Appendix 3 - Advanced Use of LIBEM* and LEBEM* routines

The subroutines LIBEM2, LIBEM3, LIBEMA, LEBEM3 and LEBEMA contain the parameter LSOL. This parameter is set .TRUE in all the test problems in this book, determining that a solution to a particular boundary-value problem is required in all cases.

Setting LSOL=.FALSE. allows a more sophisticated use of the subroutines. In this case the subroutines do not return a particular solution. The important results from the subroutine are contained in the parameters WKSPC1, WKSPC2, WKSPC3 and WKSPC4.

In chapters 4-5 the boundary functions are always found by solving a linear system of equations of the form

A f = B v + c,
subject also to a boundary condition connecting f and v. The solution at the chosen points in the domain can then be accumulated from the discrete L and M operators. If LSOL is set .FALSE. then WKSPC1 stores the matrix A and WKSPC2 stores the matrix B. WKSPC3 contains the discrete L operator and WKSPC4 contains the discrete M operator associated with the chosen domain points. The stored data can be used to solve acoustic/Helmholtz problems outside the main subroutine.

The data in these arrays enables more flexible use of the boundary element method. Some examples of more advanced use of the routines are given here.

(i) Sometimes a range of different boundary conditions is required to be applied on a boundary at one frequency. In this case it is advisable to set up the matrices A and B once only and solve the resulting linear systems in turn.

(ii) The boundary element method may only model part of a greater coupled physical system. The matrices arising the BEM form only submatrices of the complete model of the system. The WKSPC1, WKSPC2 can be used as part of the matrix that models the complete system.

The LSEM3 and LSEMA subroutines

These routines are structured similarly to the above. However, take note of the special structure of the matrices in chapter 6, before using them in the way described above.

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