Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

Year:    2012

Author:    Yunyun Ma, Fuming Ma

Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2012-CMR-19033

Communications in Mathematical Research , Vol. 28 (2012), Iss. 4 : pp. 300–312

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

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

Author Details

Yunyun Ma

Fuming Ma