SUBROUTINE LIBEM{2 or 3 or A(}
description of boundary and set of interior solution points,
boundary condition,
incident field at boundary points and at interior solution points,
control and validation parameters,
solution at boundary points and at interior solution points
(solution),
working space )
The subroutines require input of the conditions of the Laplace 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 interior domain where a solution is sought, the boundary condition and 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 LIBEM2_T, LIBEM3_T and LIBEMA_T in the next Section.
In the LIBEM* routines the interior Laplace equation is solved by the improved direct boundary element method. That is finding the solution of (65) subject to the discrete boundary condition (66). This will result in obtaining (approximations to) both f and v on S. The solution in the domain is then found using equation (67).
Subroutine
LIBEM2
computes the solution of the two-dimensional
Laplace equation in the domain interior to a closed boundary.
The boundary (S) is approximated by a set of straight line elements.
The subroutine parameters that specify the interior
two-dimensional Laplace
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 user-defined sub-programs
for example LIBEM2_T.FOR
),
LIBEM2.FOR ,
the subroutine for solving the 2D Laplace problem,
L2LC.FOR, the file for computing the discrete operators - see Chapter 3,
GLS.FOR , the file for computing the solution to a linear
system - see Appendix 1,
GEOM2D.FOR , the file for 2D geometry - see Appendix 2.
Subroutine LIBEM3 computes solution of the three-dimensional
Laplace equation in the domain interior to a closed surface.
The boundary (S) is approximated by a set of planar
triangular elements.
The subroutine parameters that specify the interior
three-dimensional Laplace
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 user-defined sub-programs
for example LIBEM3_T.FOR
),
LIBEM3.FOR ,
the subroutine for solving the 3D Laplace problem,
L3LC.FOR, the file for computing the discrete operators - see Chapter 3,
GLS.FOR , the file for computing the solution to a linear
system - see Appendix 1,
GEOM3D, the file for 3D geometry - see Appendix 2.
Subroutine LIBEMA computes solution of the three-dimensional
axisymmetric
Laplace equation in the domain interior to a closed surface.
The boundary (S) is approximated by a set of truncated
cone elements.
The subroutine parameters that specify the interior
three-dimensional axisymmetric Laplace
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 user-defined sub-programs
for example LIBEMA_T.FOR
),
LIBEMA.FOR ,
the subroutine for solving the axisymmetric Laplace problem,
L3ALC.FOR, the file for computing the discrete operators - see Chapter 3,
GLS.FOR , the file for computing the solution to a linear
system - see Appendix 1,
GEOM2D , the file for 2D geometry - see Appendix 2,
GEOM3D , the file for 3D geometry - see Appendix 2.