Interface Newton–Raphson methods solve this root-finding problem with Newton–Raphson iterations, e.g. with an approximation of the Jacobian from a linear reduced-physics model. The interface quasi-Newton method with approximation for the inverse of the Jacobian from a least-squares model couples a black-box flow solver and structural solver by means of the information that has been gathered during the coupling iterations. This technique is based on the interface block quasi-Newton technique with an approximation for the Jacobians from least-squares models which reformulates the FSI problem as a system of equations with both the interface’s position and the stress distribution on the interface as unknowns. This system is solved with block quasi-Newton iterations of the Gauss–Seidel type and the Jacobians of the flow solver and structural solver are approximated by means of least-squares models.