The Boundary Element Method - Mechanics of Structures: Variational and Computational Methods - page 575

FIGURE 9.11
Boundary element meshes.

FIGURE 9.12
Boundary divided into segments.

9.5 Direct Integration of Integral Equations

A viable alternative, especially for two-dimensional problems, to the boundary element
method and the finite element method is available. This is the solution of integral equations
by the direct application of numerical integration schemes on the boundary of the domain.
Use a two-dimensional direct formulation of the Laplace equation [Eq. (9.28) with b = 0]

as an example. Gauss quadrature will be employed in the numerical solution.
The fundamental strategy of the direct integration method is to divide the boundary of the
domain into m segments (Fig. 9.12) and use Gauss numerical integration quadrature in each
segment. The total boundary may involve sharp corners which makes the application of
Gauss quadrature difficult. Division of the whole boundary into relatively smooth segments
can avoid this problem. The integral on the whole boundary is the sum of the integrals on