[petsc-users] Stiff ODEs

[Matthew Knepley]

On Thu, Dec 5, 2013 at 5:25 AM, Katy Ghantous <katyghantous at gmail.com>wrote:

> thank you!
> i used master from petsc-dev on mac and have TSRK working now.
>
> i am using an explicit scheme since its a set of coupled nonlinear
> equations:
>
> dφn/d t = an φn-2φn-1 - bn φn-1φn+1 + cn φn+1φn+2
>
> where n can go up to 24 or so.. I didnt think it is possible to solve it
> implicitly. and TSRK works for it now.
>

It is.


> But i need petsc on linux too, and testing to verify installation (same
> options on configure as mac expect arch) gave an error:
>
>
> /home/katy/petsc/linux-gnu-cxx-debug/bin/mpicxx -o ex19.o -c -Wall
> -Wwrite-strings -Wno-strict-aliasing -Wno-unknown-pragmas -g -O0  -fPIC
> -I/home/katy/petsc/include
> -I/home/katy/petsc/linux-gnu-cxx-debug/include    `pwd`/ex19.c
> /home/katy/petsc/linux-gnu-cxx-debug/bin/mpicxx -Wall -Wwrite-strings
> -Wno-strict-aliasing -Wno-unknown-pragmas -g -O0  -o ex19  ex19.o
> -Wl,-rpath,/home/katy/petsc/linux-gnu-cxx-debug/lib
> -L/home/katy/petsc/linux-gnu-cxx-debug/lib  -lpetsc
> -Wl,-rpath,/home/katy/petsc/linux-gnu-cxx-debug/lib -lf2clapack -lf2cblas
> -lm -lpthread -lm -Wl,-rpath,/usr/lib/gcc/x86_64-linux-gnu/4.6
> -L/usr/lib/gcc/x86_64-linux-gnu/4.6 -Wl,-rpath,/usr/lib/x86_64-linux-gnu
> -L/usr/lib/x86_64-linux-gnu -Wl,-rpath,/lib/x86_64-linux-gnu
> -L/lib/x86_64-linux-gnu -lmpichcxx -lstdc++ -ldl -lmpich -lopa -lmpl -lrt
> -lpthread -lgcc_s -ldl
> /home/katy/petsc/linux-gnu-cxx-debug/lib/libpetsc.so: undefined reference
> to `SNESDefaultMatrixFreeCreate2(_p_SNES*, _p_Vec*, _p_Mat**)'
> /home/katy/petsc/linux-gnu-cxx-debug/lib/libpetsc.so: undefined reference
> to `KSPCreate_DGMRES'
> /home/katy/petsc/linux-gnu-cxx-debug/lib/libpetsc.so: undefined reference
> to `PCCreate_TFS'
>

Send make.log.

  Matt


> On Tue, Dec 3, 2013 at 6:13 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
>
>> Katy Ghantous <katyghantous at gmail.com> writes:
>>
>> > Hi,
>> > I have just started with Petsc and have very elementary equations.
>> > I am trying to solve a set of stiff ODEs explicitly.
>>
>> If your ODEs are stiff, why are you trying to use an explicit method?
>> (A common definition of "stiff" is that explicit methods do not work
>> well.)
>>
>> > They are very stiff and was hoping to use TSRK with variable time
>> > steps, but it is throwing a segmentation fault
>>
>> Always show the full error message.  Please also use 'master' from
>> petsc-dev, because TSRK was overhauled recently to be consistent with
>> the other integrators (and adding a bunch of new functionality).
>>
>>   https://bitbucket.org/petsc/petsc/wiki/
>>
>> > otherwise non existent with Euler or TSSSP.  1. should i look into the
>> > TSRK error or is it something with the new version of Petsc?  2. i
>> > read somewhere (but cant find the source again) that TSSSP is not
>> > recommended for stiff equations (even with the rk solvers set as the
>> > type).
>>
>> Yes, TSSSP is for non-stiff problems that require "strong stability"
>> (like controlling total variation or positivity in transport-dominated
>> applications).
>>
>> > Is that correct? if so, what would be most optimized to solve stiff
>> > odes explicitly.
>>
>> Stiff ODEs should be solved *implicitly*.
>>
>> > 3. If it is not correct and TSSSP is useful for stiff equations, how
>> > can i run it with variable time steps, since with TSStep it is taking
>> > equal time steps which is the time step that i am specifying as an
>> > initial time step TSSetInitialTimeStep.
>>
>> TSSSP does not have an adaptive controller.  A user can set a post-check
>> function that adapts the time step based on a custom stability function
>> (e.g., CFL criteria).
>>
>> TSROSW and TSARKIMEX are IMEX methods that can handle stiff problems.
>> They have adaptive error estimators and the like.
>>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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