In many levitation systems superconductors are used in combination with permanent magnets. In this paper we considered three types of magnetic assemblies that are most often used: with magnets oriented in one direction, oppositely oriented magnets and the Halbach array. Based on the H-formalism, we performed modeling of a magnetic field and levitation force in a system consisting of the high temperature superconductor (HTS) tape stack and the assembly of permanent magnets. It was shown that if a spatial distribution of a gradient magnetic field changes in height it is necessary to take into account the magnetic history of the superconductor. The proposed computational model includes a combination of scalar and vector potentials, as well as modeling the real movement of an HTS tape stack in a levitation system. The simulation results were verified by corresponding experiments. The proposed approach is universal for modeling levitation systems of complex configurations.