> > Sorry, the equation type is needed for when the fully implicit option is used. >
the output with -m_lhs -ts_type arkimex -ts_arkimex_type 5 -ts_arkimex_fully_implicit (case a) ) is different from -m_lhs 0 -ts_type arkimex -ts_arkimex_type 5 -ts_arkimex_fully_implicit (case b) ) > I assume you are in the b) case, No, case a) mass matrix on the left-hand side > that would correspond to "mass & stiff-nonstiff ODE" entry in Table 11 with > f(t,y)=0. Have you tried the forms suggested there, they are slightly > different from what you indicate in your original message for case b)? Also, > please use -ts_monitor and comment out the equation type. > I do have pasted the output for ts_monitor for the first three steps. The entry you are referring to in Table 11 actually breaks the TS assumption that the ODE can be written F(u,udot,t) = G(u,t) (I was thinking it was a typo) Indeed, using what is listed in Table 11 for the case "mass & stiff-nonstiff ODE", we have ODE: M * ydot = g(t,y) + f(t,y), F = M * ydot - f(t,u), G = M^-1 * g(t,y) Putting F and G in the form F(u,udot,t) = G(u,t), we will have the ODE M * ydot = f(t,u) + M^-1 * g(t,y) > In your case, you would either use the setup corresponding to "stiff ODE w/ > mass matrix" or "nonstiff ODE w/ mass matrix”. I’m not interested in solving this specific advection problem with arkimex. I came across this problem when writing a general interface to TS from a FEM library. > It is difficult to create a decision tree for every way of writing the > splittings. Do you find Table 11 not clear about what splitting to use? I > would welcome any kind of feedback for improving it. > If the entry in Table 11 is correct, please add a comment on the manual stating that ARKIMEX does not fully support the F(u,udot,t) = G(u,t) interface. > Thanks, > Emil > > On 11/14/16 11:45 AM, Stefano Zampini wrote: >> Emil, >> >> thanks for the explanations. I’ve added >> TSSetEquationType(ts,TS_EQ_IMPLICIT) and things actually got worse with >> arkimex. >> Adding -ts_arkimex_fully_implicit still gives the same inconsistency. >> >> Running with -m_lhs -snes_monitor -ts_type arkimex -ts_arkimex_type 5, >> it reports for the first three TSSteps >> >> 0 TS dt 0.01 time 0. >> 0 SNES Function norm 2.881332954700e-01 >> 1 SNES Function norm 5.764785317497e-16 >> 0 SNES Function norm 2.656435502730e-01 >> 1 SNES Function norm 1.351993391899e-15 >> 0 SNES Function norm 2.748681648224e-01 >> 1 SNES Function norm 9.153705366186e-16 >> 0 SNES Function norm 2.654405587243e-01 >> 1 SNES Function norm 2.165715847788e-15 >> 0 SNES Function norm 1.327202793622e-01 >> 1 SNES Function norm 1.851465123731e-15 >> 0 SNES Function norm 3.703291910243e-02 >> 1 SNES Function norm 1.946066132445e-15 >> 0 SNES Function norm 2.917498324433e-01 >> 1 SNES Function norm 1.680056316341e-15 >> 0 SNES Function norm 1.972362337024e-01 >> 1 SNES Function norm 1.055632173875e-15 >> 0 SNES Function norm 4.087125686933e-02 >> 1 SNES Function norm 2.555645968009e-15 >> 0 SNES Function norm 3.547915829559e-01 >> 1 SNES Function norm 2.103175616151e-15 >> 2 TS dt 0.01 time 0.02 >> 0 SNES Function norm 1.965807268111e-15 >> 1 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 1.597532788386e-19 >> 1 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 1.965807242146e-15 >> 1 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 3.815060728816e-15 >> 1 SNES Function norm 7.476292242926e-16 >> 0 SNES Function norm 1.837692463276e-15 >> 1 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 1.965807300567e-15 >> 1 SNES Function norm 0.000000000000e+00 >> 3 TS dt 0.01 time 0.03 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> 0 SNES Function norm 0.000000000000e+00 >> >> Then, all the other SNES function norms are zero. >> >> >> >> On Nov 14, 2016, at 6:23 PM, Emil Constantinescu <[email protected] >> <mailto:[email protected]>> wrote: >> >>> Stefano, thanks for your note. The consistent splittings currently >>> supported under ts_type arkimex are give in Table 11 in the manual: >>> http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf >>> >>> 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. >>> >>> 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. >>> >>> Emil >>> >>> >>> On 11/14/16 4:09 AM, Stefano Zampini wrote: >>>> I came across this thing recently, and I couldn't figure out where the >>>> issue could be. >>>> >>>> The problem I'm solving is a simple DG advection, the ode is M*udot = >>>> K*u+b, M is diagonal. >>>> >>>> Attached is a MWE that reproduces the problem. >>>> >>>> The problem is formed in two different cases depending on the command >>>> line option -m_lhs >>>> >>>> a) -m_lhs 1 : F(u,udot,t) = M*udot, G(u,t) = K*u+b >>>> b) -m_lhs 0 : F(u,udot,t) = udot, G(u,t) = M^-1(K*u+b) >>>> >>>> Using option b) and RK4, the solution is ok. >>>> If run with any implicit TS method except arkimex, no matter if I'm >>>> choosing option a) or b), the solution is always very close (say, final >>>> error < 0.05) to the expected one (computed with BDF). >>>> >>>> When using ARKIMEX, case b) gives a good solution, but not case a). In >>>> fact, the solution does not seem to be advected at all in this case. >>>> >>>> I was wondering if I'm doing something wrong or there's a bug in the >>>> ARKIMEX implementation. >>>> >>>> I also noticed that, using -ts_arkimex_fully_implicit does not produce >>>> the same output for case a) and b). Shouldn't they produce the same >>>> method with this option? >>>> >>>> Thanks, >>>> -- >>>> Stefano >>> <1_Warning.txt>
