Numerical solution of boundary integral equations by means of attenuation factors

We consider first-kind boundary integral equations with logarithmickernel such as those arising from solving Dirichlet problemsfor the Laplace equation by means of single-layer potentials.The first-kind equations are transformed into equivalent equationsof the second kind which contain the conjugation operator andwhich are then solved with a degenerate-kernel method basedon Fourier analysis and attenuation factors. The approximationswe consider, among them spline interpolants, are linear andtranslation invariant. In view of the particularly small kernel,the linear systems resulting from the discretization can besolved directly by fixed-point iteration.