[petsc-users] Field split questions
Matthew Knepley
knepley at gmail.com
Mon Aug 27 13:19:19 CDT 2012
On Mon, Aug 27, 2012 at 12:18 PM, Matthew Knepley <knepley at gmail.com> wrote:
> 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.
>
Okay, there was a bug in the Fortran stub generation for this type. I have
pushed a fix for this. In order to
get these to rebuild, you need to
rm $PETSC_DIR/$PETSC_ARCH/bin/bfort
rm -rf $PETSC_DIR/externalpackages/sowing*
cd $PETSC_DIR
cd externalpackages
hg clone http://petsc.cs.iit.edu/petsc/externalpackages/sowing-1.1.16/
./$PETSC_ARCH/conf/reconfigure-$PETSC_ARCH.py
Then you can run src/vec/vec/examples/tests/ex40f90.F
Thanks
Matt
> 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
>
--
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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