The 2stagecs project aims to efficiently solve larger coupled sparse/dense linear systems arising from the simulation of physics problems, such as the propagation of acoustic waves around aircrafts. It focuses on the heterogeneous jet flow modeling, which requires the use of both Finite Element Method (FEM) and Boundary Element Method (BEM) discretizations, leading to sparse and dense systems, respectively. The project explores the opportunity to process larger systems in spite of the constraint that modern fully-featured sparse direct solvers return the Schur complement as a non-compressed matrix.