Numerical integration of Sommerfeld integrals based on singularity extraction techniques and double exponential-type quadrature formulas

A direct integration algorithm for the evaluation of Sommerfeld integrals is presented. This algorithm does not require the deformation of the integration path to avoid spectral singularities. The integration is performed along the real axis only. The algorithm is based on the combination of an asymptotic extraction technique to remove the singularities and double-exponential quadrature rules to take the tail of the integral into account. Numerical examples confirm the validity of the proposed algorithm.