We use a novel approach to numerically calculate Fast-Oscillating Integrals (FOI) using the Picard-Lefschetz theory. In this theory, analytic oscillatory integrals are converted into sums of convex integrals by deforming the integration domain in the complex plane. Feldbrugge, Pen, and Turok 2019 introduced a new numerical integrator to evaluate the interference effects near caustics in lenses in one dimension. Recent studies have also used this numerical integrator to study lensing of gravitational waves as well, however one shortcoming of the integrator is that it is not optimal. In this work, we optimize the convergence to desired contours in the complex plane and further generalize the algorithm to work for random functions that appear in various physical applications like scintillation of radio signals in astrophysical sources.
|fast oscillating integrals
|picard lefschetz theory