Electromagnetic Waves, Materials, and Computation with MATLAB®

Advanced Topics on Finite-Element Method 411

To include the effect of mixed boundary condition,

T

ij

s

and

g

i

s

should be suitably added in

assembling the global matrix. We then get the equation

[ ][ ] [ ].A gΦ =

(17.133)

17.5.4 3D Edge Elements [1,3]

In the 3D case, there are six edges as shown in Figure 17.10.

An edge i has a beginning node i

1

and ending node i

2

as shown in Table 17.3.

We can dene vector shape functions as follows:

α α α α α

i i i i i i

i

l= ∇ − ∇( ) .

1 2 2

17.5.5 Higher-Order Edge Elements

In two dimensions, higher-order edge elements are obtained as in Figure 17.11.

The tangential projection of the vector eld along edge ...