Biomedical Engineering Reference
In-Depth Information
T
d
∼
dx
c
d
∼
K
e
=
dx
dx
e
d
dx
−
1
1
T
d
∼
d
ξ
d
dx
c
d
∼
d
dx
=
d
ξ
d
ξ
ξ
=−
1
d
∼
d
ξ
n
int
T
c
d
∼
d
dx
≈
W
i
.
(14.79)
d
ξ
ξ
=
ξ
i
i
=
1
14.8
Basic structure of a finite element program
The objective of a finite element program is, to compute the coefficient matrix
K
and the right-hand side array
f
∼
and eventually to solve the resulting system of
equations taking the boundary conditions into account. To illustrate the typical
data structure and the layout of a finite element program, consider, as an example,
the mesh depicted in Fig.
14.8
.
The MATLAB programming language is used for explanation purposes. The
following data input is needed:
•
Element topology
First of all the domain is divided into a number of elements and
each node is given a unique global number. In this example two elements have been
used, the first element
1
is a quadratic element connecting nodes 3, 4 and 2 (in that
order) and the second element is a linear element having nodes 1 and 3 (again, in that
order). The node numbers of each element are stored in the topology array
top
,such
that the
i
-th row of this array corresponds to the
i
-th element. In the current example
the topology array would be:
342
130
.
top
=
Besides the node numbers of the element, a number of identifiers may be included
for each element, for instance to refer to different material parameters
c
or different
1
3
4
2
Ω
1
Ω
2
x
1
x
3
x
4
x
2
Figure 14.8
Mesh for a one-dimensional problem, consisting of a linear and a quadratic element.
