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Volume 28, Issue 4
Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

Yunyun Ma & Fuming Ma

Commun. Math. Res., 28 (2012), pp. 300-312.

Published online: 2021-05

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  • Abstract

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.

  • Keywords

Fourier moment method, Cauchy problem, Helmholtz equation, regularization, ill-possedness.

  • AMS Subject Headings

35R30, 35R25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-300, author = {Ma , Yunyun and Ma , Fuming}, title = {Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {4}, pages = {300--312}, abstract = {

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19033.html} }
TY - JOUR T1 - Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation AU - Ma , Yunyun AU - Ma , Fuming JO - Communications in Mathematical Research VL - 4 SP - 300 EP - 312 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19033.html KW - Fourier moment method, Cauchy problem, Helmholtz equation, regularization, ill-possedness. AB -

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.

Yunyun Ma & Fuming Ma. (2021). Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation. Communications in Mathematical Research . 28 (4). 300-312. doi:
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