KUL and EPFL cooperation on numerical integration of Sommerfeld integrals

This paper reports the result of the cooperation between KUL and EPFL on the numerical integration of Sommerfeld integrals (SI). Each institution is well-known for developing specific techniques suited for the evaluation of SI: double-exponential quadrature rules to take the tail of the integral into account (EPFL) and an asymptotic extraction technique to remove the singularities (KUL). The combination of these two techniques results in a very promising algorithm, allowing to perform the integration along the real axis only. Several examples illustrate the algorithm efficiency.