<div dir="ltr"><br><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Oct 16, 2013 at 3:36 PM, Jed Brown <span dir="ltr"><<a href="mailto:jedbrown@mcs.anl.gov" target="_blank">jedbrown@mcs.anl.gov</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="im">Christophe Ortiz <<a href="mailto:christophe.ortiz@ciemat.es">christophe.ortiz@ciemat.es</a>> writes:<br>
> I found where is the problem. I had<br>
> set TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);<br>
> I found it produces wrong solutions, either with ARKIMEX3, 1BEE or A2.<br>
> Solution becomes negative. Without this option, all ARKIMEX types work very<br>
> well and very fast.<br>
<br>
</div>I'm glad they work as IMEX methods (please check that the solutions are<br>
correct), but I would like to find out why they are not working in fully<br>
implicit mode. Is your problem similar to ex25? </blockquote><div><br></div><div>Yes. The only difference is that I put everything (diffusion and reaction terms) under IFunction and IJacobian.</div><div><br></div><div>My system is</div>
<div><br></div><div>u_t - alpha.u_xx + k.u.v = 0</div><div>v_t - beta.v_xx + k.u.v = 0</div><div> </div><div>with Dirichlet boundary conditions</div><div>u(x=0,t) = u(x=L,t) = cste</div><div>v(x=0,t) = v(x=L,t) = cste</div>
<div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"> (If I remember<br>
correctly, that example uses a DAE formulation for boundary conditions<br>
and thus has trouble with some methods with explicit stages. There may<br>
be more going on.)<br></blockquote><div><br></div><div>Now you say it, I'm having some troubles. After checking that it worked very well with only diffusion terms with ARKIMEX, I introduced the reaction term. With ARKIMEX 1BEE/A2, it goes very fast up to t=0.27 s, then, steps start being rejected and then it goes very slowly, with small timesteps. See output below.</div>
<div>Do you think it is due to the fact that I use IFunction to define boundary conditions, which produces troubles with ARKIMEX methods ?</div><div>What would be the solution ?</div><div><br></div><div>Christophe</div><div>
<br></div><div><div><font size="1">TSAdapt 'basic': step 156 accepted t=0.112524 + 2.250e-02 wlte=3.07e-05 family='arkimex' scheme=0:'1bee' dt=2.701e-02 </font></div><div><font size="1"> TSAdapt 'basic': step 157 accepted t=0.135029 + 2.701e-02 wlte=5.03e-05 family='arkimex' scheme=0:'1bee' dt=3.241e-02 </font></div>
<div><font size="1"> TSAdapt 'basic': step 158 accepted t=0.162034 + 3.241e-02 wlte=8.36e-05 family='arkimex' scheme=0:'1bee' dt=3.889e-02 </font></div><div><font size="1"> TSAdapt 'basic': step 159 accepted t=0.194441 + 3.889e-02 wlte=0.000141 family='arkimex' scheme=0:'1bee' dt=4.667e-02 </font></div>
<div><font size="1"> TSAdapt 'basic': step 160 accepted t=0.233329 + 4.667e-02 wlte=0.000244 family='arkimex' scheme=0:'1bee' dt=5.000e-02 </font></div><div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 5.000e-02 retrying with dt=1.250e-02 </font></div>
<div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 1.250e-02 retrying with dt=3.125e-03 </font></div><div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 3.125e-03 retrying with dt=7.813e-04 </font></div>
<div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 7.813e-04 retrying with dt=1.953e-04 </font></div><div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 1.953e-04 retrying with dt=4.883e-05 </font></div>
<div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 4.883e-05 retrying with dt=1.221e-05 </font></div><div><font size="1"> TSAdapt 'basic': step 161 stage rejected t=0.279995 + 1.221e-05 retrying with dt=3.052e-06 </font></div>
<div><font size="1"> TSAdapt 'basic': step 161 accepted t=0.279995 + 3.052e-06 wlte=2.58e-06 family='arkimex' scheme=0:'1bee' dt=3.662e-06 </font></div><div><font size="1"> TSAdapt 'basic': step 162 accepted t=0.279998 + 3.662e-06 wlte=3.72e-06 family='arkimex' scheme=0:'1bee' dt=4.395e-06 </font></div>
<div><font size="1"> TSAdapt 'basic': step 163 stage rejected t=0.280002 + 4.395e-06 retrying with dt=1.099e-06 </font></div><div><font size="1"> TSAdapt 'basic': step 163 accepted t=0.280002 + 1.099e-06 wlte=3.35e-07 family='arkimex' scheme=0:'1bee' dt=1.318e-06 </font></div>
<div><font size="1"> TSAdapt 'basic': step 164 accepted t=0.280003 + 1.318e-06 wlte=4.82e-07 family='arkimex' scheme=0:'1bee' dt=1.582e-06 </font></div><div><font size="1"> TSAdapt 'basic': step 165 accepted t=0.280004 + 1.582e-06 wlte=6.94e-07 family='arkimex' scheme=0:'1bee' dt=1.898e-06 </font></div>
<div><font size="1"> TSAdapt 'basic': step 166 accepted t=0.280006 + 1.898e-06 wlte=1e-06 family='arkimex' scheme=0:'1bee' dt=2.278e-06 </font></div><div><font size="1"> TSAdapt 'basic': step 167 accepted t=0.280008 + 2.278e-06 wlte=1.44e-06 family='arkimex' scheme=0:'1bee' dt=2.734e-06 </font></div>
</div><div><font size="1"><br></font></div><div><font size="1"><br></font></div><div><font size="1"> </font></div></div><br></div></div>