<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;">Emil,<div><br></div><div>thanks for the explanations. I’ve added TSSetEquationType(ts,TS_EQ_IMPLICIT) and things actually got worse with arkimex.</div><div><div>Adding -ts_arkimex_fully_implicit still gives the same inconsistency.</div></div><div><br></div><div>Running with -m_lhs -snes_monitor -ts_type arkimex -ts_arkimex_type 5, it reports for the first three TSSteps</div><div><br></div><div><div style="margin: 0px; font-size: 14px; font-family: Menlo;">0 TS dt 0.01 time 0.</div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 2.881332954700e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 5.764785317497e-16 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 2.656435502730e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 1.351993391899e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 2.748681648224e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 9.153705366186e-16 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 2.654405587243e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 2.165715847788e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.327202793622e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 1.851465123731e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 3.703291910243e-02 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 1.946066132445e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 2.917498324433e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 1.680056316341e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.972362337024e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 1.055632173875e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 4.087125686933e-02 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 2.555645968009e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 3.547915829559e-01 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 2.103175616151e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;">2 TS dt 0.01 time 0.02</div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.965807268111e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.597532788386e-19 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.965807242146e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 3.815060728816e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 7.476292242926e-16 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.837692463276e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 1.965807300567e-15 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 1 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;">3 TS dt 0.01 time 0.03</div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"> 0 SNES Function norm 0.000000000000e+00 </div></div><div><div style="margin: 0px; font-size: 14px; font-family: Menlo;"><br></div></div><div>Then, all the other SNES function norms are zero.</div><div><br></div><div><br></div><div><br></div><div><div><div>On Nov 14, 2016, at 6:23 PM, Emil Constantinescu <<a href="mailto:emconsta@mcs.anl.gov">emconsta@mcs.anl.gov</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">Stefano, thanks for your note. The consistent splittings currently supported under ts_type arkimex are give in Table 11 in the manual: <a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf">http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf</a><br><br>Your case a) is not treated as you wrote it down. The reasoning behind the use cases is that M will have to be inverted directly or indirectly if you put it in F(...) because it's in implicit ODE. In your case b) you handle that directly; however, in case a) the M in F(...) is ignored in some steps leading to inconsistent formulations. That being said, there are ways of solving it as in case a) if M is full rank: some hints are in the caption in Table 11, but I can expand.<br><br>Also in Table 11, there is a note about instructing TS that the user is specifying an implicit ODE (M*ydot....): " set TSSetEquationType() to TS_EQ_IMPLICIT or higher". That sould solve the -ts_arkimex_fully_implicit inconsistency issue.<br><br>Emil<br><br><br>On 11/14/16 4:09 AM, Stefano Zampini wrote:<br><blockquote type="cite">I came across this thing recently, and I couldn't figure out where the<br>issue could be.<br><br>The problem I'm solving is a simple DG advection, the ode is M*udot =<br>K*u+b, M is diagonal.<br><br>Attached is a MWE that reproduces the problem.<br><br>The problem is formed in two different cases depending on the command<br>line option -m_lhs<br><br>a) -m_lhs 1 : F(u,udot,t) = M*udot, G(u,t) = K*u+b<br>b) -m_lhs 0 : F(u,udot,t) = udot, G(u,t) = M^-1(K*u+b)<br><br>Using option b) and RK4, the solution is ok.<br>If run with any implicit TS method except arkimex, no matter if I'm<br>choosing option a) or b), the solution is always very close (say, final<br>error < 0.05) to the expected one (computed with BDF).<br><br>When using ARKIMEX, case b) gives a good solution, but not case a). In<br>fact, the solution does not seem to be advected at all in this case.<br><br>I was wondering if I'm doing something wrong or there's a bug in the<br>ARKIMEX implementation.<br><br>I also noticed that, using -ts_arkimex_fully_implicit does not produce<br>the same output for case a) and b). Shouldn't they produce the same<br>method with this option?<br><br>Thanks,<br>--<br>Stefano<br></blockquote><span><1_Warning.txt></span></blockquote></div><br></div></body></html>