Boundary Integral Method for Exterior Dirichlet Problem of Helmholtz Equation

The kernel in the first kind integral equation arising from exterior Dirichlet problem of Helmholtz equation has a logarithmic singularity. The kernel is splitted into two parts so that the one contains a special singularity and the other doesn't contain any singularity. The Galerkin method is used to solve the integral equation. The convergence of approximate solutions is discussed and a numerical example is given.