Start with Ampère’s law for static cases ∇ × H = J and assume a uniform permeability in free space (
B = μ0 H), the magnetostatic problem reads
Applying the Coulomb gauge ∇ · A = 0 and vector calculus identity
∇ × ∇ × A =
−∇2A +
∇(∇ · A), Equation 2-23 reduces to
Equation 2-24 implies that
The Magnetic Fields, Currents Only Interface is a div-grad formulation, different from
The Magnetic Fields Interface which is a curl-curl formulation. Taking the divergence of both sides of
Equation 2-24, it is noticed that the divergence of the current is not necessarily equal to zero. Therefore,
Equation 2-24 is able to model open coils or conductors.
Different from the The Magnetic Fields Interface which uses the Curl element as shape functions in 3D,
The Magnetic Fields, Currents Only Interface employs the Lagrange element as shape functions. In this way,
The Magnetic Fields, Currents Only Interface is able to handle the continuity over nonconformal mesh elements.