Integra
A single processor public domain Fortran-77 program by
Alfio Borzí to solve
nonlinear integral equations using a multigrid method.
The INTEGRA code was originally implemented to solve the
thermodynamic Bethe ansatz problem which provides a means to link a conjectured scattering theory
with the underlying field theory. This application of the code is described
in Alfio Borzí and Anni Koubek, Computer Physics Communications 75 (1993) 118-126.
However, INTEGRA is a general code for integral equations. It does not contain the most
sophisticated MG techniques for this
type of problems, but it can be useful to those who would like to use or learn multigrid to
solve integral equations.
The INTEGRA code is an implementation of the nonlinear multigrid
method for the solution of systems of nonlinear Fredholm integral equations of the second
kind:
/ bb
ui(y)=tni(y)+| sum_j( | fij(y,x,u(x))dx) , i=0,..,nsys, j=0,..,nsys,
/-bb
where nsys is the number of equations, fij are the kernels, x one-dimensional.
The bounds -b and b are determined by the code corresponding to the region where the kernel functions are zero to some
tolerance. The initial approximation is taken to be ui=tni=ri*gni, where the
ri's are given in the input file coeff.dat. The other input file,
integra.dat, contains multigrid related data.
The convergence properties of INTEGRA are analyzed in Alfio Borzí and Anni
Koubek,
On a Multi-Grid Algorithm for the TBA Equations, in P.W. Hemker and P. Wesseling (Eds.), Multigrid Methods IV,
International Series on Numerical Mathematics, Vol. 116, Birkhäuser
Verlag, Basel, 1994.
The data structure of this code is as given in: A. Brandt,
Multi-Level Adaptive Solutions to Boundary-Value Problems,
Mathematics of Computation 31 (1977) 333-390. This code is an implementation of the Nonlinear Multi-Grid Method
of the Second Kind (FAS scheme), which is described in: W. Hackbusch,
Multi-Grid Methods and Applications, Springer-Verlag, Berlin, 1985.
This is a public domain code. The program is provided
AS IS without warranty of any kind.
There are five files
associated with this package.
You only need integra.for or
routines.tgz. I ran into a g77 compiler bug when I tried to compile
integra.for. I split the file into one program per file and compiled
each program successfully. Try integra.for first. You need both
coeff.dat and integra.dat, which are input files.
Should you have trouble unpacking routines.tgz, the contents should be consulted. General
instructions on how to unpack the files in the routines.tgz file are in this hyperlink.
