3.9  Conclusion

The codes H2LC, H3LC and H3ALC are central to development of the full boundary element method routines in the following Chapters. The subroutines of this Chapter carry out integrations over a given element. The subroutines' parameter lists give the user a great deal of flexibility. The particular Helmholtz operators that are required can be selected and the quadrature rule can be defined within the parameter list.

Within the subroutines a large number of checks on the input data are carried out if the the validation parameter is set LVALID=.TRUE. (see Subsection 3.5.4) and the results from the validation are sent to an external file. In the * Fourier * subroutines that follow this validation parameter is switched off since the necessary validation is carried out in the main BEM subroutine.

A boundary element method needs to invoke the relevant H*LC core routine hundreds or perhaps thousands of times. In a practical problem with around a thousand elements the core routine will be invoked the order of a million times. For this reason the subroutines are efficiently coded. A computational cost analysis is given to advise the user on the control of processing time.

Using higher order elements would clearly be a useful approach to improving the efficiency of the BEM further. In order to obtain the full benefit from this, a more accurate method of representing the boundary would also need to be included. However, discretising the integral operators in such cases is very difficult, particularly for the Nk operator.

We shall see it is very important that we include the Nk operator, particularly in the solution of exterior Helmholtz problems. The techniques for representing the boundary and boundary functions considered in this work are sufficient to approximate all the relevant integral operators and provide a sound basis for the boundary element methods of the next three Chapters.


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