Once we have stated or derived the mathematical equations which define the physics of the system, we must figure out how to solve these equations for the particular domain we are interested in. Most numerical methods for solving partial differential equations break up the continuous domain into discrete elements and approximate the pde using the particular numerical technique (finite element, boundary element, finite difference, or multigrid) best suited to the particular problem.

The first problem we encounter is the discretization of the solution domain
into polygons, or the * mesh generation*. Because of the complex
geometries often associated with bioelectric field problems, construction
of the polygonal mesh can turn out to be one of the most time consuming
aspects of the modeling process. After deciding upon the particular
approximation method to use (and the most appropriate type of element), we
need to construct a mesh of the solution domain which matches the number of
degrees of freedom of our fundamental element. For the sake of simplicity,
we will assume that we will use linear elements, triangles for
two-dimensional meshes and tetrahedrons for three-dimensional domains. If
we chose to use the finite difference approach, we would need to use
uniform squares of cubes.