𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation

✍ Scribed by L. Marin; L. Elliott; P.J. Heggs; D.B. Ingham; D. Lesnic; X. Wen

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
210 KB
Volume
192
Category
Article
ISSN
0045-7825

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, the iterative algorithm proposed by Kozlov et al. [Comput. Maths. Math. Phys. 31 (1991) 45] for obtaining approximate solutions to the ill-posed Cauchy problem for the Helmholtz equation is analysed. The technique is then numerically implemented using the boundary element method (BEM). The numerical results confirm that the iterative 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. An efficient stopping regularising criterion is also proposed.

πŸ“œ SIMILAR VOLUMES

A relaxation method of an alternating it
A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity
✍ Liviu Marin; B. Tomas Johansson πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 1010 KB

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in lin

Comparison of regularization methods for
Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation
✍ L. Marin; L. Elliott; P. J. Heggs; D. B. Ingham; D. Lesnic; X. Wen πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 192 KB

## Abstract In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping

Wavelet moment method for the Cauchy pro
Wavelet moment method for the Cauchy problem for the Helmholtz equation
✍ Teresa RegiΕ„ska; Andrzej Wakulicz πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 560 KB

The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from inexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the moment problem that is equivalent to a Cauchy problem for the Helmholtz equation. A