FREE_FEM_HEAT is a FORTRAN90 program, using double precision arithmetic, which applies the finite element method to solve a form of the time-dependent heat equation over an arbitrary triangulated region.
The computational region is initially unknown by the program. The user specifies it by preparing a file containing the coordinates of the nodes, and a file containing the indices of nodes that make up triangles that form a triangulation of the region.
Normally, the user does not type in this information by hand, but has a program fill in the nodes, and perhaps another program that constructs the triangulation. However, in the simplest case, the user might construct a very crude triangulation by hand, and have TRIANGULATION_REFINE refine it to something more reasonable.
For the following ridiculously small example:
10-11-12
|\ |\
| \ | \
6 7 8 9
| \| \
1-2--3--4-5
the node file would be:
0.0 0.0
1.0 0.0
2.0 0.0
3.0 0.0
4.0 0.0
0.0 1.0
1.0 1.0
2.0 1.0
3.0 1.0
0.0 2.0
1.0 2.0
2.0 2.0
and the triangle file would be
1 3 10 2 7 6
3 5 12 4 9 8
12 10 3 11 7 8
The program is set up to handle the time dependent heat equation with a right hand side function, and nonhomogeneous Dirichlet boundary conditions. The state variable U(T,X,Y) is then constrained by:
Ut - ( Uxx + Uyy ) + K(x,y,t) * U = F(x,y,t) in the region
U = G(x,y,t) on the boundary
U = H(x,y,t) at initial time TINIT.
To specify the right hand side function F(x,y,t), the linear coefficient K(x,y,t), the boundary condition function G(x,y,t), and the initial condition H(x,y,t), the user has to supply a file containing four subroutines,
To run the program, the user compiles the user routines, links them with FREE_FEM_HEAT, and runs the executable.
The program writes out a file containing an Encapsulated PostScript image of the nodes and elements, with numbers. If there are too many nodes, the plot may be too cluttered to read. For lower values, however, it is a valuable map of what is going on in the geometry.
The program is also able to write out a file containing the solution value at every node. This file may be used to create contour plots of the solution.
CVT_TRIANGULATION is a FORTRAN90 program which constructs a CVT triangulation for certain regions.
FEM is a data directory which contains a description of the data files that can be used to describe a finite element model.
FEM_50 is a MATLAB finite element program in just 50 lines of code.
FEM_50_HEAT is a modified version of FEM_50 suitable for solving the heat equation.
FEM_BASIS_T3_DISPLAY is a MATLAB program which displays a basis function associated with a linear triangle ("T3") mesh.
FEM_BASIS_T6_DISPLAY is a MATLAB program which displays a basis function associated with a quadratic triangle ("T6") mesh.
FEM_IO is a set of FORTRAN90 routines for reading or writing the node, element and data files that define a finite element model.
FEM_SAMPLE is a FORTRAN90 library of routines for evaluating a finite element function defined on an order 3 or order 6 triangulation.
FEM_TO_TEC is a MATLAB program that can convert an FEM model into a TEC graphics file.
FEM1D, is an executable FORTRAN90 program which applies the finite element method, with piecewise linear basis functions, to a linear two point boundary value problem;
FEM1D_ADAPTIVE is a FORTRAN90 program that applies the finite element method to a linear two point boundary value problem in a 1D region, using adaptive refinement to improve the solution.
FEM1D_NONLINEAR is a FORTRAN90 program that applies the finite element method to a nonlinear two point boundary value problem in a 1D region.
FEM1D_PMETHOD is a FORTRAN90 program that applies the p-method version of the finite element method to a linear two point boundary value problem in a 1D region.
FEM2D_HEAT is an executable FORTRAN90 program for solving the heat equation on the unit square, using the finite element method.
FEM2D_POISSON is an executable FORTRAN90 program for solving Poisson's equation on the unit square, using the finite element method.
FEMPACK is a FORTRAN90 library of routines for finite element calculations.
FFH_SPARSE is a MATLAB program that solves the time dependent heat equation in an arbitrary triangulated 2D region, using MATLAB's sparse matrix storage format and solver.
FREE_FEM_HEAT is also available in a C++ version and a MATLAB version.
FREE_FEM_NAVIER_STOKES is a FORTRAN90 program which solves the 2D incompressible Navier Stokes equations in an arbitrary triangulated region.
FREE_FEM_POISSON is a FORTRAN90 program that solves the steady Poisson equation on a triangulated 2D region.
FREE_FEM_STOKES is a FORTRAN90 program that solves the steady Stokes flow equations on a triangulated 2D region.
HOT_PIPE is a sample problem that can be run with FEM_50_HEAT.
HOT_POINT is a sample problem that can be run with FEM_50_HEAT.
PLOT_POINTS is an executable FORTRAN90 program that can make a plot of the nodes that define the region.
PLTMG_SINGLE is a FORTRAN77 library of routines for solving elliptic partial differential equations using the finite element method with piecewise linear triangles and the multigrid approach.
TABLE is a file format which is used to store the input and output files used by the program.
TABLE_DELAUNAY is an executable FORTRAN90 program that constructs a Delaunay triangulation of a region which is described by a set of points.
TABLE_IO is a FORTRAN90 library that supplies the routines used to read the data files.
TRIANGULATION_ORDER6 is a data directory which contains a description of the format for the two files needed to describe an order 6 triangulation.
TRIANGULATION_ORDER6_CONTOUR is a MATLAB script which can make contour plots of the computed solution.
TRIANGULATION_PLOT is an executable FORTRAN90 program that can display an image of the triangulation used by the program.
TRIANGULATION_REFINE is an executable FORTRAN90 program that can refine a triangulation.
You can go up one level to the FORTRAN90 source codes.