6.3  Subroutines LSEM3 and LSEMA

In this Section the subroutines LSEM3 and LSEMA are introduced. The purpose of the subroutines is to solve the exterior Laplace problem. Each subroutine's parameter list has the following general form:
SUBROUTINE LSEM{2 or 3 or A(}

description of shell and set of exterior solution points,

shell condition,

incident field at shell points and at exterior solution points,

control and validation parameters,

solution at shell 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 shell surface(s) (as covered in Chapter 2) and a list of the points in the exterior domain where a solution is sought, the shell condition, the incident field (if any). The subroutine returns the solution at the shell points and at the selected points in the domain. The use of the subroutines are demonstrated by the programs LSEM3_T and LSEMA_T in the next Section.

6.3.1  Solution Strategy of the LSEM* routines

In the LSEM* routines the exterior Laplace equation is solved by the shell element method. That is finding the solution of (88) subject to the discrete shell condition. This will result in obtaining (approximations to) both f and v on S. The solution in the domain is then found using equation (90).

6.3.2  Subroutine LSEM3

Subroutine LSEM3 computes solution of the three-dimensional Laplace equation in the domain exterior to a (set of) shell(s). The shell (G) 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 LSEM3_T.FOR ),

LSEM3.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.

6.3.3  Subroutine LSEMA

Subroutine LSEMA computes solutions of the axisymmetric three-dimensional Laplace equation in the domain exterior to a closed surface. The shell (G) 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 LSEMA_T.FOR ),

LSEMA.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.