Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions
The authors are concerned with an eigenvalue problem for the Laplace operator on some real 1D and 2D unbounded domains. The problem involves a Dirichlet or Neumann condition on the finite part of boundary along with a radiation condition at large distances. In solving such problems they proceed in three steps, namely: formulation of a complex scaled eigenvalue problem, truncation of the original unbounded domain to a bounded one and finally finite element solution to the eigenvalue problem on this bounded domain. They compare the numerical outcomes obtained by frequency dependent scaling with those provided by standard scaling. Then they observe that, in spite of the fact that the former scaling method leads to polynomial eigenproblems, eigenvalues (resonances) produced by such scaling are less sensitive to the discretization parameters. Actually, they suggest that this fact could lead to the construction of a reliable filter for spurious resonances. Some numerical experiments focused on the location of spurious eigenvalues are carried out.
scientific article; zbMATH DE number 6894729
scientific article