[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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