Abstract: The application of resonant magnetic perturbation (RMP) coils could break the initial axisymmetry and change the magnetic topology in tokamak systems. To understand the plasma equilibrium response to the RMP fields, three-dimensional (3D) non-linear magnetohydrodynamics equilibrium calculations have been carried out using the HINT code for an RMP field-penetration experiment on J-TEXT. The HINT code does not assume perfectly nested flux surfaces, and is able to consider directly the change of magnetic topology due to the RMP field penetrations. Correlations between 3D equilibrium calculations and experimental observations are presented. The magnetic topologies calculated by HINT were compared with the field topologies obtained from a vacuum approximation method. It turns out that the effects of redistribution of plasma pressure and current due to the formation of magnetic islands at various resonant rational surfaces should be considered self-consistently for understanding the change of magnetic structure. Such changes include changes in the shape and size of magnetic islands, and the distribution of stochastic fields around the magnetic islands and at the plasma boundary, which plays an important role for plasma-wall interactions.