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In this paper, a comprehensive open-source three-dimensional (3-D) finite-element method (FEM) is proposed to model the dynamic behavior of liquid crystal (LC) directors in complex structures. This dynamic model is based on interactively iterating the vector representation of director profile and potential distribution. The director update formulations are derived in detail from the Galerkin's approach of FEM, including the weak form approach to simplify the highly nonlinear iteration equation. The potential update formulations are derived from the Ritz's approach of FEM. A 2-D in-plane switching (IPS) structure is used as an example to compare our approach with the FEM based commercial software (2dimMOS). The results from both programs show an excellent agreement. Furthermore, our method also agrees well with the finite-difference method (FDM) in studying a 3-D super IPS LC cell with zigzag electrodes.