The general subject area of concern to this book is computational science and
engineering, with applications in potential theory and in solid mechanics (linear
elasticity). This field has undergone a revolution during the past several decades
along with the exponential growth of computational power and memory. Problems
that were too large for main frame computers 15 or 20 years ago can now be
routinely solved on desktop personal computers.
There are several popular computational methods for solving problems in potential theory and linear elasticity. The most popular, versatile and most commonly
used is the finite element method (FEM). Many hundreds of books already exist
on the subject and new books get published frequently on a regular basis. Another
popular method is the boundary element method (BEM). Compared to the FEM,
we view the BEM as a niche method, in that it is particularly well suited, from the
point of view of accuracy as well as computational efficiency, for linear problems.
The principal advantage of the BEM, relative to the FEM, is its dimensionality
advantage. The FEM is a domain method that requires discretization of the entire
domain of a body while the BEM, for linear problems, only requires discretization
of its bounding surface.