Stokes Structure and Direct Image of Irregular Singular $\mathcal{D}$-Modules

In this paper we will present a way of examining the Stokes structure of certain irregular singular $\mathcal{D}$-modules, namely the direct image of exponentially twisted regular singular meromorphic connections, in a topological point of view. This topological description enables us to compute Stokes data for an explicit example concretely.