Laplace transform isotherm .pdf - University of Hertfordshire ...

Figure 2.3: Diagram showing the discretisation of the boundary into elements
and the collocation of a typical base node with a target element for
the boundary element method
of whether they are required. It may be used on domains of most shapes,
provided the elements used are sufficiently small to accurately represent the
boundary.
However, difficulties arise when the boundary contains corners and points
with discontinuous boundary conditions. The problem with boundaries con-
taining corners is the ambiguity of the direction of the normal derivative at
the corner. An approach to overcoming this is discussed by Toutip (2001) in
which he compares the multiple node method described by Mitra and Ingber
(1993) and the gradient approach of Alarcón et al. (1979) and Paris and
Cañas (1997). He concludes that both methods produce equally acceptable
results, but the multiple node method is simpler from a programming point
of view.
Although the boundary element method is attractive in having smaller
amounts of data which need to be processed, there are difficulties in ex-
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