
GPU-accelerated envelope-following method 405
Let J
i
denote (1/h
i
)C
i
+G
i
in the remaining part of this chapter. In addition,
the LU factorizations of J
i
are already calculated since they are used to solve
the circuit state at each time step before we calculate the sensitivity.
Next, for the solution at t
2
, with the previous two steps information avail-
able, Gear-2 integration can be applied,
1
h
2
[q(x
2
) − α
1
q(x
1
) − α
2
q(x
0
)] + f(x
2
) = b
2
. (17.6)
In view of the sensitivity of x
2
with respect to the changes of x
0
, (17.6)
indicates that x
2
’s perturbation can be traced back to x
0
along two paths: x
2
is directly affected by x
0
, and x
2
is also affected indirectly b