
400 Designing Scientific Applications on GPUs
Euler rule, the sensitivity is
J =
dx
M
dx
0
=
M
Y
i=1
1
h
i
C
i
+ G
i
−1
1
h
i
C
i−1
In summary, the envelope-following method is fundamentally a boosted
version of traditional transient analysis, with certain skips over several periods
and a Newton iteration to update or correct the errors brought by the skips,
as is exhibited by Figure 17.2.
17.3 New parallel envelope-following method
In this section, we explain how to efficiently use matrix-free GMRES to
solve the Newton update problems with implicit sensitivity calculation, i.e.,
the steps enclosed by the double dashed block in Figure 17.2. Then imple-
mentation issues of