An alternating iterative procedure for the Cauchy problem for the Helmholtz equation

作者：Berntsson F; Kozlov V A; Mpinganzima L^*; Turesson B O

来源：Inverse Problems in Science and Engineering, 2014, 22(1): 45-62.

DOI：10.1080/17415977.2013.827181

• Helmholtz equation
• Cauchy problem
• alternating iterative method
• inverse problem
• ill-posed problem

We present a modification of the alternating iterative method, which was introduced by Kozlov and Maz'ya, for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The reason for this modification is that the standard alternating iterative algorithm does not always converge for the Cauchy problem for the Helmholtz equation. The method is then implemented numerically using the finite difference method.

• 出版日期2014-1-2