Technology computer-aided design (TCAD) semiconductor device simulators solve partial differential equations (PDE) using the finite volume method (FVM), or related methods. While this approach has been in use over several decades, its methods continue to be extended, and are still applicable for investigating novel devices. In this paper, we present an element edge based (EEB) FVM discretization approach suitable for capturing vector-field effects. Drawing from a 2D approach in the literature, we have extended this method to 3D. We implemented this method in a TCAD semiconductor device simulator, which uses a generalized PDE (GPDE) approach to simulate de- vices with the FVM. We describe how our EEB method is compatible with the GPDE approach, allowing the modeling of vector effects using scripting. This method is applied to solve polarization effects in a 3D ferro capacitor, and a 2D ferroelectric field-effect transistor. An example for field- dependent mobility in a 3D MOSFET is also presented.