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(First solve R T z = r ).
Copy z
r .
For i =0to n − 1where R i,i
=0:
z i
R i,i
Set z i
.
Loop over j>i where R i,j is stored:
Set z j
z j
R i,j z i .
(Next solve Rz new = z in place).
For i = n
1downto0,where R i,i
=0:
Loop over j>i where R i,j
is stored:
Set z i
z i
R i,j z j .
z i
R i,i
Set z i
.
Figure 11.3.
Applying the MIC(0) preconditioner in CSR format to get z =
( R T R ) 1 r .
and the modified factor from:
R is upper triangular, and R i,j = 0 wherever A i,j =0,
( R T R ) i,j = A i,j
wherever A i,j
=0with i<j (i.e. off the diagonal),
each row sum j ( R T R ) i,j
matches the row sum j A i,j
of A .
Without going into the picky but obvious details of using the format, Figure
11.2 presents pseudocode to construct R , with the same parameters as
before, and Figure 11.3 demonstrates how to apply the preconditioner by
solving with R and R T .
11.5 Strong Coupling
Strong coupling has been most thoroughly worked out for the rigid body
case, with an inviscid fluid (just pressure); this is where we will end the
chapter. Let's work out the equations for the continuous case before pro-
ceeding to discretization.
First we'll define some notation for a rigid body:
X the center of mass of the rigid body,
V its translation velocity,
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