SUBROUTINE HEBEM{2 or 3 or A(}
real wavenumber,
description of boundary and set of exterior solution points,
boundary condition,
incident field at boundary points and at exterior solution points,
control and validation parameters,
solution at boundary points and at exterior solution points
(solution),
working space )
The subroutines require input of the conditions of the Helmholtz field  the wavenumber, a geometrical description of the boundary of the domain (as covered in Chapter 2) and a list of the points in the exterior domain where a solution is sought, the boundary condition, the incident field (if any). The subroutine returns the solution at the boundary points and at the selected points in the domain. The use of the subroutines are demonstrated by the programs HEBEM2_T, HEBEM3_T and HEBEMA_T in the next Section.
A simple analysis of the magnitude of the integral operators suggests that a weighting of the form m ~ ^{1}/_{k} tends to ensure that the relative contribution from each integral operator on either side of the equation remains in balance, whatever the value of k. m is a parameter in the Fortran subroutines for solving the interior Helmholtz problem. In the test problems the parameter is chosen as follows:

The subroutine parameters that specify the exterior
threedimensional Helmholtz
problem must be set up in the main program. Let this be called
MAIN.FOR.
The following files must be linked together to construct the
complete program:
MAIN.FOR (and files containing any userdefined subprograms),
HEBEM3.FOR,
H3LC.FOR, the file for computing the discrete operators  see Chapter 3,
CGLS.FOR, the file for computing the solution to a linear
system  see Appendix 3,
GEOM3D.FOR, the file for 3D geometry  see Appendix 6.
The subroutine parameters that specify the exterior
threedimensional axisymmetric Helmholtz
problem must be set up in the main program. Let this be called
MAIN.FOR.
The following files must be linked together to construct the
complete program:
MAIN.FOR (and files containing any userdefined subprograms),
HIBEMA.FOR,
H3ALC.FOR, the file for computing the discrete operators  see Chapter 3,
CGLS.FOR, the file for computing the solution to a linear
system  see Appendix 3,
GEOM2D.FOR, the file for 2D geometry  see Appendix 6,
GEOM3D.FOR, the file for 3D geometry  see Appendix 6.