[2]
Alves, C. J. S. and Valtchev, S. S., Numerical comparison of two meshfree methods for acoustic wave scattering, Eng. Anal. Bound. Elem., 29 (2005), pp. 371–382.

[3]
Antunes, P. R. S., Numerical calculation of eigensolutions of 3D shapes using the method of fundamental solutions, Numer. Methods Partial Differential Equations, 27 (2011), pp. 1525–1550.

[4]
Berntsson, F., Kozlov, V. A., Mpinganzima, L. and Turesson, B. O., An alternating iterative procedure for the Cauchy problem for the Helmholtz equation, Inverse Problems Sci. Eng., 22 (2014), pp. 45–62.

[5]
Berntsson, F., Kozlov, V. A., Mpinganzima, L. and Turesson, B. O., An accelerating alternating iterative procedure for the Cauchy problem for the Helmholtz equation, Comput. Math. Appl., 68 (2014), pp. 44–60.

[6]
Beskos, D. E., Boundary element method in dynamic analysis: Part II (1986–1996), ASME Appl. Mech. Rev., 50 (1997), pp. 149–197.

[7]
Bin-Mohsin, B. and Lesnic, D., Identification of a corroded boundary and its Robin coefficient, East Asian J. Appl. Math., 2 (2012), pp. 126–149.

[8]
Borman, D., Ingham, D. B., Johansson, B. T. and Lesnic, D., The method of fundamental solutions for detection of cavities in EIT, J. Integral Equations Appl., 21 (2009), pp. 381–404.

[9]
Borsic, A., Graham, B. M., Adler, A. and Lionheart, W. R. B., In vivo impedance imaging with total variation regularization, IEEE Trans. Med. Inaging, 29 (2010), pp. 44–54.

[10]
Cessenat, O. and Després, B., Using plane waves as base functions for solving time harmonic equations with the ultra weak variational formulation, J. Comput. Acoust., 11 (2003), pp. 227–238.

[11]
Chen, C. S., Karageorghis, A. and Li, Y., On choosing the location of the sources in the MFS, Numer. Algor., 72 (2016), pp. 107–130.

[12]
Chen, J. T. and Wong, F. C., Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition, J. Sound Vibration, 217 (1998), pp. 75–95.

[13]
Chen, W., Meshfree boundary particle method applied to Helmholtz problems, Eng. Anal. Bound. Elem., 26 (2002), pp. 577–581.

[14]
Chen, W., Fu, Z. J. and Wei, X., Potential problems by singular boundary method satisfying moment condition, CMES Comput. Model. Eng. Sci., 54 (2009), pp. 65–85.

[15]
Debye, P. and Hückel, E., The theory of electrolytes. I. Lowering of freezing point and related phenomena, Phys. Z., 24 (1923), pp. 185–206.

[16]
Fairweather, G. and Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math., 9 (1998), pp. 69–95.

[17]
Hall, W. S. and Mao, X. Q., A boundary element investigation of irregular frequencies in electromagnetic scattering, Eng. Anal. Bound. Elem., 16 (1995), pp. 245–252.

[18]
Hansen, P. C., Rank-Defficient and Discrete Ill-Posed Problems: Numerical Aspects of Numerical Inversion, SIAM, Philadelphia, 1998.

[19]
Harari, I., Barbone, P. E., Slavutin, M. and Shalom, R., Boundary infinite elements for the Helmholtz equation in exterior domains, Int. J. Numer. Meth. Eng., 41 (1998), pp. 1105–1131.

[20]
Herrera, I., Boundary Methods: An Algebraic Theory, Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, MA, 1984.

[21]
Isakov, V., Inverse obstacle problems, Inverse Problems
25 (2009), 123002.

[22]
Jin, B. and Marin, L., The plane wave method for inverse problems associated with Helmholtz-type equations, Eng. Anal. Bound. Elem., 32 (2008), pp. 223–240.

[23]
Jin, B. and Zheng, Z., Boundary knot method for some inverse problems associated with the Helmholtz equation, Int. J. Numer. Meth. Eng., 62 (2005), pp. 1636–1651.

[24]
Jones, D. S., Methods in Electromagnetic Wave Propagation, Oxford University Press, New York, 1979.

[25]
Kabanikhin, S. I. and Shishlenin, M. A., Stability analysis of a continuation problem for the Helmholtz equation, Bull. Novosibirsk Comput. Center, 16 (2013), pp. 59–63.

[26]
Kabanikhin, S. I., Gasimov, Y. S., Nurseitsov, D. B., Shishlenin, M. A., Sholpanbaev, B. B. and Kasenov, S., Regularization of the continuation problem for elliptic equations, J. Inverse Ill-Posed Problems, 21 (2013), pp. 871–884.

[27]
Kaltenbacher, B., Neubauer, A. and Scherzer, O., Iterative Regularization Methods for Nonlinear Problems, de Gruyter, Berlin, 2008.

[28]
Kansa, E. J., Multiquadrics: A scattered data approximation scheme with applications to computational fluid dynamics, Comput. Math Appl., 19 (1990), pp. 147–161.

[29]
Karageorghis, A., The plane waves method for axisymmetric Helmholtz problems, Eng. Anal. Bound. Elem., 69 (2016), pp. 46–56.

[30]
Karageorghis, A. and Lesnic, D., The method of fundamental solutions for the inverse conductivity problem, Inverse Problems Sci. Eng., 18 (2010), pp. 567–583.

[31]
Karageorghis, A., Lesnic, D. and Marin, L., A survey of applications of the MFS to inverse problems, Inverse Problems Sci. Eng., 19 (2011), pp. 309–336.

[32]
Karageorghis, A., Lesnic, D. and Marin, L., The MFS for inverse geometric problems, Inverse Problems and Computational Mechanics (Munteanu, L.
Marin, L. and Chiroiu, V., eds.), vol. 1, Editura Academiei, Bucharest, 2011, pp. 191–216.

[33]
Kraus, A. D., Aziz, A. and Welty, J., Extended Surface Heat Transfer, John Wiley & Sons, New York, 2001.

[34]
Lax, P. D. and Phillips, R. S., Scattering Theory, Academic Press, New York, 1967.

[35]
Lian, J. and Subramanian, S., Computation of molecular electrostatics with boundary element methods, Biophys. J., 73 (1997), pp. 1830–1841.

[36]
Li, X., On solving boundary value problems of modified Helmholtz equations by plane wave functions, J. Comput. Appl. Math., 195 (2006), pp. 66–82.

[37]
Marin, L., Numerical boundary identification for Helmholtz-type equations, Comput. Mech., 39 (2006), pp. 25–40.

[38]
Marin, L. and Karageorghis, A., Regularized MFS-based boundary identification in two-dimensional Helmholtz-type equations, CMC Comput. Mater. Continua, 10 (2009), pp. 259–293.

[39]
Marin, L., Elliott, L., Heggs, P. J., Ingham, D. B., Lesnic, D. and Wen, X., Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations, Comput. Mech., 31 (2003), pp. 367–377.

[40]
Marin, L., Elliott, L., Heggs, P. J., Ingham, D. B., Lesnic, D. and Wen, X., BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method, Eng. Anal. Bound. Elem., 28 (2004), pp. 1025–1034.

[41] The MathWorks, Inc., 3 Apple Hill Dr., Natick, MA, Matlab.

[42] Numerical Algorithms Group Library Mark 21 (2007), NAG (UK) Ltd, Wilkinson House, Jordan Hill Road, Oxford, UK.

[43]
Tikhonov, A. N. and Arsenin, V. Y., Methods for Solving Ill-Posed Problems, Nauka, Moscow, 1986.

[44]
Valtchev, S. S., Numerical Analysis of Methods with Fundamental Solutions for Acoustic and Elastic Wave Propagation Problems, Ph.D. thesis, Department of Mathematics, Instituto Superior Téchnico, Universidade Técnica de Lisboa, Lisbon, 2008.