[petsc-users] DIVERGED_DTOL

[w_ang_temp]

I am sorry.
In my view, preconditioned resid norm:||rp||=||Bb-BAx||(B is the preconditioned matrix);
true resid norm:||rt||=||b-Ax||;  ||r(i)||/||b||:  ||rt||/||b||.   Is it right?
(1) Divergence is detected if
   
    ||rp||/||b|| > dtol     or     ||rt||/||b|| > dtol  ?
    Both of them (rt/b:1.701448294063e+04 / 6.7139E+4; rt/b:2.716078947576e+04; dtol=1.0E+5 )
are not in this example, but it is divergent?

(2) Convergence is detected at iteration k if :
    ||rp||/||b|| < rtol
    But I find that when "preconditioned resid norm" is less than rtol, it begins to be convergent(another example,rtol=1.0E-15):
19 KSP preconditioned resid norm 4.964358598559e-15 true resid norm 1.076736705942e-08 ||r(i)||/||b|| 1.603737473724e-13
120 KSP preconditioned resid norm 1.045516340849e-14 true resid norm 1.089531944048e-08 ||r(i)||/||b|| 1.622795245901e-13
121 KSP preconditioned resid norm 1.209016864072e-14 true resid norm 1.096191254361e-08 ||r(i)||/||b|| 1.632713906089e-13
122 KSP preconditioned resid norm 1.568004225873e-15 true resid norm 1.073893120243e-08 ||r(i)||/||b|| 1.599502116167e-13
123 KSP preconditioned resid norm 5.066448468788e-15 true resid norm 1.078375214589e-08 ||r(i)||/||b|| 1.606177938235e-13
124 KSP preconditioned resid norm 3.619818305395e-16 true resid norm 1.073887987132e-08 ||r(i)||/||b|| 1.599494470692e-13
Linear solve converged due to CONVERGED_RTOL iterations 124
    In iteration 124, preconditioned resid norm begins to be smaller than rtol.

    Thanks.                                 Jim






>On 2013-01-09 01:13:44，"Jed Brown" <jedbrown at mcs.anl.gov> 写道：

>>On Tue, Jan 8, 2013 at 11:08 AM, w_ang_temp <w_ang_temp at 163.com> wrote:

>>354 KSP preconditioned resid norm 2.882557881065e-01 true resid norm 3.089426814670e+04 ||r(i)||/||b|| 4.601523777979e-01



>^^ Notice how this ratio is less than 1.0? DTOL is defined in terms of the smallest residual norm seen.
 
>>355 KSP preconditioned resid norm 2.170676916299e+02 true resid norm 2.326457175403e+07 ||r(i)||/||b|| 3.465124326697e+02
>>356 KSP preconditioned resid norm 5.764266225925e+00 true resid norm 6.177943120636e+05 ||r(i)||/||b|| 9.20169 1405543e+00
>>357 KSP preconditioned resid norm 1.701448294063e+04 true resid norm 1.823554008687e+09 ||r(i)||/||b|| 2.716078947576e+04

>>Linear solve did not converge due to DIVERGED_DTOL iterations 357
 
>>I cannot understand it. Which one means that the DIVERGED_DTOL occures:preconditioned resid norm, true resid norm or ||r(i)||/||b||?
>>What is the difference between preconditioned resid norm  and true resid norm?


>It uses the norm that your method is running. In this case, it's the preconditioned norm.
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