EM.Ferma solves the Poisson equation for the electric scalar potential subject to specified boundary conditions:
<math>\Delta\varPhi(\mathbf{r}) = \nabla^2 \varPhi(\mathbf{r}) = -\frac{\varrho(\mathbf{r})}{\varepsilon_0varepsilon}</math>
where Φ(<b>r</b>) is the electric scalar potential and , ρ(<b>r</b>) is the volume charge density, and ε is the permittivity of the medium.
In a source-free region, ρ(<b>r</b>) = 0, and Poisson's equation reduces to the familiar Laplace equation:
<math>\Delta\varphi(\mathbf{r}) = \nabla^2 \varphi(\mathbf{r}) = 0</math>
Once the electric scalar potential is computed, the electric fields can easily be computed via the equation shown below. :
<math> \mathbf{E(r)} = - \nabla \varphivarPhi(\mathbf{r})</math>Â Â EM.Ferma also solves the Poisson equation for the magnetic vector potential subject to specified boundary conditions:Â <math>\Delta \mathbf{A} (\mathbf{r}) = \nabla^2 \mathbf{A}(\mathbf{r}) = - \varmu \mathbf{J}(\mathbf{r}) </math>Â where <b>A(r)</b> is the magnetic vector potential, <b>J(r)</b> is the volume current density, and μ is the permeability of the medium. The magnetic Poisson equation is vectorial in nature and involves a system of three scalar differential equations corresponding to the three components of <b>A(r)</b>.