This paper presents multi-domain topology optimization using a current-carrying coil and a ferromagnetic material in order to focus the pulsed magnetic field (PMF) onto a target area. The multi-domain design sensitivities in the harmonic magnetic field are calculated using the adjoint variable method (AVM). In numerical examples, the multi-domain topology optimization technique is applied to the designs of a C-core actuator in the magnetostatic field and a PMF generator in the time-harmonic magnetic field. The magnetic saturation effect is considered in the optimization, and optimization results using linear steel and nonlinear steel are compared.