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Computational Mechanics

, Volume 31, Issue 3–4, pp 367–377 | Cite as

Conjugate gradient-boundary element solution to the Cauchy problem for Helmholtz-type equations

  • L. Marin
  • L. Elliott
  • P. J. Heggs
  • D. B. Ingham
  • D. Lesnic
  • X. Wen
  • 116 Downloads

Abstract

 In this paper, an iterative algorithm based on the conjugate gradient method (CGM) in combination with the boundary element method (BEM) for obtaining stable approximate solutions to the Cauchy problem for Helmholtz-type equations is analysed. An efficient regularising stopping criterion for CGM proposed by Nemirovskii [25] is employed. The numerical results obtained confirm that the CGM + BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.

Keywords Inverse problem, Cauchy problem, Helmholtz-type equations, CGM, BEM 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • L. Marin
    • 1
  • L. Elliott
    • 2
  • P. J. Heggs
    • 3
  • D. B. Ingham
    • 2
  • D. Lesnic
    • 2
  • X. Wen
    • 1
  1. 1.School of the Environment, University of Leeds, Leeds LS2 9JT, UK E-mail: liviu@env.leeds.ac.ukGB
  2. 2.Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UKGB
  3. 3.Department of Chemical Engineering, UMIST, P.O. Box 88, Manchester M60 1QD, UKGB

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