One way for finding the field of a magnet is to model it (as a polarized material inside volume $V$ ) with magnetic dipoles , as lots of dipoles near each other , and then sum the produced fields of all dipoles at the desired point.
To find the field of a dipole, You can model it as two (to date, fictitious) magnetic monopoles and use coulomb force law to find its magnetic field or its interaction with other dipoles. The method gives correct result, But the problem with this , is that the situation does not describe the reality .( magnetic poles have not been observed to date)
To put it another way, theoretically , in classical electrodynamics , Maxwell's equations let (and encourage) you define a magnetic charge density. And then , in the static case ( electro- and magneto- static) the complete solution for magnetic field will be given by coulomb's law for magnetic charge.