Environmental Engineering Reference
In-Depth Information
To minimize the cost of computation, it is observed that all entries
of
M
matrix on the right hand side of (11.9) except the one at the
bottom right corner is independent of frequency. This observation
suggests that it is possible to transfer most of the computation into
a preprocessing stage of the algorithm so that computation per fre-
quency point is minimized. To achieve this, we wish to reduce the
system matrix to the upper block diagonal form by making all blocks
below the main diagonal identically zero. This is accomplished by
the following block elimination technique. Pre-multiply the first row
of
M
by and add the result to the second row. A zero is created
in the position (2,1), position (2,K) becomes and the prod-
uct is added to the second row of the right hand side vector.
Next, Pre-multiply the second row by and add to the third row.
A zero block is created in position (3,2), the position (3,K) is filled
with
and the third row of the right hand side vector be-
comes
Continuing this process,
we arrive at
where
Note that both
E
and are independent of frequency. They can be
pre-computed and stored in a pre-processing step prior to the start of
simulation. Once
is available,
can be obtained from
In applications where clock frequency is much higher than signal fre-
quency, the variation of network variables within each clock phase
Search WWH ::
Custom Search