[1] Rggińska T, Regiński K. Approximate solution of a Cauchy problem for the Helmholtz equation[J]. Inverse Probl., 2006, 22:975-989.[2] Alessandrini G, Rondi L, Rosset E, Vessella S. The stability for the Cauchy problem for elliptic equations[J] Inverse Probl., 2009, 25:1-47.[3] Isakov V. Inverse Problems for Partial Differential Equations. Springer-Verlag, New York, 1998.[4] Engl H W, Hanke M, Neubauer A. Regularization of Inverse Problems. Mathematics and Its Applications, vol. 375. Kluwer Academic, Dordrecht, 1996.[5] Kirsch A. An Introduction to the Mathematical Theory of Inverse Problems. Applied Mathematical Sciences, vol. 120. Springer, New York, 2011.[6] Jin B T, Zheng Y. Boundary knot method for some inverse problems associated with the Helmholtz equation[J] Int. J. Numer. Methods Eng., 2005, 62:1636-1651.[7] Lin J, Chen W, Wang F. A new investigation into regularization techniques for the method of fundamental solutions[J]. Math. Comput. Simul., 2011, 81:1144-1152.[8] Marin L, Lesnic D. The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations[J]. Comput. Struct., 2005, 83:267-278.[9] Wei T, Hon Y C, Ling L. Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators[J]. Eng. Anal. Bound. Elem., 2007, 31:373-385.[10] Jin B T, Marin L. The plane wave method for inverse problems associated with Helmholtz-type equations[J]. Eng. Anal. Bound. Elem., 2008, 32:223-240.[11] Karageorghis A. The plane waves method for axisymmetric Helmholtz problems[J] Eng. Anal. Bound. Elem., 2016, 69:46-56.[12] Cheng H, Fu C L, Feng X L. An optimal filtering method for the Cauchy problem of the Helmholtz equation[J]. Appl. Math. Lett., 2011, 24:958-964.[13] Sun Y, Zhang D, Ma F. A potential function method for the Cauchy problem of elliptic operators[J]. J. Math. Anal. Appl., 2012, 395:164-174.[14] Reginska T, Wakulicz A. Wavelet moment method for the Cauchy problem for the Helmholtz equation[J]. J. Comput. Appl. Math., 2009, 223:218-229.[15] Xiong X T, Zhao X C, Wang J X. Spectral Galerkinmethod and its application to a Cauchy problem of Helmholtz equation[J]. Numer. Algorithms, 2013, 63:691-711.[16] Chen W, Fu Z J. Boundary particle method for inverse Cauchy problem of inhomogeneous inhomogeneous Helmholtz equations[J]. J. Mar. Sci. Technol., 2009, 17:157-163.[17] Fu Z J, Chen W, Zhang C Z. Boundary particle method for Cauchy inhomogeneous potential problems[J] Inverse Prob. Sci. Eng., 2012, 20:189-207.[18] Gu Y, Chen W, Fu Z J. Singular boundary method for inverse heat conduction problems in general anisotropic media[J]. Inverse Prob. Sci. Eng., 2013, 22:889-909.[19] Berntsson F, Kozlov V A, Mpinganzima L, Turesson B O. An alternating iterative procedure for the Cauchy problem for the Helmholtz equation[J]. Inverse Probl. Sci. Eng., 2014, 22:45-62.[20] Berntsson F, Kozlov V A, Mpinganzima L, Turesson B O. An accelerated alternating iterative procedure for the Cauchy problem for the Helmholtz equation[J]. Comput. Math. Apll., 2014, 68:44-60.[21] Fu C L, Feng X L, Qian Z. The Fourier regularization for solving the Cauchy problem for the Helmholtz equation[J]. Appl. Numer. Math., 2009, 59:2625-2640.[22] Marin L, Elliott L, Heggs P J, et al. Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations[J]. Comput. Mech., 2003, 31:367-377.[23] Marin L, Elliott L, Heggs P J, et al. BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method[J]. Eng. Anal. Bound. Elem., 2004, 28:1025-1034[24] Marin L, Elliott L, Heggs P J, et al. Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation[J]. Int. J. Numer. Methods Eng., 2004, 60:1933-1947.[25] Sun Y, Zhang D. An integral equations method for the Cauchy problem connected with the Helmholtz equation[J]. Math. Probl. Eng., 2013, 218760.[26] Lee J W, Chen J Z, et al. Null-field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid[J]. Acta Mech., 2014, 225:873-891.[27] Chen J T, Chen K H, Chen I L, et al. A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics[J]. Mech. Res. Commun., 2003, 30:161-174.[28] Marin L, Lesnic D. Boundary element solution for the Cauchy problem in linear elasticity using singular value decomposition[J]. Comput. Methods. Appl. Mech. Eng., 2002, 191(29-30):3257-3270.[29] Chen J T, Chang Y L, Kao S K et al., Revisit of indirect boundary element method:sufficient and necessary formulation[J]. J. Sci. Comput., 2015, 65:467-485.[30] Rizzo F J. An integral equation approach to boundary value problems in classical elastostatics[J]. Q. Appl. Math., 1967, 25:83-95.[31] Altiero N J, Gavazza S D. On a unified boundary-integral equation method[J]. J. Elast., 1980, 10:1-9.[32] Hong H K, Chen J T. Derivations of integral equations of elasticity[J]. J. Eng. Mech. ASCE 114(1998), 1028-1044.[33] Sun Y. A meshless method based on the method of fundamental solution for solving the steadystate heat conduction problems[J]. Int. J. Heat Mass Transfer, 2016, 97:891-907.[34] Colton D, Kress R. Integral Equation Methods in Scattering Theory. Wiley-Interscience, New York, 1983.[35] Colton D, Kress R. Inverse Acoustic and Electromagnetic Scattering Theory. 3nd edition, SpringerVerlag, New York, 2013.[36] Kress R. Linear Integral Equations. Springer-Verlag, Berlin, 1989[37] Sun Y, Ma F, Zhang D. An integral equations method combined minimum norm solution for 3D elastostatics Cauchy problem[J]. Comput. Methods Appl. Mech. Eng., 2014, 271:231-252.[38] Sun Y, Ma F. Appropriate implementation of an invariant MFS for inverse boundary determination problem[J]. Inverse Probl. Sci. Eng., 2015, 6:1040-1055.[39] Sun Y. Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation[J]. J. Sci. Comput., 2017, 71(2):469-498.[40] Sun Y, Ma F. Recovery of the temperature and the heat flux by a novel meshless method from the measured noisy data[J]. Eng. Anal. Boundary Elem., 2015, 59:112-122. |