Multiple regions - The Boundary Element Method with Programming - page 297

u 1

x

u 1

y

Figure 11.7 Effect of application of Dirichlet boundary conditions on region II of cantilever
beam (elasticity problem)

11.3 COMPUTER IMPLEMENTATION

We now consider the computer implementation of the stiffness matrix assembly method.
We divide this into two tasks. First we develop a SUBROUTINE Stiffness_BEM for the
calculation of matrix K . If the problem is not fully coupled, then this subroutine will
also determine the matrix A and the solutions for zero values of u at the interface.
Secondly we develop a program General_purpose_BEM_Multi.
For an efficient implementation (where zero entries in the matrices are avoided) we
must consider 3 different numbering systems, each one is related to the global
numbering system as shown in Figure 11.5:

1.

Element numbering. This is the sequence in which the nodes to which an element
connects are entered in the element incidence vector. In the example in Figure 11.5
we have only two element nodes ( 1,2 ). Table 11.1 has two main columns: One
termed “in global numbering” which shows the node numbers as they appear in
Figure 11.5 and the other termed “in region numbering” as they appear on the top of
Figure 11.6.

2. Region numbering. This numbering is used for computing the “stiffness matrix” of

a region. For this the element node numbers are specified in “region numbering”.