For solving a three-dimensional structural inverse magnetic problem of finding interfaces between different magnetization media, fast component wise Newton type method for a two-layered medium and regularized gradient type methods with variable weight factors for a multilayered medium are proposed. On the base of the Newton type and gradient type methods, effective parallel algorithms for two- and three-layered medium models were numerically implemented on Intel multicore CPU and NVIDIA GPU. The optimization of the parallel algorithms was carried out. For a model magnetic problem comparison of the parallel algorithms by relative errors, numbers of iterations and computation times was carried out.