2007. “Derivation of Particular Solutions using Chebyshev Polynomial based Functions.” International Journal of Computational Methods 4 (1): 15–32. doi: 10.1142/SO219876207001096.
   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.2009.12.00.
   Web of Science ®Google Scholar
• Diersch, H. J. 2014. FEFLOW Finite Element Modeling of Flow, Mass and Heat Transport in Porous and Fractured Media. New York: Springer.
   Google Scholar
• Ding, D. H., Q. Zhang, F. Z. Wang, and L. Y. Luo. 2012. “Combination of Newmark Method and Natural Element Method for Elastodynamics.” Journal of the Chinese Institute of Engineers 35 (7): 869–877. doi: 10.1080/02533839.2012.708537.
   Web of Science ®Google Scholar
• Fairweather, G., and A. Karageorghis. 1998. “The Method of Fundamental Solutions for Elliptic Boundary Value Problems.” Advances in Computational Mathematics 9 (1–2): 69–95. doi: 10.1023/A:101898122174.
   Web of Science ®Google Scholar
• Karel, K., and M. Juraj. 2013. “A Meshless Solution for Two Dimensional Density-Driven Groundwater Flow.” Engineering Analysis with Boundary Elements 37 (2): 187–196. doi: 10.1016/j.enganabound.2012.10.005.
   Web of Science ®Google Scholar
• Katsurada, M. 1994. “Charge Simulation Method Using Exterior Mapping Functions.” Japan Journal of Industrial and Applied Mathematics 11 (1): 47–61. doi: 10.1007/BF03167213.
   Google Scholar
• Kovářík, K., J. Mužík, and M. S. Mahmood. 2012. “A Meshless Solution of Two-dimensional Unsteady Flow.” Engineering Analysis with Boundary Elements 36 (5): 738–743. doi: 10.1016/j,enganabound.2011.12.009.
   Web of Science ®Google Scholar
• Li, J., Y. Chen, and D. Pepper. 2003. “Radial Basis Function Method for 1-D and 2-D Groundwater Contaminant Transport Modeling.” Computational Mechanics 32 (1–2): 10–15. doi: 10.1007/s00466-003-0447-y.
   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. 2011. “The Method of Fundamental Solutions for Solving the Backward Heat Conduction Problem with Conditioning by a New Post-Conditioner.” Numerical Heat Transfer, Part B: Fundamentals 60 (1): 57–72. doi: 10.1080/10407790.2011.588134.
   Web of Science ®Google Scholar
• Long, Y. Q., W. Li, Y. G. Li, and Z. P. Yang. 2011. “Application of Multi-Quadric Method for Numerical Simulation of Steady Groundwater Flow.” [in Chinese] Journal of Hydrolic Engineering 42 (5) 572–578. doi: 10.13243/j.cnki.slxb.2011.05.003.
   Google Scholar
• Malik, N. H. 1989. “A Review of the Charge Simulation Method and Its Applications.” IEEE Transactions on Electrical Insulation 24 (1): 3–20. doi: 10.1109/14.19861.
   Web of Science ®Google Scholar
• Mehl, S. W., M. C. Hill, and S. A. Leake. 2006. “Comparison of Local Grid Refinement Methods for MODFLOW.” Ground Water 44 (6): 792–796. doi: 10.1111/j.1745-6584.2006.00192.x.
   PubMed Web of Science ®Google Scholar
• Partridge, P. W., C. A. Brebbia, and L. W. Wrobel. 1992. The Dual Reciprocity Boundary Element Method. Southampton: Computational Mechanic Publication.
   Google Scholar
• Saeedpanah, I., E. Jabbari, and M. A. Shayanfar. 2011. “Numerical Simulation of Ground Water Flow via a New Approach to the Local Radial Point Interpolation Meshless Method.” International Journal of Computational Fluid Dynamics 25 (1): 17–30. doi: 10.1080/10618562.2010.545772.
   Web of Science ®Google Scholar
• Sun, N. Z. 1996. Mathematical Modeling of Groundwater Pollution. New York: Springer.10.1007/978-1-4757-2558-2
   Google Scholar
• Tsai, C. C., D. L. Young, J. H. Chiang, and D. C. Lo. 2006. “The Method of Fundamental Solutions for Solving Options Pricing Models.” Applied Mathematics and Computation 181 (1): 390–401. doi: 10.1016/j.amc.2006.01.046.
   Web of Science ®Google Scholar
• Wang, F. Z. 2011. “Applicability of the Boundary Particle Method.” CMES: Computer Modeling in Engineering & Sciences 80 (3): 201–218. doi: 10.3970/cmes.2011.080.201.
   Web of Science ®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., W. Chen, and L. Ling. 2012. “Combinations of the Method of Fundamental Solutions for General Inverse Source Identification Problems.” Applied Mathematics and Computation 219 (3): 1173–1182. doi: 10.1016/j.amc.2012.07.027.
   Web of Science ®Google Scholar
• Wen, P. H., and C. S. Chen. 2010. “The Method of Particular Solutions for Solving Scalar Wave Equations.” International Journal for Numerical Methods in Engineering 26 (12): 1878–1889. doi: 10.1002/cnm.1278.
   Web of Science ®Google Scholar
• Young, D. L., C. M. Fan, C. C. Tsai, and C. W. Chen. 2006. “The Method of Fundamental Solutions and Domain Decomposition Method for Degenerate Seepage Flownet Problems.” Journal of the Chinese Institute of Engineers 29 (1): 63–73. doi: 10.1080/02533839.2006.9671099.
   Web of Science ®Google Scholar
• Zhou, D. L., and J. Zhang. 2004. “The Multiquadric Method for Steady Flow of Groundwater.” [in Chinese] Journal of Liaoning Normal University (Natural Science Edition) 27 (4): 399–402. doi: 10.3969/j.issn.1000-1735.2004.04.004.
   Google Scholar