An integral equation re-formulation can only be derived for certain classes of PDE . Hence the BEM is not widely applicable when compared to the near-universal adaptability of the finite element and finite difference method. However, in the cases in which the boundary element method is applicable, it often results in a numerical method that is easier to use and more computationally efficient than the competing methods.
The advantage in the boundary element method arises from the fact that only the boundary (or boundaries) of the domain of the PDE requires sub-division. (In the finite element method or finite difference method the whole domain of the PDE requires discretisation.) Thus the dimension of the problem is effectively reduced by one, for example an equation governing a three-dimensional region is transformed into one over its surface. In cases where the domain is exterior to the boundary, as it is in acoustic radiation and scattering models, the extent of the domain is infinite and hence the advantages of the BEM are even more striking; the equation governing the infinite domain is reduced to an equation over the (finite) boundary.
Solutions to two-dimensional, three-dimensional and axisymmetric three-dimensional acoustic problems are developed in this text. In each case boundary element techniques are developed for the solution of interior and exterior boundary-value problems and the interior eigenvalue problem, each allowing for a wide range of classes of boundary condition. The subroutines have been written so that they are applicable to a wide variety of acoustic problems. A very general form of boundary condition is assumed and it is possible to include an incident field that is necessary in acoustic scattering, for example. Nine major Fortran subroutines are developed for solving each of these problems and the source codes are available. It is the emphasis on the method development and programming that distinguishes this work from earlier texts such as Colton and Kress, Ciskowski and Brebbia and Rego Silva.
| Table 1.A: The main subroutines | ||||
| Chapter | 2-dimensional | 3-dimensional | Axisymmetric | |
| Core routines | 3 | H2LC | H3LC | H3ALC |
| Interior analysis | 4 | AIBEM2 | AIBEM3 | AIBEMA |
| Exterior analysis | 5 | AEBEM2 | AEBEM3 | AEBEMA |
| Modal analysis | 6 | AMBEM2 | AMBEM3 | AMBEMA |
[Other subordinate routines that are required are CGLS.FOR , GEOM2D.FOR , GEOM3D.FOR , FNHANK2.FOR .]
The three subroutines, for each dimensional space, call a core routine that is responsible for discretising the integral equation. Chapter 3 decribes the core routines; the underlying methods employed and the way in which the routines are called from the main programs. The major subroutines supplied with the text are listed in Table 1.A.
In science and engineering there are a wide variety of acoustic problems, only a fraction of which are considered in this work. The important example of fluid-structure interaction modelling, in which an acoustic field existing in a fluid influences and is influenced by a structure with which it is in contact (Wilton (78), Mathews (86) Kirkup (91) and Amini (92)) is not addressed in this work. However, the subroutines described in Chapters 4-6 can be adapted to include such problems.
A further important extension of the methods in this text is the use of integral equation methods for modelling the acoustic field exterior to a thin shell or shield. The traditional boundary element method is not directly applicable to such problems and alternative integral equation methods have been developed in references Ben Mariem (87), Warham (89) and Kirkup (91) has been developed as a generalisation of the boundary element method (the boundary and shell element method), which are not covered here, but software on this is being developed for this site.