The boundary element method (BEM) is now a well-established numerical
technique which provides an efficient alternative to the prevailing
finite difference and finite element methods for the solution of a wide
range of engineering problems. The main advantage of the BEM is its
unique ability to provide a complete problem solution in terms of
boundary values only, with substantial savings in computer time and data
preparation effort. An initial restriction of the BEM was that the
fundamental solution to the original partial differential equation was
required in order to obtain an equivalent boundary in- tegral equation.
Another was that non-homogeneous terms accounting for effects such as
distributed loads were included in the formulation by means of domain
integrals, thus making the technique lose the attraction of its
"boundary-only" character. Many different approaches have been developed
to overcome these problems. It is our opinion that the most successful
so far is the dual reciprocity method (DRM), which is the subject matter
of this book. The basic idea behind this approach is to employ a
fundamental solution corresponding to a simpler equation and to treat
the remaining terms, as well as other non-homogeneous terms in the
original equation, through a procedure which involves a series expansion
using global approximating functions and the application of reciprocity
principles.