𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Wavelet moment method for the Cauchy problem for the Helmholtz equation

✍ Scribed by Teresa Regińska; Andrzej Wakulicz

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
560 KB
Volume
223
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

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 method of regularization by projection with application of the Meyer wavelet subspaces is introduced and analyzed. The derived formula, describing the projection level in terms of the error bound of the inexact Cauchy data, allows us to prove the convergence and stability of the method.

📜 SIMILAR VOLUMES

On a quasi-reversibility regularization
On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation
✍ Ai-Lin Qian; Xiang-Tuan Xiong; Yu-Jiang Wu 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 609 KB

In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are for x = 0 and x = π. The solution is sought in the interval 0 < y ≤ 1. A quasi-reversibility method is applied to formulate regularized solutions wh

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 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 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