Most likely not a bug; more like a feature. BT is meant to take the full step when the descent condition is fine. The descent condition can be fine without making a ton of progress. Taking the full step avoids a lot of work (extra function evaluations) when the solve is working right, but messes up hard when it isn't. I'm wondering why your problem is doing this. The question is, therefore, why is 2x the optimum step?<br>
<br>For 1D problems this is explained by classical numerical analysis; the root the Newton's method is finding has multiplicity 2. I'm wondering what exactly would exhibit this behavior in multiple dimensions for a linear problem.<br>
<br>- Peter<br><br><div class="gmail_quote">On Tue, Aug 14, 2012 at 9:51 PM, Barry Smith <span dir="ltr"><<a href="mailto:bsmith@mcs.anl.gov" target="_blank">bsmith@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Likely a bug in our bt. It says it is taking a full step but then seems to take a half-step (based on the result from l2 Line search: lambdas = [1, 0.5, 0], fnorms = [2.1936e-08, 1.87107, 3.74214]<br>
<div class="im"><br>
> [0] SNESLineSearchApply_BT(): Initial fnorm 3.742138023215e+00 gnorm 1.871069011453e+00<br>
> Line search: Using full step: fnorm 3.742138023215e+00 gnorm 1.871069011453e+00<br>
> [0] SNESSolve_LS(): fnorm=3.7421380232151638e+00, gnorm=1.8710690114527022e+00, ynorm=2.5919210284812890e+00, lssucceed=1<br>
> 1 SNES Function norm 1.871069011453e+00<br>
<br>
</div> ^^^^^ result as if took a 1/2 step<br>
<span class="HOEnZb"><font color="#888888"><br>
Barry<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
<br>
<br>
On Aug 14, 2012, at 6:24 PM, Blaise Bourdin <<a href="mailto:bourdin@lsu.edu">bourdin@lsu.edu</a>> wrote:<br>
<br>
> Hi,<br>
><br>
><br>
> On Aug 14, 2012, at 5:58 PM, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>> wrote:<br>
><br>
>><br>
>> Blaise,<br>
>><br>
>> You can run with -snes_linesearch_monitor -info -ksp_monitor_true_residual -ksp_converged_reason<br>
>><br>
>><br>
>> to get much more information about what is happening and why the line search is failing.<br>
> Focussing on the relevant part of the output, I get the following for the first SNES step<br>
><br>
> *** Using l2<br>
> Residual norms for temp_ solve.<br>
> 0 KSP preconditioned resid norm 2.352873068990e+00 true resid norm 3.742138023215e+00 ||r(i)||/||b|| 1.000000000000e+00<br>
> [0] KSPDefaultConverged(): user has provided nonzero initial guess, computing 2-norm of preconditioned RHS<br>
> 1 KSP preconditioned resid norm 7.175926524783e-01 true resid norm 8.026926174904e-01 ||r(i)||/||b|| 2.145010719836e-01<br>
> 2 KSP preconditioned resid norm 4.099791012407e-01 true resid norm 6.219898727406e-01 ||r(i)||/||b|| 1.662124349455e-01<br>
> 3 KSP preconditioned resid norm 2.769612150659e-01 true resid norm 4.622335508644e-01 ||r(i)||/||b|| 1.235212458752e-01<br>
> 4 KSP preconditioned resid norm 8.991164116822e-02 true resid norm 1.938840972976e-01 ||r(i)||/||b|| 5.181104921701e-02<br>
> 5 KSP preconditioned resid norm 1.369794733551e-02 true resid norm 2.867541652138e-02 ||r(i)||/||b|| 7.662843097578e-03<br>
> 6 KSP preconditioned resid norm 3.522245138600e-03 true resid norm 5.452585588775e-03 ||r(i)||/||b|| 1.457077626466e-03<br>
> 7 KSP preconditioned resid norm 1.117008651636e-03 true resid norm 1.551905826961e-03 ||r(i)||/||b|| 4.147110067382e-04<br>
> 8 KSP preconditioned resid norm 5.008635361807e-04 true resid norm 6.226120116381e-04 ||r(i)||/||b|| 1.663786872038e-04<br>
> 9 KSP preconditioned resid norm 2.079118910844e-04 true resid norm 3.430664466007e-04 ||r(i)||/||b|| 9.167658821571e-05<br>
> 10 KSP preconditioned resid norm 4.528126074206e-05 true resid norm 9.520866575330e-05 ||r(i)||/||b|| 2.544231804457e-05<br>
> 11 KSP preconditioned resid norm 8.441137224072e-06 true resid norm 1.519916221879e-05 ||r(i)||/||b|| 4.061625232553e-06<br>
> 12 KSP preconditioned resid norm 1.839317974157e-06 true resid norm 3.245208227421e-06 ||r(i)||/||b|| 8.672069836252e-07<br>
> 13 KSP preconditioned resid norm 4.346353491153e-07 true resid norm 7.198101954057e-07 ||r(i)||/||b|| 1.923526580100e-07<br>
> 14 KSP preconditioned resid norm 6.321413805477e-08 true resid norm 1.280486229700e-07 ||r(i)||/||b|| 3.421803850515e-08<br>
> 15 KSP preconditioned resid norm 9.029476674935e-09 true resid norm 2.193598397200e-08 ||r(i)||/||b|| 5.861885327562e-09<br>
> [0] KSPDefaultConverged(): Linear solver has converged. Residual norm 9.029476674935e-09 is less than relative tolerance 1.000000000000e-08 times initial right hand side norm 2.352873068990e+00 at iteration 15<br>
> Linear solve converged due to CONVERGED_RTOL iterations 15<br>
> [0] SNESSolve_LS(): iter=0, linear solve iterations=15<br>
> [0] SNESLSCheckResidual_Private(): ||J^T(F-Ax)||/||F-AX|| 4.179425981164e+00 near zero implies inconsistent rhs<br>
> Line search: lambdas = [1, 0.5, 0], fnorms = [2.1936e-08, 1.87107, 3.74214]<br>
> Line search terminated: lambda = 1, fnorms = 2.19338e-08<br>
> [0] SNESSolve_LS(): fnorm=3.7421380232151638e+00, gnorm=2.1933796240714327e-08, ynorm=5.1838420564550498e+00, lssucceed=1<br>
> 1 SNES Function norm 2.193379624071e-08<br>
> [0] SNESDefaultConverged(): Converged due to function norm 2.193379624071e-08 < 3.742138023215e-08 (relative tolerance)<br>
> SNESTemp converged in in 1 iterations. SNESConvergedReason is 3<br>
><br>
> *** Using bt<br>
> Residual norms for temp_ solve.<br>
> 0 KSP preconditioned resid norm 1.176436534193e+00 true resid norm 3.742138022596e+00 ||r(i)||/||b|| 9.999999998344e-01<br>
> [0] KSPDefaultConverged(): user has provided nonzero initial guess, computing 2-norm of preconditioned RHS<br>
> 1 KSP preconditioned resid norm 3.587963259712e-01 true resid norm 8.026926179905e-01 ||r(i)||/||b|| 2.145010721173e-01<br>
> 2 KSP preconditioned resid norm 2.049895509618e-01 true resid norm 6.219898720314e-01 ||r(i)||/||b|| 1.662124347560e-01<br>
> 3 KSP preconditioned resid norm 1.384806072424e-01 true resid norm 4.622335514699e-01 ||r(i)||/||b|| 1.235212460370e-01<br>
> 4 KSP preconditioned resid norm 4.495582078268e-02 true resid norm 1.938840967382e-01 ||r(i)||/||b|| 5.181104906751e-02<br>
> 5 KSP preconditioned resid norm 6.848973644691e-03 true resid norm 2.867541656135e-02 ||r(i)||/||b|| 7.662843108259e-03<br>
> 6 KSP preconditioned resid norm 1.761122593261e-03 true resid norm 5.452585577786e-03 ||r(i)||/||b|| 1.457077623530e-03<br>
> 7 KSP preconditioned resid norm 5.585043310756e-04 true resid norm 1.551905808041e-03 ||r(i)||/||b|| 4.147110016822e-04<br>
> 8 KSP preconditioned resid norm 2.504317746421e-04 true resid norm 6.226120013063e-04 ||r(i)||/||b|| 1.663786844429e-04<br>
> 9 KSP preconditioned resid norm 1.039559493091e-04 true resid norm 3.430664433173e-04 ||r(i)||/||b|| 9.167658733830e-05<br>
> 10 KSP preconditioned resid norm 2.264063167431e-05 true resid norm 9.520867156897e-05 ||r(i)||/||b|| 2.544231959867e-05<br>
> 11 KSP preconditioned resid norm 4.220568874641e-06 true resid norm 1.519916304124e-05 ||r(i)||/||b|| 4.061625452335e-06<br>
> 12 KSP preconditioned resid norm 9.196589910150e-07 true resid norm 3.245208482213e-06 ||r(i)||/||b|| 8.672070517123e-07<br>
> 13 KSP preconditioned resid norm 2.173176852660e-07 true resid norm 7.198102176806e-07 ||r(i)||/||b|| 1.923526639624e-07<br>
> 14 KSP preconditioned resid norm 3.160707194729e-08 true resid norm 1.280486368595e-07 ||r(i)||/||b|| 3.421804221680e-08<br>
> 15 KSP preconditioned resid norm 4.514738683754e-09 true resid norm 2.193598711826e-08 ||r(i)||/||b|| 5.861886168328e-09<br>
> [0] KSPDefaultConverged(): Linear solver has converged. Residual norm 4.514738683754e-09 is less than relative tolerance 1.000000000000e-08 times initial right hand side norm 1.176436534495e+00 at iteration 15<br>
> Linear solve converged due to CONVERGED_RTOL iterations 15<br>
> [0] SNESSolve_LS(): iter=0, linear solve iterations=15<br>
> [0] SNESLSCheckResidual_Private(): ||J^T(F-Ax)||/||F-AX|| 8.358851664967e+00 near zero implies inconsistent rhs<br>
> [0] VecScatterCreate(): Special case: sequential vector general scatter<br>
> [0] SNESLineSearchApply_BT(): Initial fnorm 3.742138023215e+00 gnorm 1.871069011453e+00<br>
> Line search: Using full step: fnorm 3.742138023215e+00 gnorm 1.871069011453e+00<br>
> [0] SNESSolve_LS(): fnorm=3.7421380232151638e+00, gnorm=1.8710690114527022e+00, ynorm=2.5919210284812890e+00, lssucceed=1<br>
> 1 SNES Function norm 1.871069011453e+00<br>
><br>
><br>
> As expected, the KSP residuals are exactly the same. I am not sure what to make of<br>
> [0] SNESLSCheckResidual_Private(): ||J^T(F-Ax)||/||F-AX|| 8.358851664967e+00 near zero implies inconsistent rhs.<br>
> Which RHS is this referring to? the RHS for SNESSolve is 0 (second argument of SNESSolve is PETSC_NULL_OBJECT). Could this mean that there is an incompatibility between my Jacobian and my Function?<br>
><br>
> In all case that diverge, it looks like the gnorm in the linesearch does not decrease.<br>
><br>
>><br>
>> If that doesn't help you can send the code and we can play with it.<br>
><br>
> The code is a bit of a pain to build but both Matt and Jed have accounts on my systems. I can arrange to give access to others if necessary.<br>
><br>
> Blaise<br>
><br>
><br>
>><br>
>> Barry<br>
>><br>
>><br>
>><br>
>> On Aug 14, 2012, at 5:53 PM, Blaise Bourdin <<a href="mailto:bourdin@lsu.edu">bourdin@lsu.edu</a>> wrote:<br>
>><br>
>>> HI,<br>
>>><br>
>>> I am trying to understand if the following behavior is normal / expected:<br>
>>><br>
>>> I am solving a quasi-static evolution where at each time step, SNESSolve is called. My validation problem is a _static_ problem with 2 time steps (i.e. 2 successive calls to SNESSolve with the same operator, jacobian, and right hand side). Furthermore, the problem is linear, so that the Jacobian is constant. I even reset the solution vector to the same value at each time step.<br>
>>><br>
>>> In this setting, I am expecting that at each time step, each SNESSolve should converge in exactly one iteration no matter what linesearch / snes type I use. Indeed, when setting the linesearch to l2 or cp, this is what I get. However, for all other choices, the second call to SNESSolve fails to converge with a SNESConvergedReason of -5 or -6.<br>
>>><br>
>>> The relevant code is as follow:<br>
>>> Call VecSet(solTemp,0.0_Kr,ierr);CHKERRQ(ierr)<br>
>>> Call FormInitialGuess(snesTemp,solTemp,MEF90Ctx,ierr);CHKERRQ(ierr)<br>
>>> Call VecCopy(solTemp,tmpvec,ierr)<br>
>>><br>
>>> Call SNESSolve(snesTemp,PETSC_NULL_OBJECT,solTemp,ierr);CHKERRQ(ierr)<br>
>>><br>
>>> Call VecCopy(tmpvec,soltemp,ierr)<br>
>>> Call SNESSolve(snesTemp,PETSC_NULL_OBJECT,solTemp,ierr);CHKERRQ(ierr)<br>
>>><br>
>>><br>
>>> Is this expected? I tried to call SNESLineSearchReset before the second call to SNESSolve, but this does not seem to have any effect.<br>
>>><br>
>>> Blaise<br>
>>><br>
>>><br>
>>><br>
>>> Below is the sample output using cp as the linesearch type in which case I get the expected convergence:<br>
>>> Solving time step 1: t= 1.00000E+00<br>
>>> 0 SNES Function norm 3.742138023215e+00<br>
>>> Line search terminated: lambda = 1, fnorms = 2.1936e-08<br>
>>> 1 SNES Function norm 2.193598339906e-08<br>
>>> SNES Object:(temp_) 1 MPI processes<br>
>>> type: ls<br>
>>> maximum iterations=50, maximum function evaluations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08<br>
>>> total number of linear solver iterations=15<br>
>>> total number of function evaluations=3<br>
>>> KSP Object: (temp_) 1 MPI processes<br>
>>> type: cg<br>
>>> maximum iterations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000<br>
>>> left preconditioning<br>
>>> using nonzero initial guess<br>
>>> using PRECONDITIONED norm type for convergence test<br>
>>> PC Object: (temp_) 1 MPI processes<br>
>>> type: icc<br>
>>> 0 levels of fill<br>
>>> tolerance for zero pivot 2.22045e-14<br>
>>> using Manteuffel shift<br>
>>> matrix ordering: natural<br>
>>> factor fill ratio given 1, needed 1<br>
>>> Factored matrix follows:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqsbaij<br>
>>> rows=104, cols=104<br>
>>> package used to perform factorization: petsc<br>
>>> total: nonzeros=381, allocated nonzeros=381<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> block size is 1<br>
>>> linear system matrix = precond matrix:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqaij<br>
>>> rows=104, cols=104<br>
>>> total: nonzeros=658, allocated nonzeros=658<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> not using I-node routines<br>
>>> SNESLineSearch Object: (temp_) 1 MPI processes<br>
>>> type: cp<br>
>>> maxstep=1.000000e+08, minlambda=1.000000e-12<br>
>>> tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08<br>
>>> maximum iterations=1<br>
>>> SNESTemp converged in in 1 iterations. SNESConvergedReason is 3<br>
>>> 0 SNES Function norm 3.742138023215e+00<br>
>>> Line search: lambdas = [1, 0], ftys = [2.42597, 4.85193]<br>
>>> Line search terminated: lambda = 2, fnorms = 2.1936e-08<br>
>>> 1 SNES Function norm 2.193598717772e-08<br>
>>> SNES Object:(temp_) 1 MPI processes<br>
>>> type: ls<br>
>>> maximum iterations=50, maximum function evaluations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08<br>
>>> total number of linear solver iterations=15<br>
>>> total number of function evaluations=3<br>
>>> KSP Object: (temp_) 1 MPI processes<br>
>>> type: cg<br>
>>> maximum iterations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000<br>
>>> left preconditioning<br>
>>> using nonzero initial guess<br>
>>> using PRECONDITIONED norm type for convergence test<br>
>>> PC Object: (temp_) 1 MPI processes<br>
>>> type: icc<br>
>>> 0 levels of fill<br>
>>> tolerance for zero pivot 2.22045e-14<br>
>>> using Manteuffel shift<br>
>>> matrix ordering: natural<br>
>>> factor fill ratio given 1, needed 1<br>
>>> Factored matrix follows:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqsbaij<br>
>>> rows=104, cols=104<br>
>>> package used to perform factorization: petsc<br>
>>> total: nonzeros=381, allocated nonzeros=381<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> block size is 1<br>
>>> linear system matrix = precond matrix:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqaij<br>
>>> rows=104, cols=104<br>
>>> total: nonzeros=658, allocated nonzeros=658<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> not using I-node routines<br>
>>> SNESLineSearch Object: (temp_) 1 MPI processes<br>
>>> type: cp<br>
>>> maxstep=1.000000e+08, minlambda=1.000000e-12<br>
>>> tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08<br>
>>> maximum iterations=1<br>
>>> SNESTemp converged in in 1 iterations. SNESConvergedReason is 3<br>
>>><br>
>>><br>
>>> when using the default linesearch (bt), the second SNESSolve fails:<br>
>>><br>
>>> Solving time step 1: t= 1.00000E+00<br>
>>> 0 SNES Function norm 3.742138023215e+00<br>
>>> Line search: Using full step: fnorm 3.742138023215e+00 gnorm 2.193598339906e-08<br>
>>> 1 SNES Function norm 2.193598339906e-08<br>
>>> SNES Object:(temp_) 1 MPI processes<br>
>>> type: ls<br>
>>> maximum iterations=50, maximum function evaluations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08<br>
>>> total number of linear solver iterations=15<br>
>>> total number of function evaluations=2<br>
>>> KSP Object: (temp_) 1 MPI processes<br>
>>> type: cg<br>
>>> maximum iterations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000<br>
>>> left preconditioning<br>
>>> using nonzero initial guess<br>
>>> using PRECONDITIONED norm type for convergence test<br>
>>> PC Object: (temp_) 1 MPI processes<br>
>>> type: icc<br>
>>> 0 levels of fill<br>
>>> tolerance for zero pivot 2.22045e-14<br>
>>> using Manteuffel shift<br>
>>> matrix ordering: natural<br>
>>> factor fill ratio given 1, needed 1<br>
>>> Factored matrix follows:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqsbaij<br>
>>> rows=104, cols=104<br>
>>> package used to perform factorization: petsc<br>
>>> total: nonzeros=381, allocated nonzeros=381<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> block size is 1<br>
>>> linear system matrix = precond matrix:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqaij<br>
>>> rows=104, cols=104<br>
>>> total: nonzeros=658, allocated nonzeros=658<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> not using I-node routines<br>
>>> SNESLineSearch Object: (temp_) 1 MPI processes<br>
>>> type: bt<br>
>>> interpolation: cubic<br>
>>> alpha=1.000000e-04<br>
>>> maxstep=1.000000e+08, minlambda=1.000000e-12<br>
>>> tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08<br>
>>> maximum iterations=40<br>
>>> SNESTemp converged in in 1 iterations. SNESConvergedReason is 3<br>
>>> 0 SNES Function norm 3.742138023215e+00<br>
>>> Line search: Using full step: fnorm 3.742138023215e+00 gnorm 1.871069011453e+00<br>
>>> 1 SNES Function norm 1.871069011453e+00<br>
>>> Line search: Using full step: fnorm 1.871069011453e+00 gnorm 1.247379340865e+00<br>
>>> 2 SNES Function norm 1.247379340865e+00<br>
>>> Line search: Using full step: fnorm 1.247379340865e+00 gnorm 9.355345056231e-01<br>
>>> 3 SNES Function norm 9.355345056231e-01<br>
>>> Line search: Using full step: fnorm 9.355345056231e-01 gnorm 7.484276044882e-01<br>
>>> 4 SNES Function norm 7.484276044882e-01<br>
>>> Line search: Using full step: fnorm 7.484276044882e-01 gnorm 6.236896704016e-01<br>
>>> 5 SNES Function norm 6.236896704016e-01<br>
>>> Line search: Using full step: fnorm 6.236896704016e-01 gnorm 5.345911460556e-01<br>
>>> 6 SNES Function norm 5.345911460556e-01<br>
>>> Line search: Using full step: fnorm 5.345911460556e-01 gnorm 4.677672528597e-01<br>
>>> 7 SNES Function norm 4.677672528597e-01<br>
>>> Line search: Using full step: fnorm 4.677672528597e-01 gnorm 4.157931136937e-01<br>
>>> 8 SNES Function norm 4.157931136937e-01<br>
>>> Line search: Using full step: fnorm 4.157931136937e-01 gnorm 3.742138023528e-01<br>
>>> 9 SNES Function norm 3.742138023528e-01<br>
>>> Line search: Using full step: fnorm 3.742138023528e-01 gnorm 3.401943657960e-01<br>
>>> 10 SNES Function norm 3.401943657960e-01<br>
>>> Line search: Using full step: fnorm 3.401943657960e-01 gnorm 3.118448353285e-01<br>
>>> 11 SNES Function norm 3.118448353285e-01<br>
>>> Line search: Using full step: fnorm 3.118448353285e-01 gnorm 2.878567710844e-01<br>
>>> 12 SNES Function norm 2.878567710844e-01<br>
>>> Line search: Using full step: fnorm 2.878567710844e-01 gnorm 2.672955731592e-01<br>
>>> 13 SNES Function norm 2.672955731592e-01<br>
>>> Line search: Using full step: fnorm 2.672955731592e-01 gnorm 2.494758682895e-01<br>
>>> 14 SNES Function norm 2.494758682895e-01<br>
>>> Line search: Using full step: fnorm 2.494758682895e-01 gnorm 2.338836265275e-01<br>
>>> 15 SNES Function norm 2.338836265275e-01<br>
>>> Line search: Using full step: fnorm 2.338836265275e-01 gnorm 2.201257661485e-01<br>
>>> 16 SNES Function norm 2.201257661485e-01<br>
>>> Line search: Using full step: fnorm 2.201257661485e-01 gnorm 2.078965569222e-01<br>
>>> 17 SNES Function norm 2.078965569222e-01<br>
>>> Line search: Using full step: fnorm 2.078965569222e-01 gnorm 1.969546328772e-01<br>
>>> 18 SNES Function norm 1.969546328772e-01<br>
>>> Line search: Using full step: fnorm 1.969546328772e-01 gnorm 1.871069012364e-01<br>
>>> 19 SNES Function norm 1.871069012364e-01<br>
>>> Line search: Using full step: fnorm 1.871069012364e-01 gnorm 1.781970487991e-01<br>
>>> 20 SNES Function norm 1.781970487991e-01<br>
>>> Line search: Using full step: fnorm 1.781970487991e-01 gnorm 1.700971829468e-01<br>
>>> 21 SNES Function norm 1.700971829468e-01<br>
>>> Line search: Using full step: fnorm 1.700971829468e-01 gnorm 1.627016532554e-01<br>
>>> 22 SNES Function norm 1.627016532554e-01<br>
>>> Line search: Using full step: fnorm 1.627016532554e-01 gnorm 1.559224177048e-01<br>
>>> 23 SNES Function norm 1.559224177048e-01<br>
>>> Line search: Using full step: fnorm 1.559224177048e-01 gnorm 1.496855209981e-01<br>
>>> 24 SNES Function norm 1.496855209981e-01<br>
>>> Line search: Using full step: fnorm 1.496855209981e-01 gnorm 1.439283855764e-01<br>
>>> 25 SNES Function norm 1.439283855764e-01<br>
>>> Line search: Using full step: fnorm 1.439283855764e-01 gnorm 1.385977046303e-01<br>
>>> 26 SNES Function norm 1.385977046303e-01<br>
>>> Line search: Using full step: fnorm 1.385977046303e-01 gnorm 1.336477866088e-01<br>
>>> 27 SNES Function norm 1.336477866088e-01<br>
>>> Line search: Using full step: fnorm 1.336477866088e-01 gnorm 1.290392422439e-01<br>
>>> 28 SNES Function norm 1.290392422439e-01<br>
>>> Line search: Using full step: fnorm 1.290392422439e-01 gnorm 1.247379341700e-01<br>
>>> 29 SNES Function norm 1.247379341700e-01<br>
>>> Line search: Using full step: fnorm 1.247379341700e-01 gnorm 1.207141298427e-01<br>
>>> 30 SNES Function norm 1.207141298427e-01<br>
>>> Line search: Using full step: fnorm 1.207141298427e-01 gnorm 1.169418132858e-01<br>
>>> 31 SNES Function norm 1.169418132858e-01<br>
>>> Line search: Using full step: fnorm 1.169418132858e-01 gnorm 1.133981219747e-01<br>
>>> 32 SNES Function norm 1.133981219747e-01<br>
>>> Line search: Using full step: fnorm 1.133981219747e-01 gnorm 1.100628830937e-01<br>
>>> 33 SNES Function norm 1.100628830937e-01<br>
>>> Line search: Using full step: fnorm 1.100628830937e-01 gnorm 1.069182292915e-01<br>
>>> 34 SNES Function norm 1.069182292915e-01<br>
>>> Line search: Using full step: fnorm 1.069182292915e-01 gnorm 1.039482784783e-01<br>
>>> 35 SNES Function norm 1.039482784783e-01<br>
>>> Line search: Using full step: fnorm 1.039482784783e-01 gnorm 1.011388655469e-01<br>
>>> 36 SNES Function norm 1.011388655469e-01<br>
>>> Line search: Using full step: fnorm 1.011388655469e-01 gnorm 9.847731645400e-02<br>
>>> 37 SNES Function norm 9.847731645400e-02<br>
>>> Line search: Using full step: fnorm 9.847731645400e-02 gnorm 9.595225705796e-02<br>
>>> 38 SNES Function norm 9.595225705796e-02<br>
>>> Line search: Using full step: fnorm 9.595225705796e-02 gnorm 9.355345063171e-02<br>
>>> 39 SNES Function norm 9.355345063171e-02<br>
>>> Line search: Using full step: fnorm 9.355345063171e-02 gnorm 9.127165915308e-02<br>
>>> 40 SNES Function norm 9.127165915308e-02<br>
>>> Line search: Using full step: fnorm 9.127165915308e-02 gnorm 8.909852441151e-02<br>
>>> 41 SNES Function norm 8.909852441151e-02<br>
>>> Line search: Using full step: fnorm 8.909852441151e-02 gnorm 8.702646570443e-02<br>
>>> 42 SNES Function norm 8.702646570443e-02<br>
>>> Line search: Using full step: fnorm 8.702646570443e-02 gnorm 8.504859148402e-02<br>
>>> 43 SNES Function norm 8.504859148402e-02<br>
>>> Line search: Using full step: fnorm 8.504859148402e-02 gnorm 8.315862278451e-02<br>
>>> 44 SNES Function norm 8.315862278451e-02<br>
>>> Line search: Using full step: fnorm 8.315862278451e-02 gnorm 8.135082663716e-02<br>
>>> 45 SNES Function norm 8.135082663716e-02<br>
>>> Line search: Using full step: fnorm 8.135082663716e-02 gnorm 7.961995798542e-02<br>
>>> 46 SNES Function norm 7.961995798542e-02<br>
>>> Line search: Using full step: fnorm 7.961995798542e-02 gnorm 7.796120886084e-02<br>
>>> 47 SNES Function norm 7.796120886084e-02<br>
>>> Line search: Using full step: fnorm 7.796120886084e-02 gnorm 7.637016378216e-02<br>
>>> 48 SNES Function norm 7.637016378216e-02<br>
>>> Line search: Using full step: fnorm 7.637016378216e-02 gnorm 7.484276050661e-02<br>
>>> 49 SNES Function norm 7.484276050661e-02<br>
>>> Line search: Using full step: fnorm 7.484276050661e-02 gnorm 7.337525539874e-02<br>
>>> 50 SNES Function norm 7.337525539874e-02<br>
>>> SNES Object:(temp_) 1 MPI processes<br>
>>> type: ls<br>
>>> maximum iterations=50, maximum function evaluations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, solution=1e-08<br>
>>> total number of linear solver iterations=693<br>
>>> total number of function evaluations=51<br>
>>> KSP Object: (temp_) 1 MPI processes<br>
>>> type: cg<br>
>>> maximum iterations=10000<br>
>>> tolerances: relative=1e-08, absolute=1e-50, divergence=10000<br>
>>> left preconditioning<br>
>>> using nonzero initial guess<br>
>>> using PRECONDITIONED norm type for convergence test<br>
>>> PC Object: (temp_) 1 MPI processes<br>
>>> type: icc<br>
>>> 0 levels of fill<br>
>>> tolerance for zero pivot 2.22045e-14<br>
>>> using Manteuffel shift<br>
>>> matrix ordering: natural<br>
>>> factor fill ratio given 1, needed 1<br>
>>> Factored matrix follows:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqsbaij<br>
>>> rows=104, cols=104<br>
>>> package used to perform factorization: petsc<br>
>>> total: nonzeros=381, allocated nonzeros=381<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> block size is 1<br>
>>> linear system matrix = precond matrix:<br>
>>> Matrix Object: 1 MPI processes<br>
>>> type: seqaij<br>
>>> rows=104, cols=104<br>
>>> total: nonzeros=658, allocated nonzeros=658<br>
>>> total number of mallocs used during MatSetValues calls =0<br>
>>> not using I-node routines<br>
>>> SNESLineSearch Object: (temp_) 1 MPI processes<br>
>>> type: bt<br>
>>> interpolation: cubic<br>
>>> alpha=1.000000e-04<br>
>>> maxstep=1.000000e+08, minlambda=1.000000e-12<br>
>>> tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08<br>
>>> maximum iterations=40<br>
>>> SNESTemp converged in in 50 iterations. SNESConvergedReason is -5<br>
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>>> --<br>
>>> Department of Mathematics and Center for Computation & Technology<br>
>>> Louisiana State University, Baton Rouge, LA 70803, USA<br>
>>> Tel. +1 (225) 578 1612, Fax +1 (225) 578 4276 <a href="http://www.math.lsu.edu/%7Ebourdin" target="_blank">http://www.math.lsu.edu/~bourdin</a><br>
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>><br>
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> --<br>
> Department of Mathematics and Center for Computation & Technology<br>
> Louisiana State University, Baton Rouge, LA 70803, USA<br>
> Tel. <a href="tel:%2B1%20%28225%29%20578%201612" value="+12255781612">+1 (225) 578 1612</a>, Fax <a href="tel:%2B1%20%28225%29%20578%204276" value="+12255784276">+1 (225) 578 4276</a> <a href="http://www.math.lsu.edu/%7Ebourdin" target="_blank">http://www.math.lsu.edu/~bourdin</a><br>
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