Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation (Communications in Mathematical Research, 2021)
In this paper, we consider the reconstruction of the wave field in abounded domain. By choosing a special family of functions, the Cauchy problemcan be transformed into a Fourier moment problem. This problem is ill-posed. Wepropose a regularization method for obtaining an approximate solution to the wavefield on the unspecified boundary. We also give the convergence analysis and errorestimate of the numerical algorithm. Finally, we present some numerical examples toshow the effectiveness of this method.
Keywords: Fourier moment method; Cauchy problem; Helmholtz equation; regularization; ill-possedness.