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<div>On Feb 21, 2023, at 8:54 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:</div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">CN or BEular doesn’t work. They produce negative densities at the lower boundary even RHS functions are positive. So for TS, all equations must include udot?</div>
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<div>You have algebraic constraints only for the boundary points. For all the other points, you must have udot in IFunction. I recommend you to take a look at the example src/ts/tutorials/ex25.c </div>
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<div>Hong (Mr.)</div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,</div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan</div>
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<b>From:<span class="Apple-converted-space"> </span></b><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;">Zhang, Hong</a><br>
<b>Sent:<span class="Apple-converted-space"> </span></b>Monday, February 20, 2023 11:07 AM<br>
<b>To:<span class="Apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu" style="color: purple; text-decoration: underline;">Tu, Jiannan</a><br>
<b>Cc:<span class="Apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;">Barry Smith</a>;<span class="Apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org" style="color: purple; text-decoration: underline;">Hong
Zhang</a>;<span class="Apple-converted-space"> </span><a href="mailto:emconsta@anl.gov" style="color: purple; text-decoration: underline;">Constantinescu, Emil M.</a>;<span class="Apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;">petsc-users</a><br>
<b>Subject:<span class="Apple-converted-space"> </span></b>Re: [petsc-users] TS failed due to diverged_step_rejected</div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div>
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<b><span style="font-size: 12pt;">CAUTION:</span></b><span style="font-size: 12pt;"><span class="Apple-converted-space"> </span>This email was sent from outside the UMass Lowell network.<o:p></o:p></span></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">If you have to include the boundary points, I would suggest starting from a fully implicit solver such as CN or BEuler with a finite-difference approximated Jacobian. When this works
for a small scale setting, you can build up more functionalities such as IMEX and analytical Jacobians and extend the problem to a larger scale. But the udot issue needs to be fixed in the first place.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 19, 2023, at 9:23 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">It is the second order derivative of, say electron temperature = 0 at the boundary.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">I am not sure how I can exclude the boundary points because the values of unknowns must be specified at the boundary. Are there any other solvers, e.g., CN, good to solve the equation
system?<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Zhang,
Hong</span></a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Sunday, February 19, 2023 4:48 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry Smith</span></a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Hong
Zhang</span></a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Constantinescu, Emil M.</span></a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<b><span style="font-size: 12pt;">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;">This email was sent from outside the UMass Lowell network.</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">It is fine to drop udot for the boundary points, but you need to keep udot for all the other points.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">In addition, which boundary condition do you use in IFunction? The way you are treating the boundary points actually leads to a system of differential-algebraic equations, which could
be difficult to solve with the ARKIMEX solver. Can you try to exclude the boundary points from the computational domain so that you will have just a system of ODEs? <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 18, 2023, at 4:28 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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?<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Zhang,
Hong</span></a><br>
<b>Sent:<span class="apple-converted-space"> </span></b>Saturday, February 18, 2023 12:40 PM<br>
<b>To:<span class="apple-converted-space"> </span></b><a href="mailto:Jiannan_Tu@uml.edu" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry Smith</span></a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Hong
Zhang</span></a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Constantinescu, Emil M.</span></a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);">You don't often get email from<span class="apple-converted-space"> </span><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">hongzhang@anl.gov</span></a>.<span class="apple-converted-space"> </span><a href="https://aka.ms/LearnAboutSenderIdentification" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Learn
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 18, 2023, at 8:44 AM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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 class="apple-converted-space"> </span><span style="color: rgb(255, 38, 0);">F(u,
udot) = X[i=0].</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Hong (Mr.)<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Zhang,
Hong</span></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" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry Smith</span></a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Hong
Zhang</span></a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Constantinescu, Emil M.</span></a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 9pt; font-family: "Segoe UI", sans-serif; color: rgb(33, 33, 33);">You don't often get email from<span class="apple-converted-space"> </span><a href="mailto:hongzhang@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">hongzhang@anl.gov</span></a>.<span class="apple-converted-space"> </span><a href="https://aka.ms/LearnAboutSenderIdentification" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Learn
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 17, 2023, at 6:19 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">A good IMEX example can be found at ts/tutorial/advection-diffusion-reaction/ex5.c (and reaction_diffusion.c).<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Hong (Mr.)<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">The solution from TSStep is checked for positivity of densities and temperatures.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">----------------------------------<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">G(u) = 1.86534e-07<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072183e+03<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 8.641749325070e-04<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 2.779985176426e-08<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 3.607702491344e-04<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 4.345809629121e-08<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> TSAdapt none arkimex 0:3 step 0 accepted t=42960 + 2.189e-02 dt=2.189e-02<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">electron temperature = -3.6757e-15 at (i, j, k) = (0, 1, 0)<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry
Smith</span></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" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a>;<span class="apple-converted-space"> </span><a href="mailto:hong.zhang@aspiritech.org" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Hong
Zhang</span></a>;<span class="apple-converted-space"> </span><a href="mailto:emconsta@anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Emil Constantinescu</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<b><span style="font-size: 12pt;">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;">This email was sent from outside the UMass Lowell network.</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 17, 2023, at 3:32 PM, Tu, Jiannan <Jiannan_Tu@uml.edu> wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">BTW, what is this ts_adapt? Is it by default on?<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Have you tried with the argument -ts_arkimex_fully_implicit ?<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:knepley@gmail.com" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Matthew
Knepley</span></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" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry Smith</span></a>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<b><span style="font-size: 12pt;">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;">This email was sent from outside the UMass Lowell network.</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">to change when you make the step smaller, so something is off. You can shut off the adaptivity using<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> -ts_adapt_type none<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Thanks,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Matt<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Fri, Feb 17, 2023 at 3:01 PM Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Jiannan_Tu@uml.edu</span></a>>
wrote:<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">These are what I got with the options you suggested.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank you,<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Jiannan<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">-------------------------------------------------------------------------------<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.673091274668e-03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 8.715428433630e-02<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 4.995727626692e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 5.498018152230e-08<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.237461568254e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 7.988531005091e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 1.280948196292e-07<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 4.881903203545e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 7.562592690785e-02<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.143078818923e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 9.834547907735e-09<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.683968949758e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.838028436639e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 2 SNES Function norm 9.470813523140e-09<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.821562431175e-04<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 1.005443458812e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 3.633336946661e-05<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 1.515368382715e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 3.389298316830e-05<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 4.541003359206e-05<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 1.713800906043e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.179958172167e-05<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.020265094117e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.513971290464e-05<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.136603895703e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.877474016012e-06<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.127812462507e-01<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.713146825704e-06<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.793512213059e-06<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.205196267430e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.572653773308e-06<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.260057361977e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.705816087598e-06<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.764855860446e-05<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.212505522844e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.958996472386e-05<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.273222034162e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.994512887620e-05<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072186e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 3.317240589134e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.213246532918e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.799468604767e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.274570888397e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 3.066048050994e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072189e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.653507278572e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.213869585841e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.177156902895e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.275136370365e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.962849131557e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473072218e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 5.664907315679e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.223208399368e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 5.688863091415e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.287121218919e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 4.085338521320e-03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.274473071968e+03<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 4.694691905235e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 2.211786508657e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 1.503497433939e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 0 SNES Function norm 3.272667798977e-01<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 1 SNES Function norm 2.176132327279e-04<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1<o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> 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></div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: TSStep has failed due to DIVERGED_STEP_REJECTED<o:p></o:p></div>
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<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[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%7Ce26f36670ab44d9403b508db135c90da%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638125060538031187%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=vmlHEXtZIOA4oNOi7ZK1xBK%2BL0Cz52XVoJLrqJL06sw%3D&reserved=0" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">https://petsc.org/release/faq/</span></a><span class="apple-converted-space"> </span>for
trouble shooting.<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: ./iditm3d on a named office by jtu Fri Feb 17 14:54:22 2023<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">[0]PETSC ERROR: #1 TSStep() at /home/jtu/Downloads/petsc-3.16.6/src/ts/interface/ts.c:3583<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><b>From:<span class="apple-converted-space"> </span></b><a href="mailto:bsmith@petsc.dev" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Barry
Smith</span></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" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Tu, Jiannan</span></a><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">petsc-users</span></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></div>
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<b><span style="font-size: 12pt;">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size: 12pt;"> </span></span><span style="font-size: 12pt;">This email was sent from outside the UMass Lowell network.</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> Can you please run with also the options -ts_monitor -ts_adapt_monitor ?<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> The output is confusing because it prints that the Nonlinear solve has converged but then <span style="font-size: 12pt; background-color: white;">TSStep has failed due to DIVERGED_STEP_REJECTED
which seems contradictory</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">On Feb 17, 2023, at 12:09 PM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">Jiannan_Tu@uml.edu</span></a>>
wrote:<o:p></o:p></div>
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<span style="font-size: 12pt;">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></div>
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<span style="font-size: 12pt;">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></div>
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<span style="font-size: 12pt;">Could you help me to identify what is going wrong?</span><o:p></o:p></div>
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<span style="font-size: 12pt;">Thank you very much!</span><o:p></o:p></div>
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<span style="font-size: 12pt;">Jiannan</span><o:p></o:p></div>
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<span style="font-size: 12pt;">---------------------------------------------------------------------------------------------------</span><o:p></o:p></div>
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<span style="font-size: 12pt;">Run command with options</span><o:p></o:p></div>
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<span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(51, 51, 51);">mpiexec -n</span></span><span class="m-5136506635804366231apple-converted-space"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(51, 51, 51);"> </span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(119, 119, 119);">$</span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(122, 62, 157);">1</span></span><span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(51, 51, 51);"> ./iditm3d
-ts_type arkimex -snes_tyep ngmres -ksp_type gmres -pc_type asm \</span></span><o:p></o:p></div>
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<span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(51, 51, 51);">-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></div>
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<span class="m-5136506635804366231contentpasted1"><span style="font-size: 10.5pt; font-family: "Courier New"; color: rgb(51, 51, 51);">-snes_converged_reason</span></span><o:p></o:p></div>
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<span style="font-size: 12pt;">The output message is </span><o:p></o:p></div>
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<span style="font-size: 12pt;">Start time advancing ...<span class="apple-converted-space"> </span></span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 1.673091274668e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 8.715428433630e-02<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 4.995727626692e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 2 SNES Function norm 5.498018152230e-08<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 0 SNES Function norm 3.237461568254e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 7.988531005091e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 2 SNES Function norm 1.280948196292e-07<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 4.881903203545e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 0 SNES Function norm 7.562592690785e-02<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 1.143078818923e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 2 SNES Function norm 9.834547907735e-09<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 0 SNES Function norm 2.683968949758e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 1.838028436639e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 2 SNES Function norm 9.470813523140e-09<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 2</span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<span style="font-size: 12pt;"> 1 SNES Function norm 1.821562431175e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 1.005443458812e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 3.633336946661e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 1.515368382715e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 3.389298316830e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 4.541003359206e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 1.713800906043e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 1.179958172167e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.020265094117e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 1.513971290464e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 6.090269704320e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.136603895703e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 1.877474016012e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.127812462507e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.713146825704e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.793512213059e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.205196267430e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.572653773308e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.260057361977e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.705816087598e-06<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.764855860446e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.212505522844e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.958996472386e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.273222034162e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.994512887620e-05<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072186e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 3.317240589134e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.213246532918e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.799468604767e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.274570888397e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 3.066048050994e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072189e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.653507278572e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.213869585841e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.177156902895e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.275136370365e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 1.962849131557e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473072218e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 5.664907315679e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.223208399368e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 5.688863091415e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.287121218919e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
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<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 4.085338521320e-03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.274473071968e+03<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 4.694691905235e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 1</span><o:p></o:p></div>
</div>
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</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 2.211786508657e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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</div>
</div>
</div>
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<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 1.503497433939e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
</div>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
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<div>
<div>
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<div>
<div>
<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 0 SNES Function norm 3.272667798977e-01<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<div>
<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> 1 SNES Function norm 2.176132327279e-04<span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;"> Nonlinear solve converged due to CONVERGED_SNORM_RELATIVE iterations 1</span><o:p></o:p></div>
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<span style="font-size: 12pt;">[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[0]PETSC ERROR: <span class="m-5136506635804366231apple-converted-space"> </span></span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[0]PETSC ERROR: TSStep has failed due to DIVERGED_STEP_REJECTED</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[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%7Ce26f36670ab44d9403b508db135c90da%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638125060538031187%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=vmlHEXtZIOA4oNOi7ZK1xBK%2BL0Cz52XVoJLrqJL06sw%3D&reserved=0" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">https://petsc.org/release/faq/</span></a><span class="m-5136506635804366231apple-converted-space"> </span>for
trouble shooting.</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[0]PETSC ERROR: ./iditm3d on a named office by jtu Fri Feb 17 11:59:43 2023</span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; background-color: white;">
<span style="font-size: 12pt;">[0]PETSC ERROR: #1 TSStep() at /home/jtu/Downloads/petsc-3.16.6/src/ts/interface/ts.c:3583</span><o:p></o:p></div>
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</blockquote>
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<p class="MsoNormal" style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class="MsoNormal" style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><br clear="all">
<o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">--<span class="apple-converted-space"> </span><o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">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></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <o:p></o:p></div>
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<div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><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%7Ce26f36670ab44d9403b508db135c90da%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C638125060538187398%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=NNlNDia1%2BSjeZvLng2bo83b1V%2BBClTEp5bz2JkuwYm0%3D&reserved=0" target="_blank" style="color: purple; text-decoration: underline;"><span style="color: rgb(149, 79, 114);">https://www.cse.buffalo.edu/~knepley/</span></a></div>
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