[petsc-users] Field split questions
Matthew Knepley
knepley at gmail.com
Mon Aug 27 12:18:38 CDT 2012
On Sun, Aug 26, 2012 at 8:42 PM, Colin McAuliffe <cjm2176 at columbia.edu>wrote:
> Im getting segmentation faults when I call PetscSectionSetChart, gdb is
> telling me this:
>
> Program received signal EXC_BAD_ACCESS, Could not access memory.
> Reason: 13 at address: 0x0000000000000000
> 0x00000001005f9585 in PetscTrFreeDefault (aa=0x4008000000000000, line=296,
> function=0x1016bd470 "PetscSectionSetChart",
> file=0x1016bcbb8 "/Users/christina/Desktop/**
> COLIN/Work/petsc-dev/src/vec/**vec/impls/seq/vsection.c", dir=0x1016bca50
> "")
> at /Users/christina/Desktop/**COLIN/Work/petsc-dev/src/sys/**
> memory/mtr.c:279
> 279 if (head->classid != CLASSID_VALUE) {
> (gdb) ba
> #0 0x00000001005f9585 in PetscTrFreeDefault (aa=0x4008000000000000,
> line=296, function=0x1016bd470 "PetscSectionSetChart",
> file=0x1016bcbb8 "/Users/christina/Desktop/**
> COLIN/Work/petsc-dev/src/vec/**vec/impls/seq/vsection.c", dir=0x1016bca50
> "")
> at /Users/christina/Desktop/**COLIN/Work/petsc-dev/src/sys/**
> memory/mtr.c:279
> #1 0x000000010075120b in PetscSectionSetChart (s=0x102e06910, pStart=1,
> pEnd=0)
> at /Users/christina/Desktop/**COLIN/Work/petsc-dev/src/vec/**
> vec/impls/seq/vsection.c:296
> #2 0x00000001006e99f3 in petscsectionsetchart_ (s=0x7fff5fbfee38,
> pStart=0x10165bc1c, pEnd=0x10165bc18, __ierr=0x7fff5fbfee4c)
> at /Users/christina/Desktop/**COLIN/Work/petsc-dev/src/vec/**
> vec/impls/seq/ftn-auto/**vsectionf.c:148
> #3 0x0000000100020c4c in setfs_ (fsind=<value temporarily unavailable,
> due to optimizations>,
> numfields=<value temporarily unavailable, due to optimizations>) at
> umacr8.F:96
>
It looks like you never create the PetscSection in the call above. Can you
send the code?
> Also, calling:
>
> call PetscSectionCreate(PETSC_COMM_**WORLD,sec,ierr)
> call PetscSectionGetChart(sec,**pStart,pEnd,ierr)
>
> returns pStart = 1 and pEnd = 0. Shouldn't PetscSectionCreate set pStart
> and pEnd to -1 and -1?
>
Yes, that is true. I will create a Fortran example to check this.
Matt
> I am a bit stumped here, any idea what is going on?
>
> thanks
> Colin
>
> Quoting Matthew Knepley <knepley at gmail.com>:
>
> On Mon, Aug 20, 2012 at 7:47 AM, Colin McAuliffe <cjm2176 at columbia.edu
>> >wrote:
>>
>> I am just not seeing where in the section such an IS would go. As far as
>>> I
>>> can tell from the functions in vsection.c, the only item in the section
>>> which is an IS is bcIndices, defining points where bcs are applied.
>>>
>>>
>> If you have no structure other than dof, you can make a Section where the
>> points
>> just number dofs. Then you just run through the ints p in your IS can call
>>
>> PetscSectionSetDof(section, p, 1)
>>
>> Then PetscSectionSetUp(). Stick this in a DMSHELL, or really any DM you
>> want,
>> and FS will use it.
>>
>> Matt
>>
>>
>> 38 ierr = PetscNew(struct _n_PetscSection, s);CHKERRQ(ierr);
>>> 39 (*s)->atlasLayout.comm = comm;
>>> 40 (*s)->atlasLayout.pStart = -1;
>>> 41 (*s)->atlasLayout.pEnd = -1;
>>> 42 (*s)->atlasLayout.numDof = 1;
>>> 43 (*s)->atlasDof = PETSC_NULL;
>>> 44 (*s)->atlasOff = PETSC_NULL;
>>> 45 (*s)->bc = PETSC_NULL;
>>> 46 (*s)->bcIndices = PETSC_NULL;
>>> 47 (*s)->setup = PETSC_FALSE;
>>> 48 (*s)->numFields = 0;
>>> 49 (*s)->fieldNames = PETSC_NULL;
>>> 50 (*s)->field = PETSC_NULL;
>>>
>>> Quoting Matthew Knepley <knepley at gmail.com>:
>>>
>>> On Mon, Aug 20, 2012 at 7:17 AM, Colin McAuliffe <cjm2176 at columbia.edu
>>>
>>>> >wrote:
>>>>
>>>> Yes, just call DMSetDefaultSection(). However, note that you will have
>>>>
>>>>>
>>>>> everything sized
>>>>>> correctly, but handling topology and iteration for the residual
>>>>>> calculation
>>>>>> would be completely
>>>>>> up to you.
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>> It would be really great to define the initial data layout using IS
>>>>> to
>>>>> define the equation numbers of the splits, while letting the new DM
>>>>> stuff
>>>>> handle creating all the nested splits given command line options. Is
>>>>> something like this possible?
>>>>>
>>>>>
>>>>> This is just what I say above. Is something not working?
>>>>
>>>> Matt
>>>>
>>>>
>>>> Colin
>>>>
>>>>>
>>>>> Quoting Matthew Knepley <knepley at gmail.com>:
>>>>>
>>>>> On Mon, Aug 13, 2012 at 4:06 PM, Colin McAuliffe <
>>>>> cjm2176 at columbia.edu
>>>>>
>>>>> >wrote:
>>>>>>
>>>>>> No, No, No. You do not have to write a DM implementation.
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> You just have to define the data layout in a PetscSection and attach
>>>>>>>> it
>>>>>>>> to
>>>>>>>> the DM with DMSetDefaultSection.
>>>>>>>>
>>>>>>>> Matt
>>>>>>>>
>>>>>>>>
>>>>>>>> Does use of the PetscSection mean that it is neccesary to define a
>>>>>>>>
>>>>>>> DMMesh?
>>>>>>> In other
>>>>>>> words is there a way to create the data layout for the physics
>>>>>>> without
>>>>>>> having to specify
>>>>>>> any information about the mesh?
>>>>>>>
>>>>>>>
>>>>>>> Yes, just call DMSetDefaultSection(). However, note that you will
>>>>>>> have
>>>>>>>
>>>>>> everything sized
>>>>>> correctly, but handling topology and iteration for the residual
>>>>>> calculation
>>>>>> would be completely
>>>>>> up to you.
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>> Thanks
>>>>>>
>>>>>> Colin
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Quoting Matthew Knepley <knepley at gmail.com>:
>>>>>>>
>>>>>>> On Thu, Aug 9, 2012 at 10:22 AM, Dmitry Karpeev <
>>>>>>> karpeev at mcs.anl.gov>
>>>>>>>
>>>>>>> wrote:
>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Thu, Aug 9, 2012 at 10:02 AM, Colin McAuliffe <
>>>>>>>>
>>>>>>>>> cjm2176 at columbia.edu
>>>>>>>>> >wrote:
>>>>>>>>>
>>>>>>>>> Sanjay, thanks for the reply but I am avoiding using blocked
>>>>>>>>> format
>>>>>>>>>
>>>>>>>>> since
>>>>>>>>>
>>>>>>>>>> my problem has 10 dofs per node but only has either dofs 1-3 or
>>>>>>>>>> 4-10
>>>>>>>>>> active
>>>>>>>>>> on a particular node. If I use block the equations I run out of
>>>>>>>>>> memory
>>>>>>>>>> pretty quickly on my machine but can get to reasonable sized
>>>>>>>>>> problems
>>>>>>>>>> with
>>>>>>>>>> the unblocked format.
>>>>>>>>>>
>>>>>>>>>> Matt, sorry I am not getting this, but I am still not sure how the
>>>>>>>>>> DM
>>>>>>>>>> interface works. I can see in the function PCFieldSplitSetDefaults
>>>>>>>>>> that
>>>>>>>>>> there is an initial call to DMCreateFieldDecomposition and
>>>>>>>>>> subsequent
>>>>>>>>>> calls
>>>>>>>>>> to DMCreateSubDM based on the command line options. What I am
>>>>>>>>>> missing
>>>>>>>>>> is
>>>>>>>>>> how the first call to DMCreateFieldDecomposition is able to figure
>>>>>>>>>> out
>>>>>>>>>> which equations belong to which field just from command line info
>>>>>>>>>> such
>>>>>>>>>> as
>>>>>>>>>> -pc_fieldsplit_0_fields 2,0. Where/how are the fields 2 and 0
>>>>>>>>>> defined?
>>>>>>>>>>
>>>>>>>>>> This might change slightly in the near future in petsc-dev to
>>>>>>>>>> allow
>>>>>>>>>>
>>>>>>>>>> one to
>>>>>>>>>>
>>>>>>>>> define splits using named fields.
>>>>>>>>> In any event, there has to be DM support to implement the
>>>>>>>>> decompositions
>>>>>>>>> over a particular mesh/problem over that mesh.
>>>>>>>>> With DMDA you can essentially get combinations of strided fields in
>>>>>>>>> each
>>>>>>>>> split. DMCOMPOSITE allows you
>>>>>>>>> to pull out combinations of the subproblems that were put in there
>>>>>>>>> to
>>>>>>>>> begin with. If you have your own mesh, you have to write
>>>>>>>>> a DM implementation around it to expose the available fields.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> No, No, No. You do not have to write a DM implementation.
>>>>>>>>>
>>>>>>>>>
>>>>>>>> You just have to define the data layout in a PetscSection and attach
>>>>>>>> it
>>>>>>>> to
>>>>>>>> the DM with DMSetDefaultSection.
>>>>>>>>
>>>>>>>> Matt
>>>>>>>>
>>>>>>>>
>>>>>>>> Dmitry.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>> Thanks
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> Colin
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Quoting Matthew Knepley <knepley at gmail.com>:
>>>>>>>>>>
>>>>>>>>>> On Thu, Aug 9, 2012 at 9:21 AM, Sanjay Govindjee <
>>>>>>>>>> s_g at berkeley.edu
>>>>>>>>>> >
>>>>>>>>>>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> Colin,
>>>>>>>>>>>
>>>>>>>>>>> I you block the equations in FEAP, then the restrained BCs are
>>>>>>>>>>>
>>>>>>>>>>> 'included' in assembled PETSc matrix (these dofs have rows that
>>>>>>>>>>>> are
>>>>>>>>>>>> zero
>>>>>>>>>>>> modulo a value of unity on the diagonal and the restrained value
>>>>>>>>>>>> on
>>>>>>>>>>>> the
>>>>>>>>>>>> right-hand side).
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> However, this is not necessary with the DM interface.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Matt
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> -sg
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> On 8/9/12 8:41 AM, Colin McAuliffe wrote:
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> From what I can gather from the petsc-dev source it looks like
>>>>>>>>>>>> the
>>>>>>>>>>>>
>>>>>>>>>>>> commands in 4) will then generate the splits using strided
>>>>>>>>>>>> blocks.
>>>>>>>>>>>>
>>>>>>>>>>>> The
>>>>>>>>>>>>> problem with that is the fortran code I am using (FEAP) uses
>>>>>>>>>>>>> petsc
>>>>>>>>>>>>> to
>>>>>>>>>>>>> assemble and solve the linear problem within its own nonlinear
>>>>>>>>>>>>> and
>>>>>>>>>>>>> time
>>>>>>>>>>>>> stepping schemes. The linear problem that petsc solves already
>>>>>>>>>>>>> has
>>>>>>>>>>>>> boundary
>>>>>>>>>>>>> conditions applied to it so petsc only sees the active
>>>>>>>>>>>>> (unrestrained)
>>>>>>>>>>>>> equations. So then in general fields can't be extracted from
>>>>>>>>>>>>> the
>>>>>>>>>>>>> active
>>>>>>>>>>>>> equations using strided blocks and I am stuck with generating
>>>>>>>>>>>>> the
>>>>>>>>>>>>> index
>>>>>>>>>>>>> sets defining the splits on my own. Will it still be possible
>>>>>>>>>>>>> to
>>>>>>>>>>>>> make
>>>>>>>>>>>>> use
>>>>>>>>>>>>> of the new DM functions in this case?
>>>>>>>>>>>>>
>>>>>>>>>>>>> FEAP website:
>>>>>>>>>>>>> http://www.ce.berkeley.edu/************projects/feap/<http://www.ce.berkeley.edu/**********projects/feap/>
>>>>>>>>>>>>> <http://**www.ce.berkeley.edu/**********projects/feap/<http://www.ce.berkeley.edu/********projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**www.ce.berkeley.edu/**********projects/feap/<http://www.ce.berkeley.edu/********projects/feap/>
>>>>>>>>>>>>> <http://**www.ce.berkeley.edu/********projects/feap/<http://www.ce.berkeley.edu/******projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.**ce.berkeley.edu/********projects/**feap/<http://ce.berkeley.edu/******projects/**feap/>
>>>>>>>>>>>>> <http://**ce.berkeley.edu/****projects/****feap/<http://ce.berkeley.edu/****projects/**feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**www.ce.berkeley.edu/********projects/feap/<http://www.ce.berkeley.edu/******projects/feap/>
>>>>>>>>>>>>> <http://**www.ce.berkeley.edu/******projects/feap/<http://www.ce.berkeley.edu/****projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/********projects/feap/<http://berkeley.edu/******projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/****projects/**feap/<http://berkeley.edu/****projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**berkeley.edu/****projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/**projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.**ce.berkeley.edu/******projects/**feap/<http://ce.berkeley.edu/****projects/**feap/>
>>>>>>>>>>>>> <http://**ce.berkeley.edu/**projects/****feap/<http://ce.berkeley.edu/**projects/**feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.**ce.berkeley.edu/****projects/**feap/<http://ce.berkeley.edu/**projects/**feap/>
>>>>>>>>>>>>> <http://www.**ce.berkeley.edu/**projects/**feap/<http://www.ce.berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/********projects/feap/<http://berkeley.edu/******projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/****projects/**feap/<http://berkeley.edu/****projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**berkeley.edu/****projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/**projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**berkeley.edu/****projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**berkeley.edu/**projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/******projects/feap/<http://berkeley.edu/****projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/**projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://**berkeley.edu/**projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/****projects/feap/<http://berkeley.edu/**projects/feap/>
>>>>>>>>>>>>> <http://**berkeley.edu/projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**projects/feap/<http://berkeley.edu/projects/feap/>
>>>>>>>>>>>>> <http://www.ce.**berkeley.edu/projects/feap/<http://www.ce.berkeley.edu/projects/feap/>
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>> >
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Colin
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Quoting Matthew Knepley <knepley at gmail.com>:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Wed, Aug 8, 2012 at 10:51 PM, Matthew Knepley <
>>>>>>>>>>>>> knepley at gmail.com
>>>>>>>>>>>>> >
>>>>>>>>>>>>>
>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Wed, Aug 8, 2012 at 10:23 PM, Colin McAuliffe <
>>>>>>>>>>>>>> cjm2176 at columbia.edu
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> >wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks all, regarding use of DM in 3.3, is the procedure now
>>>>>>>>>>>>>>> to
>>>>>>>>>>>>>>> create
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> the fields with PCFieldSplitSetIS and then use
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> DMCreateFieldDecompositionDM
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> to create a new DM based from the new fields and the DM for
>>>>>>>>>>>>>>>> the
>>>>>>>>>>>>>>>> original
>>>>>>>>>>>>>>>> problem?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> 1) Use petsc-dev
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> 2) PCFieldSplitSetIS() is independent. This allows you to
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> define
>>>>>>>>>>>>>>> splits
>>>>>>>>>>>>>>> however you want, but then recursive gets harder
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 3) In 3.3., it uses DMCreateFieldDecompositionDM() to split
>>>>>>>>>>>>>>> all
>>>>>>>>>>>>>>> fields
>>>>>>>>>>>>>>> apart at once
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> 4) In petsc-dev, it uses DMCreateSubDM() which can split off
>>>>>>>>>>>>>>> any
>>>>>>>>>>>>>>> combination of fields, which from the command line is
>>>>>>>>>>>>>>> something
>>>>>>>>>>>>>>> like
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> -pc_fieldsplit_0_fields 2,0 -pc_fieldsplit_1_fields 1,3
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I should have shown recursive:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> -fieldsplit_0_pc_type fieldsplit
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> will split 2,0 into two blocks.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Colin
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Colin McAuliffe
>>>>>>>>>>>>>>>> PhD Candidate
>>>>>>>>>>>>>>>> Columbia University
>>>>>>>>>>>>>>>> Department of Civil Engineering and Engineering Mechanics
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> 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
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> ------------------------------************-----------------
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>> Sanjay Govindjee, PhD, PE
>>>>>>>>>>>> Professor of Civil Engineering
>>>>>>>>>>>> Vice Chair for Academic Affairs
>>>>>>>>>>>>
>>>>>>>>>>>> 779 Davis Hall
>>>>>>>>>>>> Structural Engineering, Mechanics and Materials
>>>>>>>>>>>> Department of Civil Engineering
>>>>>>>>>>>> University of California
>>>>>>>>>>>> Berkeley, CA 94720-1710
>>>>>>>>>>>>
>>>>>>>>>>>> Voice: +1 510 642 6060
>>>>>>>>>>>> FAX: +1 510 643 5264
>>>>>>>>>>>> s_g at berkeley.edu
>>>>>>>>>>>> http://www.ce.berkeley.edu/~************sanjay<http://www.ce.berkeley.edu/~**********sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~********sanjay<http://www.ce.berkeley.edu/~********sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**~******sanjay<http://berkeley.edu/~******sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~******sanjay<http://www.ce.berkeley.edu/~******sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/****~****sanjay<http://berkeley.edu/**~****sanjay>
>>>>>>>>>>>> <http://berkeley.**edu/~****sanjay<http://berkeley.edu/~****sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**~****sanjay<http://berkeley.edu/~****sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~****sanjay<http://www.ce.berkeley.edu/~****sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/******~**sanjay<http://berkeley.edu/****~**sanjay>
>>>>>>>>>>>> <http://berkeley.**edu/**~**sanjay<http://berkeley.edu/**~**sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://berkeley.**edu/~****sanjay <
>>>>>>>>>>>> http://berkeley.edu/~**sanjay**>>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/****~**sanjay<http://berkeley.edu/**~**sanjay>
>>>>>>>>>>>> <http://berkeley.**edu/~**sanjay<http://berkeley.edu/~**sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**~**sanjay<http://berkeley.edu/~**sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~**sanjay<http://www.ce.berkeley.edu/~**sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> ><
>>>>>>>>>>>> http://www.ce.berkeley.edu/~**********sanjay<http://www.ce.berkeley.edu/~********sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~******sanjay<http://www.ce.berkeley.edu/~******sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**~****sanjay<http://berkeley.edu/~****sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~****sanjay<http://www.ce.berkeley.edu/~****sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/****~**sanjay<http://berkeley.edu/**~**sanjay>
>>>>>>>>>>>> <http://berkeley.**edu/~**sanjay<http://berkeley.edu/~**sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/**~**sanjay<http://berkeley.edu/~**sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~**sanjay<http://www.ce.berkeley.edu/~**sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> <http://www.ce.berkeley.**edu/******~sanjay<http://www.ce.**
>>>>>>>>>>>> berkeley.edu/~sanjay <http://www.ce.berkeley.edu/~****sanjay<http://www.ce.berkeley.edu/~**sanjay>
>>>>>>>>>>>> <http://www.ce.**berkeley.edu/~sanjay<http://www.ce.berkeley.edu/~sanjay>
>>>>>>>>>>>> >
>>>>>>>>>>>> >>
>>>>>>>>>>>> >
>>>>>>>>>>>> >
>>>>>>>>>>>> ------------------------------************-----------------
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>>
>>>>>>>>>>>> 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
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>>
>>>>>>>>>> Colin McAuliffe
>>>>>>>>>> PhD Candidate
>>>>>>>>>> Columbia University
>>>>>>>>>> Department of Civil Engineering and Engineering Mechanics
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> --
>>>>>>>>>
>>>>>>>> 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
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>> Colin McAuliffe
>>>>>>> PhD Candidate
>>>>>>> Columbia University
>>>>>>> Department of Civil Engineering and Engineering Mechanics
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> --
>>>>>> 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
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>> --
>>>>> Colin McAuliffe
>>>>> PhD Candidate
>>>>> Columbia University
>>>>> Department of Civil Engineering and Engineering Mechanics
>>>>>
>>>>>
>>>>>
>>>>
>>>> --
>>>> 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
>>>>
>>>>
>>>>
>>>
>>> --
>>> Colin McAuliffe
>>> PhD Candidate
>>> Columbia University
>>> Department of Civil Engineering and Engineering Mechanics
>>>
>>>
>>
>>
>> --
>> 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
>>
>>
>
>
> --
> Colin McAuliffe
> PhD Candidate
> Columbia University
> Department of Civil Engineering and Engineering Mechanics
>
--
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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