Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation

Modified Tikhonov regularization method for the Cauchy problem of the Helmholtz equation

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical resu...

A Spectral Regularization Method for a Cauchy Problem of the Modified Helmholtz Equation

The Cauchy problem for Helmholtz equation arises from inverse scattering problems. Specific backgrounds can be seen in the existing literature; we can refer to 1–6 and so forth. A number of numerical methods for stabilizing this problem are developed. Several boundary element methods combined with iterative, conjugate gradient, Tikhonov regularization, and singular value decomposition methods a...

A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

A regularization method for solving the Cauchy problem for the Helmholtz equation

Article history: Received 18 February 2010 Received in revised form 31 December 2010 Accepted 11 January 2011 Available online 19 January 2011

A Cauchy Problem for Helmholtz Equation : Regularization and Error Estimates

In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based on the solution given by the method of separation of variables. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness ...