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Shouldn't be, but it seems that is is close to singular in computer
arithmetic. I would like to understand we it's so. The matrix is a
2x2 block matrix with no coupling between the main blocks. I know
that this does not make much sense but its for tests only and I
would like to add some couplings later. Both blocks are nonsingular
and easy solvable with direct solvers. But when adding both
together, the condition number rise to something around 10^23. Is it
only a question of scaling both matrices to the same order?<br>
<br>
Thomas<br>
<br>
Am 02.02.2012 15:32, schrieb Jed Brown:
<blockquote
cite="mid:CAM9tzSkZ0XGkdp4r-=OFF2M+E3vv-9C_m8hsxQDh16QF0rpGKg@mail.gmail.com"
type="cite">Is this problem singular?<br>
<br>
<div class="gmail_quote">On Thu, Feb 2, 2012 at 13:47, Thomas
Witkowski <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:thomas.witkowski@tu-dresden.de">thomas.witkowski@tu-dresden.de</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">For some
tests I use richardson iterations with direct solver for
preconditioning (if everything is fine, richardson should be
replaces by preonly).<br>
<br>
-ksp_type richardson -pc_type lu
-pc_factor_mat_solver_package mumps -ksp_monitor
-ksp_monitor_true_residual -ksp_max_it 10<br>
<br>
For some matrices I see that it converges fine in true
residual norm but not in the preconditioned one:<br>
<br>
0 KSP Residual norm 1.540366130785e+05<br>
0 KSP preconditioned resid norm 1.540366130785e+05 true resid
norm 4.257656834616e+04 ||r(i)||/||b|| 1.000000000000e+00<br>
1 KSP Residual norm 1.355077212761e+05<br>
1 KSP preconditioned resid norm 1.355077212761e+05 true resid
norm 1.468758291284e-11 ||r(i)||/||b|| 3.449686877867e-16<br>
2 KSP Residual norm 3.775360693480e+05<br>
2 KSP preconditioned resid norm 3.775360693480e+05 true resid
norm 5.008860262312e-12 ||r(i)||/||b|| 1.176435879376e-16<br>
3 KSP Residual norm 1.714431257209e+05<br>
3 KSP preconditioned resid norm 1.714431257209e+05 true resid
norm 5.365631839419e-12 ||r(i)||/||b|| 1.260231166541e-16<br>
4 KSP Residual norm 7.164219897555e+04<br>
4 KSP preconditioned resid norm 7.164219897555e+04 true resid
norm 5.582291603774e-12 ||r(i)||/||b|| 1.311118256030e-16<br>
5 KSP Residual norm 2.480147180914e+05<br>
5 KSP preconditioned resid norm 2.480147180914e+05 true resid
norm 5.464714292269e-12 ||r(i)||/||b|| 1.283502758569e-16<br>
6 KSP Residual norm 1.749548383255e+05<br>
6 KSP preconditioned resid norm 1.749548383255e+05 true resid
norm 6.601924132117e-12 ||r(i)||/||b|| 1.550600339239e-16<br>
7 KSP Residual norm 1.873773824295e+05<br>
7 KSP preconditioned resid norm 1.873773824295e+05 true resid
norm 6.368611865551e-12 ||r(i)||/||b|| 1.495802060366e-16<br>
8 KSP Residual norm 2.610223461339e+05<br>
8 KSP preconditioned resid norm 2.610223461339e+05 true resid
norm 8.365362648969e-12 ||r(i)||/||b|| 1.964780858090e-16<br>
9 KSP Residual norm 2.459609758347e+05<br>
9 KSP preconditioned resid norm 2.459609758347e+05 true resid
norm 8.427381039077e-12 ||r(i)||/||b|| 1.979347177668e-16<br>
10 KSP Residual norm 1.611793769272e+05<br>
10 KSP preconditioned resid norm 1.611793769272e+05 true
resid norm 8.325158481093e-12 ||r(i)||/||b||
1.955338066095e-16<br>
<br>
<br>
Would could be the reason for?<br>
<font color="#888888">
<br>
Thomas<br>
</font></blockquote>
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<br>
</blockquote>
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