The following boundary conditions can be specified at outward and inner boundaries of the region.
Dirichlet condition specifies a known value of electric potential U0 at the vertex or at the edge of the model (for example on a capacitor plate). This kind of boundary condition is also useful at an outward boundary of the region that is formed by the plane of electric antisymmetry of the problem (opposite charges in symmetrical geometry). U0 value at the edge can be specified as a linear function of coordinates. The function parameters can vary from one edge to another, but have to be adjusted to avoid discontinuities at edges' junction points.
Note. For problem to be defined correctly the Dirichlet condition has to be specified at least at one point. If the region consists of two or more disjoint subregions, the Dirichlet conditions have to be specified at least at one point of every part.
Neumann condition is defined by the following equations:
Dn = σ |
- at outward boundaries, |
Dn+ - Dn- = σ |
- at inner boundaries, |
where Dn is a normal component of electric induction, "+" and "–" superscripts denote quantities to the left and to the right side of the boundary, σ is a surface charge density. If σ value is zero, the boundary condition is called homogeneous. It indicates vanishing of the normal component of electric field intensity vector. This kind of boundary condition is used at an outward boundary of the region that is formed by the symmetry plane of the problem. The homogeneous Neumann condition is the natural one, it is defaulted at all outward boundary parts where no explicit boundary condition is specified.
If the surface-bound charge is to be specified at the plane of problem symmetry and this plane is the outward boundary of the region, the surface charge density has to be halved.
Constant potential boundary condition is used to describe surface of an isolated «floating» conductor that has constant but unknown potential value.
Note. The edge described as possessing constant potential should not have common points with any Dirichlet edge. In that case the constant potential edge has to be described by a Dirichlet condition with appropriate potential value.