
Engineering applications 335
the percentage. The values of the nodal parameters at the eld nodes are
computed after the convergence of PNP equations as
UAf{} {}
F
n
V
m1
1
1
=
×
−
×
(7.79)
where
A
Nmn
NN mn
A
n
AN
[] if
[][] if
and
if
[]if
mn
T
nm mn
T
nm
1
1
1
=
≡
≠
=
≡
≠
×
××
−
−
−
×
(7.80)
where [N] is the linear transformation matrix interpolating the values of
the function at the virtual nodes with the values of nodal parameters at the
surrounding eld nodes. U
F
and
f
V
are the vectors of the nodal param-
eter values at the eld nodes and the eld variable values at the virtual
nodes, respectively, and m and n are the numbers of total virtual and eld
nodes i ...