# Dirichlet Boundary Conditions¶

In solving partial differential equations, such as the *Laplace Equation*
or *Poisson Equation* where we seek to find the value of
potential throughout some volume of space (using methods like SIMION Refine),
it can be necessary to impose constraints on that variable ()
at the boundary surface of that space in order to obtain a unique solution
(see *First Uniqueness Theorem*).
The two main types of these **boundary conditions** are
*Neumann Boundary Condition* and Dirichlet boundary conditions.

A **Dirichlet boundary condition** in the Laplace equation imposes the restriction
that the potential is some value at some location. A common case of Dirichlet
boundary conditions are surfaces of perfectly conductive electrodes.
Free charges in such a conductor will rearrange themselves over the conductive
surfaces so that the potential will be uniform over the entire conductor.
Typically, electrodes are held to some known potential by attaching them to
a power supply or ground, so the Dirichlet condition is known directly,
but conductive surfaces may alternately be *floating*.