In this Section the subroutines
LEBEM3 and LEBEMA are introduced.
The routines are
available as part of the BEMLAP package
(
Order via Amazon/science-books.net ).
The purpose of the subroutines is to solve the exterior
Laplace problem.
Each subroutine's parameter list has the following general form:
SUBROUTINE LEBEM{2 or 3 or A(}
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 Laplace field - 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 LEBEM3_T and LEBEMA_T in the next Section.
In the LEBEM* routines the exterior Laplace equation is solved by the improved direct boundary element method. That is finding the solution of (88) subject to the discrete boundary condition (89). This will result in obtaining (approximations to) both f and v on S. The solution in the domain is then found using equation (90).
Subroutine LEBEM3 computes solution of the three-dimensional
Laplace equation in the domain exterior to a closed surface.
The boundary (S) is approximated by a set of planar
triangular elements.
The subroutine parameters that specify the exterior
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 LEBEM3_T.FOR
),
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 LEBEMA computes solutions of the axisymmetric
three-dimensional
Laplace equation in the domain exterior to a closed surface.
The boundary (S) is approximated by a set of conical
elements.
The subroutine parameters that specify the exterior
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 LEBEMA_T.FOR
),
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.