Solution of Helmholtz equation in the exterior domain by elementary boundary integral methods
This paper is concerned with the direct and indirect boundary integral equations, based on Green's formula or the layer potential representation, for the Helmholtz equation in a smooth two-dimensional exterior domain. It surveys results on the solvability of the integral equations and on their approximate solution by spline collocation methods. In particular, spectral properties and conditioning of the boundary integral operators and their discrete boundary element counterparts are studied near characteristic wavenumbers. The effect of quadrature errors on the accuracy of the discrete collocation methods is also investigated. Numerical results are presented for the solution of several Dirichlet and Neumann problems.
scientific article; zbMATH DE number 758627