Abstract:

A numerical method was proposed for the Cauchy problem in accordance with the Helmholtz equation in the halfspace. With the help of DirichlettoNeumann map, this problem was transformed into a compact operator equation for the initial value of the wave field. The asymptotic behavior of the singular values of the compact operator was rigorously justified firstly. Then a projection method with regularization was applied to solving the operator equation. Finally, several numerical examples were presented to illustrate the approach. The results show that the algorithm is effective.

Key words: Helmholtz equation, Cauchy problem, projection method; regularization