A.V. Setukha. The singular integral equation method in a 3-d boundary problems and it applications. In AIP Conf.proc, volume 1479, pages 720–723. American nstitute of Phisics, 2012.
The integral equations with hypersingular integrals on closed and opened surfaces which appear when finding the solution of the 3-dimensional Neumann boundary value problem for Laplace or Helmholtz equations in double-layer potential form are considered in the paper. Author presents his results regarding the solvability of equations of this type, the convergence of the numerical method of their solution like method of discrete singularities in uniform metric on a grid. Also examples of the method practical implementation in applied problems of aerodynamics and acoustics are given.
boundary value problems, integral equations, singular integrals, vortex methods