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<p class="MsoNormal">Thanks for the instruction. This is the boundary condition and there is no udot in the equation. I think this is the way to define IFunction at the boundary. Maybe I’m wrong? Or is there some way to introduce udot into the specification
of the equation at the boundary from the aspect of the implementation for TS?</p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thank you,</p>
<p class="MsoNormal">Jiannan</p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="border:none;padding:0in"><b>From: </b><a href="mailto:hongzhang@anl.gov">Zhang, Hong</a><br>
<b>Sent: </b>Saturday, February 18, 2023 12:40 PM<br>
<b>To: </b><a href="mailto:Jiannan_Tu@uml.edu">Tu, Jiannan</a><br>
<b>Cc: </b><a href="mailto:bsmith@petsc.dev">Barry Smith</a>; <a href="mailto:hong.zhang@aspiritech.org">
Hong Zhang</a>; <a href="mailto:emconsta@anl.gov">Constantinescu, Emil M.</a>; <a href="mailto:petsc-users@mcs.anl.gov">
petsc-users</a><br>
<b>Subject: </b>Re: [petsc-users] TS failed due to diverged_step_rejected</p>
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span style="font-size:12.0pt;color:black"> This email was sent from outside the UMass Lowell network.</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal">On Feb 18, 2023, at 8:44 AM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></p>
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<p class="MsoNormal">The RHS function at the bottom boundary is determined by the boundary condition, which is the second order derivative = 0, i.e. G(u) = 2*X[i=1] – X[i=2]. Then in IFunction,
<span style="color:#FF2600">F(u, udot) = X[i=0].</span><o:p></o:p></p>
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<p class="MsoNormal">This might be the problem. Your F(u, udot) is missing udot according to your description. Take a simple ODE udot = f(u) + g(u) for example. One way to partition this ODE is to define F = udot - f(u) as the IFunction and G = g(u) as the
RHSFunction.<o:p></o:p></p>
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<p class="MsoNormal">Hong (Mr.)<o:p></o:p></p>
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<p class="MsoNormal">Thank you,<o:p></o:p></p>
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<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:hongzhang@anl.gov">Zhang, Hong</a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Friday, February 17, 2023 11:54 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu">Tu, Jiannan</a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev">Barry Smith</a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org">Hong Zhang</a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov">Constantinescu,
Emil M.</a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users</a><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] TS failed due to diverged_step_rejected<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<span style="font-size:9.0pt;font-family:"Segoe UI",sans-serif;color:#212121">You don't often get email from<span class="apple-converted-space"> </span><a href="mailto:hongzhang@anl.gov">hongzhang@anl.gov</a>.<span class="apple-converted-space"> </span><a href="https://aka.ms/LearnAboutSenderIdentification">Learn
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black">This
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<p class="MsoNormal">On Feb 17, 2023, at 6:19 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></p>
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<p class="MsoNormal">I need to find out what causes negative temperature first. Following is the message with adaptivity turned off. The G(u) gives right-hand equation for electron temperature at bottom boundary. The F(u, u’) function is F(u, u’) = X = G(u)
and the jacobian element is d F(u, u’) / dX =1.<o:p></o:p></p>
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<p class="MsoNormal">This looks strange. Can you elaborate a bit on your partitioned ODE? For example, how are your F(u,udot) (IFunction) and G(u) (RHSFunction) defined?<o:p></o:p></p>
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<p class="MsoNormal">A good IMEX example can be found at ts/tutorial/advection-diffusion-reaction/ex5.c (and reaction_diffusion.c).<o:p></o:p></p>
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<p class="MsoNormal">Hong (Mr.)<o:p></o:p></p>
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<p class="MsoNormal">The solution from TSStep is checked for positivity of densities and temperatures.<o:p></o:p></p>
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<p class="MsoNormal">From the message below, it is seen that G(u) > 0 (I added output of right-hand equation for electron temperature). The solution for electron temperature X should be X * jacobian element = G(u) > 0 since jacobian element = 1. I don’t understand
why it becomes negative. Is my understanding of TS formula incorrect?<o:p></o:p></p>
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<p class="MsoNormal">Thank you,<o:p></o:p></p>
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<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal">----------------------------------<o:p></o:p></p>
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<p class="MsoNormal">G(u) = 1.86534e-07<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072183e+03<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 8.641749325070e-04<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal">G(u) = 1.86534e-07<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 8.716501970511e-02<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.213263548813e-04<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 2.779985176426e-08<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal">G(u) = 1.86534e-07<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.177195995186e-01<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 3.607702491344e-04<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 4.345809629121e-08<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal">G(u) = 1.86534e-07<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt none arkimex 0:3 step 0 accepted t=42960 + 2.189e-02 dt=2.189e-02<o:p></o:p></p>
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<p class="MsoNormal">electron temperature = -3.6757e-15 at (i, j, k) = (0, 1, 0)<o:p></o:p></p>
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<p class="MsoNormal"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev">Barry Smith</a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Friday, February 17, 2023 3:45 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu">Tu, Jiannan</a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org">Hong Zhang</a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov">Emil
Constantinescu</a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users</a><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] TS failed due to diverged_step_rejected<o:p></o:p></p>
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black">This
email was sent from outside the UMass Lowell network.</span><o:p></o:p></p>
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<p class="MsoNormal">On Feb 17, 2023, at 3:32 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></p>
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<p class="MsoNormal">The ts_type arkimex is used. There is right hand-side function RHSFunction set by TSSetRHSFunction() and also stiff function set by TSSetIFunction().<o:p></o:p></p>
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<p class="MsoNormal">With adaptivity shut off, TS can finish its first time step after the 3rd “Nonlinear solve converged due to …”. The solution gives negative electron and neutral temperatures at the bottom boundary. I need to fix the negative temperatures
and see how the code works.<o:p></o:p></p>
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<p class="MsoNormal">BTW, what is this ts_adapt? Is it by default on?<o:p></o:p></p>
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<p class="MsoNormal"> It is default for some of the TSTypes (in particular, the better ones). It adapts the timestep to ensure some local error estimate is below a certain tolerance. As Matt notes normally as it tries smaller and smaller time steps the local
error estimate would get smaller and smaller; this is not happening here, hence the error.<o:p></o:p></p>
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<p class="MsoNormal"> Have you tried with the argument -ts_arkimex_fully_implicit ?<o:p></o:p></p>
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<p class="MsoNormal"> I am not an expert but my guess is something is "odd" about your functions, either the RHSFunction or the Function or both. Do you have a hierarchy of models for your problem? Could you try runs with fewer terms in your functions, that
may be producing the difficulties? If you can determine what triggers the problem with the local error estimators, that might help the experts in ODE solution (not me) determine what could be going wrong.<o:p></o:p></p>
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<p class="MsoNormal"> Barry<o:p></o:p></p>
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<p class="MsoNormal">Thank you,<o:p></o:p></p>
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<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:knepley@gmail.com">Matthew Knepley</a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Friday, February 17, 2023 3:15 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu">Tu, Jiannan</a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev">Barry Smith</a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users</a><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] TS failed due to diverged_step_rejected<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black">This
email was sent from outside the UMass Lowell network.</span><o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">I am not sure what TS you are using, but the estimate of the local truncation error is 91.4, and does not seem<o:p></o:p></p>
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<p class="MsoNormal">to change when you make the step smaller, so something is off. You can shut off the adaptivity using<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"> -ts_adapt_type none<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"> Thanks,<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"> Matt<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">On Fri, Feb 17, 2023 at 3:01 PM Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu">Jiannan_Tu@uml.edu</a>> wrote:<o:p></o:p></p>
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<blockquote style="border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt">
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<p class="MsoNormal">These are what I got with the options you suggested.<o:p></o:p></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal">Thank you,<o:p></o:p></p>
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<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal">-------------------------------------------------------------------------------<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.673091274668e-03<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 8.715428433630e-02<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 4.995727626692e-04<o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 5.498018152230e-08<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.237461568254e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 7.988531005091e-04<o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 1.280948196292e-07<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 2.189e-02 dt=4.374e-03 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 4.881903203545e-04<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 7.562592690785e-02<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.143078818923e-04<o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 9.834547907735e-09<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.683968949758e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.838028436639e-04<o:p></o:p></p>
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<p class="MsoNormal"> 2 SNES Function norm 9.470813523140e-09<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-03 dt=4.374e-04 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.821562431175e-04<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 1.005443458812e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 3.633336946661e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 1.515368382715e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 3.389298316830e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-04 dt=4.374e-05 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 4.541003359206e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 1.713800906043e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.179958172167e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.020265094117e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.513971290464e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-05 dt=4.374e-06 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 6.090269704320e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.136603895703e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.877474016012e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.127812462507e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.713146825704e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-06 dt=4.374e-07 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.793512213059e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.205196267430e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.572653773308e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.260057361977e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.705816087598e-06<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-07 dt=4.374e-08 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.764855860446e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.212505522844e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.958996472386e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.273222034162e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.994512887620e-05<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-08 dt=4.374e-09 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 3.317240589134e-04<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.213246532918e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.799468604767e-04<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.274570888397e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 3.066048050994e-04<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-09 dt=4.374e-10 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.274473072189e+03<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.653507278572e-03<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 2.213869585841e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 2.177156902895e-03<o:p></o:p></p>
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<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
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<p class="MsoNormal"> 0 SNES Function norm 3.275136370365e-01<o:p></o:p></p>
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<p class="MsoNormal"> 1 SNES Function norm 1.962849131557e-03<o:p></o:p></p>
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<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-10 dt=4.374e-11 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 2.274473072218e+03<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 5.664907315679e-03<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 2.223208399368e-01<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 5.688863091415e-03<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 3.287121218919e-01<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 4.085338521320e-03<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-11 dt=4.374e-12 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 2.274473071968e+03<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 4.694691905235e-04<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 2.211786508657e-01<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 1.503497433939e-04<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 0 SNES Function norm 3.272667798977e-01<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> 1 SNES Function norm 2.176132327279e-04<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> TSAdapt basic arkimex 0:3 step 0 rejected t=42960 + 4.374e-12 dt=4.374e-13 wlte= 91.4 wltea= -1 wlter= -1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: <o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: TSStep has failed due to DIVERGED_STEP_REJECTED<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: See<span class="apple-converted-space"> </span><a href="https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Ffaq%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C683af8c0511e4499d31308db11d72edb%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638123388160203530%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=WX7OoIK9oSACKQMSj95fkJ8VilF3QvPVRNw30kyZwB0%3D&reserved=0" target="_blank">https://petsc.org/release/faq/</a><span class="apple-converted-space"> </span>for
trouble shooting.<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: ./iditm3d on a named office by jtu Fri Feb 17 14:54:22 2023<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: Configure options --prefix=/usr/local --with-mpi-dir=/usr/local --with-fc=0 --with-openmp --with-hdf5-dir=/usr/local --download-f2cblaslapack=1<o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal">[0]PETSC ERROR: #1 TSStep() at /home/jtu/Downloads/petsc-3.16.6/src/ts/interface/ts.c:3583<o:p></o:p></p>
</div>
</div>
</div>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in">
<div>
<div>
<div>
<p class="MsoNormal"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" target="_blank">Barry Smith</a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Friday, February 17, 2023 12:58 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu" target="_blank">Tu, Jiannan</a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users</a><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] TS failed due to diverged_step_rejected<o:p></o:p></p>
</div>
</div>
</div>
</div>
<p class="MsoNormal"> </p>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black">This
email was sent from outside the UMass Lowell network.</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<p class="MsoNormal"> </p>
<div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> Can you please run with also the options -ts_monitor -ts_adapt_monitor ?<o:p></o:p></p>
</div>
</div>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal"> The output is confusing because it prints that the Nonlinear solve has converged but then <span style="font-size:12.0pt;color:black;background:white">TSStep has failed due to DIVERGED_STEP_REJECTED which seems contradictory</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<div>
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
</div>
<div>
<div style="margin-bottom:12.0pt">
<div>
<p class="MsoNormal"> <o:p></o:p></p>
</div>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<div>
<div>
<p class="MsoNormal">On Feb 17, 2023, at 12:09 PM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" target="_blank">Jiannan_Tu@uml.edu</a>> wrote:<o:p></o:p></p>
</div>
</div>
</div>
</div>
<p class="MsoNormal"> </p>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">My code uses TS to solve a set of multi-fluid MHD equations. The jacobian is provided with function F(t, u, u'). Both linear and nonlinear solvers converge but snes repeats
itself until gets "TSStep has failed due to diverged_step_rejected."<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Is it because I used TSStep rather than TSSolve? I have checked the condition number. The condition number with pc_type asm is about 1 (without precondition it is about
4x10^4). The maximum ratio of off-diagonal jacobian element over diagonal element is about 21.</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Could you help me to identify what is going wrong?</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Thank you very much!</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Jiannan</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">---------------------------------------------------------------------------------------------------</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Run command with options</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="line-height:14.25pt;background:whitesmoke"><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#333333">mpiexec -n</span></span><span class="m-5136506635804366231apple-converted-space"><span style="font-size:10.5pt;font-family:"Courier New";color:#333333"> </span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#777777">$</span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#7A3E9D">1</span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#333333"> ./iditm3d
-ts_type arkimex -snes_tyep ngmres -ksp_type gmres -pc_type asm \</span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="line-height:14.25pt;background:whitesmoke"><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#333333">-ts_rtol 1.0e-4 -ts_atol 1.0e-4 -snes_monitor -snes_rtol 1.0e-4 -snes_atol
1.0e-4 \</span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<p class="MsoNormal" style="line-height:14.25pt;background:whitesmoke"><span class="m-5136506635804366231contentpasted1"><span style="font-size:10.5pt;font-family:"Courier New";color:#333333">-snes_converged_reason</span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">The output message is </span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> </span></p>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">Start time advancing ...<span class="apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.673091274668e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 8.715428433630e-02<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 4.995727626692e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 2 SNES Function norm 5.498018152230e-08<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.237461568254e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 7.988531005091e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 2 SNES Function norm 1.280948196292e-07<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 4.881903203545e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 7.562592690785e-02<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.143078818923e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 2 SNES Function norm 9.834547907735e-09<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.683968949758e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.838028436639e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 2 SNES Function norm 9.470813523140e-09<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.821562431175e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 1.005443458812e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 3.633336946661e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 1.515368382715e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 3.389298316830e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 4.541003359206e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 1.713800906043e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.179958172167e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.020265094117e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.513971290464e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 6.090269704320e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.136603895703e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.877474016012e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.127812462507e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.713146825704e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.793512213059e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.205196267430e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.572653773308e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.260057361977e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.705816087598e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.764855860446e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.212505522844e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.958996472386e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.273222034162e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.994512887620e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 3.317240589134e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.213246532918e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.799468604767e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.274570888397e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 3.066048050994e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072189e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.653507278572e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.213869585841e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.177156902895e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.275136370365e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.962849131557e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473072218e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 5.664907315679e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.223208399368e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 5.688863091415e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.287121218919e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 4.085338521320e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.274473071968e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 4.694691905235e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 2.211786508657e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 1.503497433939e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 0 SNES Function norm 3.272667798977e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> 1 SNES Function norm 2.176132327279e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: <span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: TSStep has failed due to DIVERGED_STEP_REJECTED</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: See<span class="m-5136506635804366231apple-converted-space"> </span><a href="https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Ffaq%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C683af8c0511e4499d31308db11d72edb%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638123388160203530%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=WX7OoIK9oSACKQMSj95fkJ8VilF3QvPVRNw30kyZwB0%3D&reserved=0" target="_blank">https://petsc.org/release/faq/</a><span class="m-5136506635804366231apple-converted-space"> </span>for
trouble shooting.</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: ./iditm3d on a named office by jtu Fri Feb 17 11:59:43 2023</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: Configure options --prefix=/usr/local --with-mpi-dir=/usr/local --with-fc=0 --with-openmp --with-hdf5-dir=/usr/local --download-f2cblaslapack=1</span><o:p></o:p></p>
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<p class="MsoNormal" style="background:white"><span style="font-size:12.0pt;color:black">[0]PETSC ERROR: #1 TSStep() at /home/jtu/Downloads/petsc-3.16.6/src/ts/interface/ts.c:3583</span><o:p></o:p></p>
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</blockquote>
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<p class="MsoNormal"> </p>
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<p class="MsoNormal"><br clear="all">
<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal">--<span class="apple-converted-space"> </span><o:p></o:p></p>
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<p class="MsoNormal">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"><a href="https://nam10.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.cse.buffalo.edu%2F~knepley%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C683af8c0511e4499d31308db11d72edb%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638123388160203530%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=RwNvX0Wqg7tkKs%2BIYG1svHVyEgXae1JAbwouhjZdLrE%3D&reserved=0" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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