Biomedical Engineering Reference
In-Depth Information
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Figure 4.17:
Plot of the characteristic curves along which
F
is constant.
complexity, and accuracy, and provide different advantages. All three strategies
are presented here.
The Extended Finite Element Method
The extended finite element method (X-FEM) [29,81,121] is a numerical method
to model internal (or external) boundaries without the need for the mesh to con-
form to these boundaries. The X-FEM is based on a standard Galerkin proce-
dure and uses the concept of partition of unity [80] to accommodate the internal
boundaries in the discrete model. The partition of unity method [80] generalized
finite element approximations by presenting a means to embed local solutions
of boundary-value problems into the finite element approximation.
For a standard finite element approximation, consider a point
x
of
R
d
that
lies inside a finite element
e
. Denote the nodal set N =
{
n
1
,
n
2
,...,
n
m
}
, where
m
is the number of nodes of element
e
. The approximation for a vector-valued