MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of second order linear elliptic partial differential equations (PDEs) of the form
with boundary conditions of the form
where 
are functions of x and y,
is a polygonal domain in 
(possibly with holes),
is the boundary of , and
is differentiation with respect to
a counterclockwise parameterization of the boundary 
.
The first form of the boundary condition is called Dirichlet,
and the second form is called mixed. When c=0, the second
form is called natural.
When p=q=1, the natural boundary condition reduces to the
Neumann boundary condition 
where
is differentiation in the direction of
the outward normal.
For more information on specifying
Neumann boundary conditions, see section 5.2.
MGGHAT is callable as a FORTRAN subroutine, making it useful for user applications in which a major operation is the solution of an elliptic PDE. This includes systems of PDEs, time dependent PDEs and nonlinear PDEs where the user's main program contains an iteration loop in which the major operation is the solution of one or more elliptic PDEs.
MGGHAT solves the elliptic PDE by the finite element method. The elements are continuous, but not differentiable, piecewise linear, quadratic or cubic (degree is user selectable) functions over a triangulation of the 2D domain. Given an initial (coarse) triangulation, an adaptive refinement procedure (based on the newest vertex bisection method) provides the properly graded final nonuniform triangulation. The full multigrid (FMG) method is used to solve the linear system of equations. Details of the methods used can be found in [1], [2], [3].
Send any questions, gripes, or praises concerning MGGHAT to
mitchell@cam.nist.gov or
na.wmitchell@na-net.ornl.gov.
