On boundary integral operators for the Laplace and the Helmholtz equations and their discretisations
The author investigates the main boundary integral operators (single layer potential operator, double layer potential operator, Hilbert operator, hypersingular operator) that arise from certain boundary integral formulation of the interior, or exterior, Dirichlet, or Neumann boundary value problems for the Laplace and the Helmholtz equations in some circle. He presents all eigenvalues and the corresponding eigenfunctions explicitly. Moreover, for the simplest boundary element collocation discretization, the explicit matrix entries as well as the eigenvalues of the matrix and the corresponding eigenvectors are given. This information can be used for the construction of efficient preconditioners for other boundary element matrices.
scientific article; zbMATH DE number 1389927
scientific article