[petsc-users] Problem with DMDAVecGetArrayF90 and DMDAVecRestoreArrayF90

Matthew Knepley knepley at gmail.com
Sat Apr 19 09:55:16 CDT 2014


On Sat, Apr 19, 2014 at 9:14 AM, TAY wee-beng <zonexo at gmail.com> wrote:

>  On 19/4/2014 6:48 PM, Matthew Knepley wrote:
>
>  On Sat, Apr 19, 2014 at 4:59 AM, TAY wee-beng <zonexo at gmail.com> wrote:
>
>>  On 19/4/2014 1:17 PM, Barry Smith wrote:
>>
>>> On Apr 19, 2014, at 12:11 AM, TAY wee-beng <zonexo at gmail.com> wrote:
>>>
>>>  On 19/4/2014 12:10 PM, Barry Smith wrote:
>>>>
>>>>> On Apr 18, 2014, at 9:57 PM, TAY wee-beng <zonexo at gmail.com> wrote:
>>>>>
>>>>>  On 19/4/2014 3:53 AM, Barry Smith wrote:
>>>>>>
>>>>>>>    Hmm,
>>>>>>>
>>>>>>>        Interface DMDAVecGetArrayF90
>>>>>>>          Subroutine DMDAVecGetArrayF903(da1, v,d1,ierr)
>>>>>>>            USE_DM_HIDE
>>>>>>>            DM_HIDE da1
>>>>>>>            VEC_HIDE v
>>>>>>>            PetscScalar,pointer :: d1(:,:,:)
>>>>>>>            PetscErrorCode ierr
>>>>>>>          End Subroutine
>>>>>>>
>>>>>>>     So the d1 is a F90 POINTER. But your subroutine seems to be
>>>>>>> treating it as a “plain old Fortran array”?
>>>>>>> real(8), intent(inout) :: u(:,:,:),v(:,:,:),w(:,:,:)
>>>>>>>
>>>>>>  Hi,
>>>>
>>>> So d1 is a pointer, and it's different if I declare it as "plain old
>>>> Fortran array"? Because I declare it as a Fortran array and it works w/o
>>>> any problem if I only call DMDAVecGetArrayF90 and DMDAVecRestoreArrayF90
>>>> with "u".
>>>>
>>>> But if I call DMDAVecGetArrayF90 and DMDAVecRestoreArrayF90 with "u",
>>>> "v" and "w", error starts to happen. I wonder why...
>>>>
>>>> Also, supposed I call:
>>>>
>>>> call DMDAVecGetArrayF90(da_u,u_local,u_array,ierr)
>>>>
>>>>     call DMDAVecGetArrayF90(da_v,v_local,v_array,ierr)
>>>>
>>>>     call DMDAVecGetArrayF90(da_w,w_local,w_array,ierr)
>>>>
>>>> u_array ....
>>>>
>>>> v_array .... etc
>>>>
>>>> Now to restore the array, does it matter the sequence they are restored?
>>>>
>>>     No it should not matter. If it matters that is a sign that memory
>>> has been written to incorrectly earlier in the code.
>>>
>>>   Hi,
>>
>> Hmm, I have been getting different results on different intel compilers.
>> I'm not sure if MPI played a part but I'm only using a single processor. In
>> the debug mode, things run without problem. In optimized mode, in some
>> cases, the code aborts even doing simple initialization:
>>
>>
>> call DMDAVecGetArrayF90(da_u,u_local,u_array,ierr)
>>
>>     call DMDAVecGetArrayF90(da_v,v_local,v_array,ierr)
>>
>>     call DMDAVecGetArrayF90(da_w,w_local,w_array,ierr)
>>
>>      call DMDAVecGetArrayF90(da_p,p_local,p_array,ierr)
>>
>>     u_array = 0.d0
>>
>>     v_array = 0.d0
>>
>>     w_array = 0.d0
>>
>>     p_array = 0.d0
>>
>>
>>     call DMDAVecRestoreArrayF90(da_p,p_local,p_array,ierr)
>>
>>
>>     call DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)
>>
>>     call DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>
>>     call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>
>>  The code aborts at call
>> DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr), giving segmentation
>> error. But other version of intel compiler passes thru this part w/o error.
>> Since the response is different among different compilers, is this PETSc or
>> intel 's bug? Or mvapich or openmpi?
>
>
>  We do this is a bunch of examples. Can you reproduce this different
> behavior in src/dm/examples/tutorials/ex11f90.F?
>
>
> Hi Matt,
>
> Do you mean putting the above lines into ex11f90.F and test?
>

It already has DMDAVecGetArray(). Just run it.

   Matt


> Thanks
>
> Regards.
>
>
>     Matt
>
>
>>   As in w, then v and u?
>>>>
>>>> call DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)
>>>> call DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>>> call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>>>
>>>> thanks
>>>>
>>>>>      Note also that the beginning and end indices of the u,v,w, are
>>>>>>> different for each process see for example
>>>>>>> http://www.mcs.anl.gov/petsc/petsc-3.4/src/dm/examples/tutorials/ex11f90.F (and they do not start at 1). This is how to get the loop bounds.
>>>>>>>
>>>>>> Hi,
>>>>>>
>>>>>> In my case, I fixed the u,v,w such that their indices are the same. I
>>>>>> also checked using DMDAGetCorners and DMDAGetGhostCorners. Now the problem
>>>>>> lies in my subroutine treating it as a “plain old Fortran array”.
>>>>>>
>>>>>> If I declare them as pointers, their indices follow the C 0 start
>>>>>> convention, is that so?
>>>>>>
>>>>>     Not really. It is that in each process you need to access them
>>>>> from the indices indicated by DMDAGetCorners() for global vectors and
>>>>> DMDAGetGhostCorners() for local vectors.  So really C or Fortran doesn’t
>>>>> make any difference.
>>>>>
>>>>>
>>>>>  So my problem now is that in my old MPI code, the u(i,j,k) follow the
>>>>>> Fortran 1 start convention. Is there some way to manipulate such that I do
>>>>>> not have to change my u(i,j,k) to u(i-1,j-1,k-1)?
>>>>>>
>>>>>    If you code wishes to access them with indices plus one from the
>>>>> values returned by DMDAGetCorners() for global vectors and
>>>>> DMDAGetGhostCorners() for local vectors then you need to manually subtract
>>>>> off the 1.
>>>>>
>>>>>    Barry
>>>>>
>>>>>  Thanks.
>>>>>>
>>>>>>>    Barry
>>>>>>>
>>>>>>> On Apr 18, 2014, at 10:58 AM, TAY wee-beng <zonexo at gmail.com> wrote:
>>>>>>>
>>>>>>>  Hi,
>>>>>>>>
>>>>>>>> I tried to pinpoint the problem. I reduced my job size and hence I
>>>>>>>> can run on 1 processor. Tried using valgrind but perhaps I'm using the
>>>>>>>> optimized version, it didn't catch the error, besides saying "Segmentation
>>>>>>>> fault (core dumped)"
>>>>>>>>
>>>>>>>> However, by re-writing my code, I found out a few things:
>>>>>>>>
>>>>>>>> 1. if I write my code this way:
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>
>>>>>>>> u_array = ....
>>>>>>>>
>>>>>>>> v_array = ....
>>>>>>>>
>>>>>>>> w_array = ....
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>
>>>>>>>> The code runs fine.
>>>>>>>>
>>>>>>>> 2. if I write my code this way:
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecGetArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>
>>>>>>>> call uvw_array_change(u_array,v_array,w_array) -> this subroutine
>>>>>>>> does the same modification as the above.
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr) -> error
>>>>>>>>
>>>>>>>> where the subroutine is:
>>>>>>>>
>>>>>>>> subroutine uvw_array_change(u,v,w)
>>>>>>>>
>>>>>>>> real(8), intent(inout) :: u(:,:,:),v(:,:,:),w(:,:,:)
>>>>>>>>
>>>>>>>> u ...
>>>>>>>> v...
>>>>>>>> w ...
>>>>>>>>
>>>>>>>> end subroutine uvw_array_change.
>>>>>>>>
>>>>>>>> The above will give an error at :
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>
>>>>>>>> 3. Same as above, except I change the order of the last 3 lines to:
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>
>>>>>>>> call DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>
>>>>>>>> So they are now in reversed order. Now it works.
>>>>>>>>
>>>>>>>> 4. Same as 2 or 3, except the subroutine is changed to :
>>>>>>>>
>>>>>>>> subroutine uvw_array_change(u,v,w)
>>>>>>>>
>>>>>>>> real(8), intent(inout) ::
>>>>>>>> u(start_indices(1):end_indices(1),start_indices(2):end_indices(2),start_indices(3):end_indices(3))
>>>>>>>>
>>>>>>>> real(8), intent(inout) ::
>>>>>>>> v(start_indices(1):end_indices(1),start_indices(2):end_indices(2),start_indices(3):end_indices(3))
>>>>>>>>
>>>>>>>> real(8), intent(inout) ::
>>>>>>>> w(start_indices(1):end_indices(1),start_indices(2):end_indices(2),start_indices(3):end_indices(3))
>>>>>>>>
>>>>>>>> u ...
>>>>>>>> v...
>>>>>>>> w ...
>>>>>>>>
>>>>>>>> end subroutine uvw_array_change.
>>>>>>>>
>>>>>>>> The start_indices and end_indices are simply to shift the 0 indices
>>>>>>>> of C convention to that of the 1 indices of the Fortran convention. This is
>>>>>>>> necessary in my case because most of my codes start array counting at 1,
>>>>>>>> hence the "trick".
>>>>>>>>
>>>>>>>> However, now no matter which order of the DMDAVecRestoreArrayF90
>>>>>>>> (as in 2 or 3), error will occur at "call
>>>>>>>> DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr) "
>>>>>>>>
>>>>>>>> So did I violate and cause memory corruption due to the trick
>>>>>>>> above? But I can't think of any way other than the "trick" to continue
>>>>>>>> using the 1 indices convention.
>>>>>>>>
>>>>>>>> Thank you.
>>>>>>>>
>>>>>>>> Yours sincerely,
>>>>>>>>
>>>>>>>> TAY wee-beng
>>>>>>>>
>>>>>>>> On 15/4/2014 8:00 PM, Barry Smith wrote:
>>>>>>>>
>>>>>>>>>    Try running under valgrind
>>>>>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On Apr 14, 2014, at 9:47 PM, TAY wee-beng <zonexo at gmail.com>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>  Hi Barry,
>>>>>>>>>>
>>>>>>>>>> As I mentioned earlier, the code works fine in PETSc debug mode
>>>>>>>>>> but fails in non-debug mode.
>>>>>>>>>>
>>>>>>>>>> I have attached my code.
>>>>>>>>>>
>>>>>>>>>> Thank you
>>>>>>>>>>
>>>>>>>>>> Yours sincerely,
>>>>>>>>>>
>>>>>>>>>> TAY wee-beng
>>>>>>>>>>
>>>>>>>>>> On 15/4/2014 2:26 AM, Barry Smith wrote:
>>>>>>>>>>
>>>>>>>>>>>    Please send the code that creates da_w and the declarations
>>>>>>>>>>> of w_array
>>>>>>>>>>>
>>>>>>>>>>>    Barry
>>>>>>>>>>>
>>>>>>>>>>> On Apr 14, 2014, at 9:40 AM, TAY wee-beng
>>>>>>>>>>> <zonexo at gmail.com>
>>>>>>>>>>>   wrote:
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>  Hi Barry,
>>>>>>>>>>>>
>>>>>>>>>>>> I'm not too sure how to do it. I'm running mpi. So I run:
>>>>>>>>>>>>
>>>>>>>>>>>>   mpirun -n 4 ./a.out -start_in_debugger
>>>>>>>>>>>>
>>>>>>>>>>>> I got the msg below. Before the gdb windows appear (thru x11),
>>>>>>>>>>>> the program aborts.
>>>>>>>>>>>>
>>>>>>>>>>>> Also I tried running in another cluster and it worked. Also
>>>>>>>>>>>> tried in the current cluster in debug mode and it worked too.
>>>>>>>>>>>>
>>>>>>>>>>>> mpirun -n 4 ./a.out -start_in_debugger
>>>>>>>>>>>>
>>>>>>>>>>>> --------------------------------------------------------------------------
>>>>>>>>>>>> An MPI process has executed an operation involving a call to the
>>>>>>>>>>>> "fork()" system call to create a child process.  Open MPI is
>>>>>>>>>>>> currently
>>>>>>>>>>>> operating in a condition that could result in memory corruption
>>>>>>>>>>>> or
>>>>>>>>>>>> other system errors; your MPI job may hang, crash, or produce
>>>>>>>>>>>> silent
>>>>>>>>>>>> data corruption.  The use of fork() (or system() or other calls
>>>>>>>>>>>> that
>>>>>>>>>>>> create child processes) is strongly discouraged.
>>>>>>>>>>>>
>>>>>>>>>>>> The process that invoked fork was:
>>>>>>>>>>>>
>>>>>>>>>>>>    Local host:          n12-76 (PID 20235)
>>>>>>>>>>>>    MPI_COMM_WORLD rank: 2
>>>>>>>>>>>>
>>>>>>>>>>>> If you are *absolutely sure* that your application will
>>>>>>>>>>>> successfully
>>>>>>>>>>>> and correctly survive a call to fork(), you may disable this
>>>>>>>>>>>> warning
>>>>>>>>>>>> by setting the mpi_warn_on_fork MCA parameter to 0.
>>>>>>>>>>>>
>>>>>>>>>>>> --------------------------------------------------------------------------
>>>>>>>>>>>> [2]PETSC ERROR: PETSC: Attaching gdb to ./a.out of pid 20235 on
>>>>>>>>>>>> display localhost:50.0 on machine n12-76
>>>>>>>>>>>> [0]PETSC ERROR: PETSC: Attaching gdb to ./a.out of pid 20233 on
>>>>>>>>>>>> display localhost:50.0 on machine n12-76
>>>>>>>>>>>> [1]PETSC ERROR: PETSC: Attaching gdb to ./a.out of pid 20234 on
>>>>>>>>>>>> display localhost:50.0 on machine n12-76
>>>>>>>>>>>> [3]PETSC ERROR: PETSC: Attaching gdb to ./a.out of pid 20236 on
>>>>>>>>>>>> display localhost:50.0 on machine n12-76
>>>>>>>>>>>> [n12-76:20232] 3 more processes have sent help message
>>>>>>>>>>>> help-mpi-runtime.txt / mpi_init:warn-fork
>>>>>>>>>>>> [n12-76:20232] Set MCA parameter "orte_base_help_aggregate" to
>>>>>>>>>>>> 0 to see all help / error messages
>>>>>>>>>>>>
>>>>>>>>>>>> ....
>>>>>>>>>>>>
>>>>>>>>>>>>   1
>>>>>>>>>>>> [1]PETSC ERROR:
>>>>>>>>>>>> ------------------------------------------------------------------------
>>>>>>>>>>>> [1]PETSC ERROR: Caught signal number 11 SEGV: Segmentation
>>>>>>>>>>>> Violation, probably memory access out of range
>>>>>>>>>>>> [1]PETSC ERROR: Try option -start_in_debugger or
>>>>>>>>>>>> -on_error_attach_debugger
>>>>>>>>>>>> [1]PETSC ERROR: or see
>>>>>>>>>>>>
>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind[1]PETSCERROR: or try
>>>>>>>>>>>> http://valgrind.org
>>>>>>>>>>>>   on GNU/linux and Apple Mac OS X to find memory corruption
>>>>>>>>>>>> errors
>>>>>>>>>>>> [1]PETSC ERROR: configure using --with-debugging=yes,
>>>>>>>>>>>> recompile, link, and run
>>>>>>>>>>>> [1]PETSC ERROR: to get more information on the crash.
>>>>>>>>>>>> [1]PETSC ERROR: User provided function() line 0 in unknown
>>>>>>>>>>>> directory unknown file (null)
>>>>>>>>>>>> [3]PETSC ERROR:
>>>>>>>>>>>> ------------------------------------------------------------------------
>>>>>>>>>>>> [3]PETSC ERROR: Caught signal number 11 SEGV: Segmentation
>>>>>>>>>>>> Violation, probably memory access out of range
>>>>>>>>>>>> [3]PETSC ERROR: Try option -start_in_debugger or
>>>>>>>>>>>> -on_error_attach_debugger
>>>>>>>>>>>> [3]PETSC ERROR: or see
>>>>>>>>>>>>
>>>>>>>>>>>> http://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind[3]PETSCERROR: or try
>>>>>>>>>>>> http://valgrind.org
>>>>>>>>>>>>   on GNU/linux and Apple Mac OS X to find memory corruption
>>>>>>>>>>>> errors
>>>>>>>>>>>> [3]PETSC ERROR: configure using --with-debugging=yes,
>>>>>>>>>>>> recompile, link, and run
>>>>>>>>>>>> [3]PETSC ERROR: to get more information on the crash.
>>>>>>>>>>>> [3]PETSC ERROR: User provided function() line 0 in unknown
>>>>>>>>>>>> directory unknown file (null)
>>>>>>>>>>>>
>>>>>>>>>>>> ...
>>>>>>>>>>>> Thank you.
>>>>>>>>>>>>
>>>>>>>>>>>> Yours sincerely,
>>>>>>>>>>>>
>>>>>>>>>>>> TAY wee-beng
>>>>>>>>>>>>
>>>>>>>>>>>> On 14/4/2014 9:05 PM, Barry Smith wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>     Because IO doesn’t always get flushed immediately it may
>>>>>>>>>>>>> not be hanging at this point.  It is better to use the option
>>>>>>>>>>>>> -start_in_debugger then type cont in each debugger window and then when you
>>>>>>>>>>>>> think it is “hanging” do a control C in each debugger window and type where
>>>>>>>>>>>>> to see where each process is you can also look around in the debugger at
>>>>>>>>>>>>> variables to see why it is “hanging” at that point.
>>>>>>>>>>>>>
>>>>>>>>>>>>>     Barry
>>>>>>>>>>>>>
>>>>>>>>>>>>>    This routines don’t have any parallel communication in them
>>>>>>>>>>>>> so are unlikely to hang.
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Apr 14, 2014, at 6:52 AM, TAY wee-beng
>>>>>>>>>>>>>
>>>>>>>>>>>>> <zonexo at gmail.com>
>>>>>>>>>>>>>
>>>>>>>>>>>>>   wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>  Hi,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> My code hangs and I added in mpi_barrier and print to catch
>>>>>>>>>>>>>> the bug. I found that it hangs after printing "7". Is it because I'm doing
>>>>>>>>>>>>>> something wrong? I need to access the u,v,w array so I use
>>>>>>>>>>>>>> DMDAVecGetArrayF90. After access, I use DMDAVecRestoreArrayF90.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>          call DMDAVecGetArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"3"
>>>>>>>>>>>>>>          call DMDAVecGetArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"4"
>>>>>>>>>>>>>>          call DMDAVecGetArrayF90(da_w,w_local,w_array,ierr)
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"5"
>>>>>>>>>>>>>>          call
>>>>>>>>>>>>>> I_IIB_uv_initial_1st_dm(I_cell_no_u1,I_cell_no_v1,I_cell_no_w1,I_cell_u1,I_cell_v1,I_cell_w1,u_array,v_array,w_array)
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"6"
>>>>>>>>>>>>>>          call
>>>>>>>>>>>>>> DMDAVecRestoreArrayF90(da_w,w_local,w_array,ierr)  !must be in reverse order
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"7"
>>>>>>>>>>>>>>          call
>>>>>>>>>>>>>> DMDAVecRestoreArrayF90(da_v,v_local,v_array,ierr)
>>>>>>>>>>>>>>          call MPI_Barrier(MPI_COMM_WORLD,ierr);  if (myid==0)
>>>>>>>>>>>>>> print *,"8"
>>>>>>>>>>>>>>          call
>>>>>>>>>>>>>> DMDAVecRestoreArrayF90(da_u,u_local,u_array,ierr)
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> Thank you.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Yours sincerely,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> TAY wee-beng
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>   <code.txt>
>>>>>>>>>>
>>>>>>>>>
>>
>
>
>  --
> 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
>
>
>


-- 
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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20140419/a0548cdc/attachment-0001.html>


More information about the petsc-users mailing list