Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation

@inproceedings{Qin2008ModifiedTR,
  title={Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation},
  author={H. H. Qin and T. Wei and Ran Shi},
  year={2008}
}
In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method. 

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 35 references

Method of fundamental solutions with regularization techniques for Cauchy problems of elliptic operators, Engineering Analysis with Boundary Elements

  • T. Wei, Y. C. Hon, L. Ling
  • 2007
1 Excerpt

A meshless method for some inverse problems associated with the Helmholtz equation

  • B. T. Jin, Y. Zheng
  • Computer Methods in Applied Mechanics and…
  • 2006
1 Excerpt

Approximate solution of a Cauchy problem for the Helmholtz equation

  • K. Regiński T. Regińska
  • Inverse Problems
  • 2006

Regiński, Approximate solution of a Cauchy problem for the Helmholtz equation, Inverse Problems

  • K. T. Regińska
  • 2006
1 Excerpt

Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation ,

  • B. T. Jin, Y. Zheng
  • Engineering Analysis with Boundary Elements
  • 2005

Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation, Engineering Analysis with Boundary Elements

  • B. T. Jin, Y. Zheng
  • 2005
1 Excerpt

The method of fundamental solutions for the Cauchy problem associated with two-dimensional Helmholtz-type equations, Computers and Structures

  • L. Marin, D. Lesnic
  • 2005
1 Excerpt

Wakulicz, Wavelet moment method for Cauchy problem for the Helmholtz equation, 2005

  • A. T. Regińska
  • Preprint IMPAN No 662
  • 2005
2 Excerpts

Wavelet moment method for Cauchy problem for the Helmholtz equation ,

  • A. Wakulicz T. Regińska
  • 2005

Similar Papers

Loading similar papers…