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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 5
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Articles

The truncation method for the Cauchy problem of the inhomogeneous Helmholtz equation

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Pages 991-1004 | Received 08 Aug 2017, Accepted 14 Nov 2017, Published online: 30 Nov 2017

References

  • Hararj I , Barbone PE , Slavutin M , et al . Boundary infinite elements for the Helmholtz equation in exterior domains. Inter. J Num Meth Eng. 1998;41:1105–1131.
  • Beskos DE . Boundary element methods in dynamic analysis: part II (1986--1996). Appl Mech Rev. 1997;50:149–197.
  • Chen JT , Wong FC . Dual formulation of multiple reciprocity method for the acoustic mode of a cavity with a thin partition. J Sound Vib. 1998;217:75–95.
  • Hall WS , Mao XQ . Boundary element investigation of irregular frequencies in electromagnetic scattering. Eng Anal Bound Elem. 1995;16:245–252.
  • Regińska T , Regiński K . Approximate solution of a Cauchy problem for the Helmholtz equation. Inverse Probl. 2006;22:975–989.
  • Wei T , Qin HH , Shi R . Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation. Inverse Probl. 2008;24:035003.
  • DeLillo T , Isakov V , Valdivia N , et al . The detection of the source of acoustical nosie in two dimensions. SIAM J Appl Math. 2001;61:2104–2121.
  • Isakov V . Inverse problems for partial differential equations. Vol. 127, Applied Mathematical Sciences. New York (NY): Springer-Verlag; 1998.
  • Marin L , Elliott L , Heggs PJ , et al . Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations. Comput Mech. 2003;31(3–4):367–377.
  • Marin L , Elliott L , Heggs PJ , et al . Comparision of regularization methods for solving the Cauchy problem associated with the Helmholtz equation. Int J Numer Meth Eng. 2004;60:1933–1947.
  • Marin L , Elliott L , Heggs PJ , et al . BEM solution for the Cauchy problem associated with Helmholtz-type equations by the Landweber method. Eng Anal Bound Elem. 2004;28(9):1025–1034.
  • Yu C , Zhou ZF , Zhuang M . An acoustic intensity-based method for reconstruction of radiated fields. J Acoust Soc Am. 2008;123:1892–1901.
  • Eldén L , Berntsson F , Regińska T . Wavelet and Fourier methods for solving the sideways heat equation. SIAM J Sci Comput. 2000;21:2187–2205.
  • Fu CL , Feng XL , Qian Z . The Fourier regularization for solving the Cauchy problem for the Helmholtz equation. Appl Num Math. 2011;59:2625–2640.
  • Marin L , Lesnic D . The method of fundamental solutions for Cauchy problem associated with two-dimensional Helmholtz-type equations. Comput Struct. 2005;83:267–278.
  • Jin BT , Zheng Y . Boundary knot method for some inverse problems associated with the Helmholtz equation. Int J Numer Meth Eng. 2005;62:1636–1651.
  • Jin BT , Marin L . The plane wave method for inverse problems associated with Helmholtz type equations. Eng Anal Bound Elem. 2008;32:223–240.
  • Marin L . Boundary element-minimal error method for the Cauchy problem associated with two dimensional Helmholtz-type equations. Comput Mech. 2009;44:205–219.
  • Qin HH , Wei T . Two regularization methods for the Cauchy problems of the Helmholtz equation. Appl Math Model. 2010;34:947–967.
  • Qin HH , Wei T . Modified regularization method for the Cauchy problem of the Helmholtz equation. Appl Math Model. 2009;33:2334–2348.
  • Qin HH , Lu JM . A modified method for a Cauchy problem of the Helmholtz equation. Bull Malays Math Sci Soc. 2017;40(4):1493–1522.
  • Tuan NH , Lesnic LD . A new general filter regularization method for Cauchy problems for elliptic equations with a locally Lipschitz nonlinear source. J Math Anal Appl. 2016;434:1376–1393.
  • Zhang HW , Wei T . A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation. J Inv Ill-posed Probl. 2014;22:143–168.
  • Zhang YX , Fu CL , Deng ZL . An a-posteriori truncation method for some Cauchy problems associated with Helmholtz-type equation. Inverse Probl Sci Eng. 2013;21(7):1151–1168.
  • Trong DD , Long NT , Alain PND . Nonhomogeneous heat equation: identification and regularization for the inhomogeneous term. J Math Anal Appl. 2005;312:93–104.
  • Yang F . The truncation method for identifying an unknown source in the Possion equation. Appl Math Comput. 2011;217:9334–9339.
  • Li XX , Yang F . The truncation method for identifying the heat source dependent on a spatial variable. Appl Math Comput. 2011;62(6):2497–2505.
  • Zhang YX , Yan L . The general a-posteriori truncation method and its application to radiogenic source identification for the Helium production-diffusion equation. Appl Math Model. 2017;43:126–138.
  • Zhang ZQ , Wei T . Identifying an unknown source in time-fractional diffusion equation by a truncation method. Appl Math Comput. 2013;219:5972–5983.
  • Yang F , Zhang M , Li XX , et al . A posteriori truncated regularization method for identifying unknown heat source on a spherical symmetric domain. Adv Differ Equ. 2017;2017:1–11.

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