Discretisation and Interpolation - The Boundary Element Method with Programming - page 30

in the boundary method and start building the library of subroutines needed later. For the
treatment of non-linear problems discussed in Chapter 15 we will also need two- and
three-dimensional cells, which are also discussed here.

3.2 ONE-DIMENSIONAL BOUNDARY ELEMENTS

One-dimensional elements are used for the description of a boundary in the x-y plane.
The first step in the description of the boundary is to specify a discrete number of points
on the boundary (Figure 3.1). Next we specify an interpolation between these points. In
the simplest case we have linear segments (or boundary elements) which connect two
nodes i and j , the positions of which are defined by Cartesian coordinates. For each
element it is convenient to define a local ( intrinsic ) coordinate [ which follows the
direction of the element, equals zero at the centre and has the value of r 1 at the ends
(Figure 3.2).

10

9

11

8

12

1

7

y

2

e

6

x

3

5

4

Figure 3.1 Plane domain, boundary approximated by linear elements

6

y

[

x

1 2

[

e

5

[

[ [

b)

a)

Figure 3.2 Boundary element shown in a) global and b) local (intrinsic) coordinate space