When subjected to dynamic excitations, liquid-filled tanks are particularly prone to sloshing, a phenomenon that can become critical in rockets, tank trucks or liquid storage facilities, where it may lead to a loss of control or ultimate damage. A common mitigation strategy is to introduce internal baffles in order to attenuate fluid motion [1]. In this context, a numerical method is developed to address a general sloshing problem while accounting for the discontinuity in the pressure field along the internal tank baffle modeled as a shell. The present work formulates the problem in the frequency domain, avoiding costly time integration and directly provides key engineering quantities such as FRFs. The fluid is modeled as incompressible and inviscid, and its motion is assumed to be irrotational, allowing the use of potential flow theory. The dynamic free-surface boundary condition is linearized, as assumed in small-amplitude sloshing analyses. The structure satisfies the governing equations of linear elastodynamic theory. Despite these simplifications, the primary challenge in industrial design offices remains the reduction of computational cost, especially when repeated evaluations are required for parametric studies or optimization loops, involving the shape and position of the baffle. To address this issue, the approach of this present work relies on a partition of unity strategy (XFEM [2] [3]), which eliminates the need for remeshing and the repeated reconstruction of the associated operators for each baffle position and shape. This feature enables an efficient geometric parametrization and is expected to significantly improve the efficiency of subsequent optimization procedures. The proposed method is implemented for a three-dimensional fluid and validated on a parallelepiped tank sloshing problem with an internal baffle under harmonic excitation. The method successfully captures the discontinuity of the pressure field induced by the immersed structure. Finally, the results show that the geometrical parameters strongly influence the frequency response. A complete performance analysis is carried out on this example, both in terms of accuracy and computational cost.