Biomedical Engineering Reference
In-Depth Information
Fig. 5.8 Shape parameter p
effect on the V1P0 NNRPIM
solution accuracy. a Regular
nodal distribution. b Irregular
nodal distribution.
Logarithmic scales
1.0E+03
(a)
E
f
med
tot
1.0E+00
1.0E-03
1.0E-06
1.0E-09
1.0E-12
p
1.0E-15
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+03
(b)
E
f
med
tot
1.0E+00
1.0E-03
1.0E-06
1.0E-09
1.0E-12
p
1.0E-15
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
the studied NNRPIM formulations using second degree influence-cells the chosen
optimal MQ-RBF c shape parameter is c
opt
¼ 0
:
0001.
Afterwards, using the obtained optimal MQ-RBF c shape parameters for each
respective NNRPIM formulation, the MQ-RBF shape parameter p is varied
between p ¼½10
4
;
5
until an optimal p is achieved for each NNRPIM formu-
lation analysed. The results for the V2P0 NNRPIM formulation are shown in
Fig.
5.15
and the results obtained with the V2P1, V2P3 and V2P6 NNRPIM
formulations are respectively presented in Figs.
5.16
,
5.17
and
5.18
. Once again it
is desirable to avoid integer values to the shape parameter p, since those values
lead to a singular moment matrix.
As Fig.
5.15
shows, for the V2P0 NNRPIM formulation the optimization
curves shows an optimal value for the shape parameter p near the value 1.0. For
the V2P1 NNRPIM formulation, Fig.
5.16
, it is possible to identify the same
optimal value. Therefore, for both V2P0 and V2P1 NNRPIM formulations the
