A new iterative algorithm is developed to model 2D and 3D magnetization of the high temperature superconductor by using the A-V-A formulation in ANSYS. This algorithm can simulate the critical state model by forcing the trapped JT to Jc for all superconducting elements after each iterative load step, as well as simulating the flux creep model by updating the E-J power law based resistivity values. Benchmarks on a disked shaped HTS bulk during zero field cooling (ZFC) and field cooling (FC) magnetization are simulated and compared with using the H-formulation in COMSOL. Specially, we confirm this new method is friendly of adding ferromagnetic materials into the FEA model or defining the Jc as a function of magnetic field, field angle or mechanical strain. The simulation results are reported for more complex FEA models, like the HTS tape stack and the HTS bulk staged array undulator. The advantages and disadvantages of this new method are seriously discussed.