follows:
1. Select trial values for { η 0} (i.e. 0th iteration) for all nodes in model domain
$
where the solution is desired.
2. Compute for all points the residual {r0} = {f} - [A] { η 0}and the left hand side
$
of Equation 125 as {p0} = [A*]{r0}.
2
[A * ]{ri }
3. Compute for the ith iteration the parameters αi, defined as: α i =
2
[A ]{p i }
4. Update {ηi + 1} = {ηi } + α i {p i } for all points.
$
$
5. Check for convergence of the solution. The criterion for convergence used in
CGWAVE is
2
[A]{ηi + 1} - {f}
$
<ε
(143)
2
{ηi+ 1}
$
where ε is a prescribed tolerance. If Equation 126 is satisfied, stop.
6. If Equation 126 is not satisfied, compute, for each grid point,
{ri +1} = {ri } - α i [A ]{p i } .
2
[A * ]{ri + 1}
7. Compute for the ith iteration : βi =
.
2
*
[A ]{ri }
8. Compute {p i + 1} = [A * ]{ri + 1} + βi {p i } .
9. Set i = i + 1, and go to step 3.
In the procedure above, the module of an array {x} is defined as
1/2
2
N
{x} = ∑ x i
(144)
i =1
43
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