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    <div class="moz-cite-prefix">Dave,<br>
      <br>
      coupled staggered grid possesses a non-trivial null space. That
      means it probably contains not just three translations, three
      rotations and a constant pressure. It would be nice if somebody
      finally figures out how it looks like. Any ideas? This information
      is valuable for building a proper coupled algebraic multigrid
      preconditioner.<br>
      <br>
      As for the fake dofs, I really don't like them. It's perfectly
      possible to design a numbering scheme that would only contain real
      dofs, and implement it with PETSc. I'm working on it.<br>
      <br>
      Anton<br>
      <br>
      On 7/26/13 6:05 PM, Dave May wrote:<br>
    </div>
    <blockquote
cite="mid:CAJ98EDrcztF+jjDzs+-cEuy0wey174tOZtC1QOOqouGLwQqkrQ@mail.gmail.com"
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        <div>Yes, the nullspace is important.<br>
        </div>
        <div>There is definitely a pressure null space of constants
          which needs to be considered.<br>
        </div>
        <div>I don't believe ONLY using<br>
            -fieldsplit_1_ksp_constant_null_space<br>
        </div>
        <div>is not sufficient. <br>
          <br>
          You need to inform the KSP for the outer syetem (the coupled
          u-p system) that there is a null space of constants in the
          pressure system. This cannot (as far as I'm aware) be set via
          command line args. You need to write a null space removal
          function which accepts the complete (u,p) vector which only
          modifies the pressure dofs.<br>
          <br>
        </div>
        <div>Take care though when you write this though. Because of the
          DMDA formulation you are using, you have introduced
          dummy/ficticious pressure dofs on the right/top/front faces of
          your mesh. Thus your null space removal function should ignore
          those dofs when your define the constant pressure constraint.<br>
          <br>
          <br>
        </div>
        <div><br>
          Cheers,<br>
        </div>
          Dave<br>
      </div>
      <div class="gmail_extra"><br>
        <br>
        <div class="gmail_quote">On 26 July 2013 17:42, Matthew Knepley
          <span dir="ltr"><<a moz-do-not-send="true"
              href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span>
          wrote:<br>
          <blockquote class="gmail_quote" style="margin:0 0 0
            .8ex;border-left:1px #ccc solid;padding-left:1ex">
            <div dir="ltr">
              <div>
                <div class="h5">On Fri, Jul 26, 2013 at 10:13 AM,
                  Bishesh Khanal <span dir="ltr"><<a
                      moz-do-not-send="true"
                      href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span>
                  wrote:<br>
                </div>
              </div>
              <div class="gmail_extra">
                <div class="gmail_quote">
                  <div>
                    <div class="h5">
                      <blockquote class="gmail_quote" style="margin:0px
                        0px 0px
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                        <div dir="ltr"><br>
                          <div class="gmail_extra"><br>
                            <br>
                            <div class="gmail_quote">
                              On Fri, Jul 26, 2013 at 4:22 PM, Matthew
                              Knepley <span dir="ltr"><<a
                                  moz-do-not-send="true"
                                  href="mailto:knepley@gmail.com"
                                  target="_blank">knepley@gmail.com</a>></span>
                              wrote:<br>
                              <blockquote class="gmail_quote"
                                style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                <div dir="ltr">
                                  <div>
                                    <div>On Fri, Jul 26, 2013 at 9:11
                                      AM, Bishesh Khanal <span
                                        dir="ltr"><<a
                                          moz-do-not-send="true"
                                          href="mailto:bisheshkh@gmail.com"
                                          target="_blank">bisheshkh@gmail.com</a>></span>
                                      wrote:<br>
                                    </div>
                                  </div>
                                  <div class="gmail_extra">
                                    <div class="gmail_quote">
                                      <div>
                                        <div>
                                          <blockquote
                                            class="gmail_quote"
                                            style="margin:0px 0px 0px
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                                            <div dir="ltr"><br>
                                              <div class="gmail_extra"><br>
                                                <br>
                                                <div class="gmail_quote">
                                                  On Fri, Jul 26, 2013
                                                  at 2:32 PM, Matthew
                                                  Knepley <span
                                                    dir="ltr"><<a
                                                      moz-do-not-send="true"
href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span>
                                                  wrote:<br>
                                                  <blockquote
                                                    class="gmail_quote"
                                                    style="margin:0px
                                                    0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                                    <div dir="ltr">
                                                      <div>On Fri, Jul
                                                        26, 2013 at 7:28
                                                        AM, Bishesh
                                                        Khanal <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>></span>
                                                        wrote:<br>
                                                      </div>
                                                      <div
                                                        class="gmail_extra">
                                                        <div
                                                          class="gmail_quote">
                                                          <div>
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                                                          class="gmail_quote"
                                                          style="margin:0px
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                                                          <div dir="ltr"><br>
                                                          <div
                                                          class="gmail_extra"><br>
                                                          <br>
                                                          <div
                                                          class="gmail_quote">
                                                          On Wed, Jul
                                                          17, 2013 at
                                                          9:48 PM, Jed
                                                          Brown <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:jedbrown@mcs.anl.gov"
                                                          target="_blank">jedbrown@mcs.anl.gov</a>></span>
                                                          wrote:<br>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:0px
                                                          0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                                          <div>Bishesh
                                                          Khanal <<a
moz-do-not-send="true" href="mailto:bisheshkh@gmail.com" target="_blank">bisheshkh@gmail.com</a>>
                                                          writes:<br>
                                                          <br>
                                                          > Now, I
                                                          implemented
                                                          two different
                                                          approaches,
                                                          each for both
                                                          2D and 3D, in<br>
                                                          > MATLAB.
                                                          It works for
                                                          the smaller
                                                          sizes but I
                                                          have problems
                                                          solving it for<br>
                                                          > the
                                                          problem size I
                                                          need (250^3
                                                          grid size).<br>
                                                          > I use
                                                          staggered grid
                                                          with p on cell
                                                          centers, and
                                                          components of
                                                          v on cell<br>
                                                          > faces.
                                                          Similar split
                                                          up of K to
                                                          cell center
                                                          and faces to
                                                          account for
                                                          the<br>
                                                          > variable
                                                          viscosity
                                                          case)<br>
                                                          <br>
                                                          </div>
                                                          Okay, you're
                                                          using a
                                                          staggered-grid
                                                          finite
                                                          difference
                                                          discretization
                                                          of<br>
                                                          variable-viscosity
                                                          Stokes.  This
                                                          is a common
                                                          problem and I
                                                          recommend<br>
                                                          starting with
                                                          PCFieldSplit
                                                          with Schur
                                                          complement
                                                          reduction
                                                          (make that<br>
                                                          work first,
                                                          then switch to
                                                          block
                                                          preconditioner).
                                                           </blockquote>
                                                          <div><br>
                                                          </div>
                                                          <div>Ok, I
                                                          made my 3D
                                                          problem work
                                                          with
                                                          PCFieldSplit
                                                          with Schur
                                                          complement
                                                          reduction
                                                          using the
                                                          options:<br>
                                                          -pc_fieldsplit_type
                                                          schur
                                                          -pc_fieldsplit_detect_saddle_point
-fieldsplit_1_ksp_constant_null_space<br>
                                                          </div>
                                                          <div> <br>
                                                          <br>
                                                          </div>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:0px
                                                          0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">You
                                                          can use PCLSC
                                                          or<br>
                                                          (probably
                                                          better for
                                                          you), assemble
                                                          a
                                                          preconditioning
                                                          matrix
                                                          containing<br>
                                                          the inverse
                                                          viscosity in
                                                          the
                                                          pressure-pressure
                                                          block.  This
                                                          diagonal<br>
                                                          matrix is a
                                                          spectrally
                                                          equivalent (or
                                                          nearly so,
                                                          depending on<br>
                                                          discretization)
                                                          approximation
                                                          of the Schur
                                                          complement.
                                                           The velocity<br>
                                                          block can be
                                                          solved with
                                                          algebraic
                                                          multigrid.
                                                           Read the
                                                          PCFieldSplit<br>
                                                          docs (follow
                                                          papers as
                                                          appropriate)
                                                          and let us
                                                          know if you
                                                          get stuck.<br>
                                                          </blockquote>
                                                          </div>
                                                          <br>
                                                          </div>
                                                          <div
                                                          class="gmail_extra">Now, 
                                                          I got a little
                                                          confused in
                                                          how exactly to
                                                          use command
                                                          line options
                                                          to use
                                                          multigrid for
                                                          the velocity
                                                          bock and PCLS
                                                          for the
                                                          pressure
                                                          block. After
                                                          going through
                                                          the manual I
                                                          tried the
                                                          following:<br>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          <div> </div>
                                                          </div>
                                                          <div>You want
                                                          Algebraic
                                                          Multigrid</div>
                                                          <div><br>
                                                          </div>
                                                          <div>-pc_type
                                                          fieldsplit
                                                          -pc_fieldsplit_detect_saddle_point</div>
                                                          <div>-pc_fieldsplit_type
                                                          schur</div>
                                                          <div> 
                                                          -fieldsplit_0_pc_type
                                                          gamg</div>
                                                          <div>
                                                          <div> 
                                                          -fieldsplit_1_ksp_type
                                                          fgmres</div>
                                                          <div> 
                                                           -fieldsplit_1_ksp_constant_null_space</div>
                                                          <div> 
                                                           -fieldsplit_1_ksp_monitor_short</div>
                                                          <div> 
                                                           -fieldsplit_1_pc_type
                                                          lsc</div>
                                                          <div>-ksp_converged_reason<br>
                                                          </div>
                                                          <div><br>
                                                          </div>
                                                          </div>
                                                        </div>
                                                      </div>
                                                    </div>
                                                  </blockquote>
                                                  <div>I tried the above
                                                    set of options but
                                                    the solution I get
                                                    seem to be not
                                                    correct. The
                                                    velocity field I get
                                                    are quite different
                                                    than the one I got
                                                    before without using
                                                    gamg which were the
                                                    expected one.<br>
                                                    Note: (Also, I had
                                                    to add one extra
                                                    option of
                                                    -fieldsplit_1_ksp_gmres_restart
                                                    100 , because the
                                                    fieldsplit_1_ksp
                                                    residual norm did
                                                    not converge within
                                                    default 30
                                                    iterations before
                                                    restarting).</div>
                                                </div>
                                              </div>
                                            </div>
                                          </blockquote>
                                          <div><br>
                                          </div>
                                        </div>
                                      </div>
                                      <div>These are all iterative
                                        solvers. You have to make sure
                                        everything converges. </div>
                                    </div>
                                  </div>
                                </div>
                              </blockquote>
                              <div><br>
                              </div>
                              <div>When I set restart to 100, and do
                                -ksp_monitor, it does converge (for the
                                fieldsplit_1_ksp). Are you saying that
                                in spite of having -ksp_converged_reason
                                in the option and petsc completing the
                                run with the message "Linear solve
                                converged due to CONVERGED_RTOL .." not
                                enough to make sure that everything is
                                converging ? If that is the case what
                                should I do for this particular problem
                                ?<br>
                              </div>
                            </div>
                          </div>
                        </div>
                      </blockquote>
                      <div><br>
                      </div>
                    </div>
                  </div>
                  <div>If your outer iteration converges, and you do not
                    like the solution, there are usually two
                    possibilities:</div>
                  <div><br>
                  </div>
                  <div>  1) Your tolerance is too high, start with it
                    cranked down all the way (1e-10) and slowly relax it</div>
                  <div><br>
                  </div>
                  <div>  2) You have a null space that you are not
                    accounting for</div>
                  <div class="im">
                    <div><br>
                    </div>
                    <blockquote class="gmail_quote" style="margin:0px
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                        <div class="gmail_extra">
                          <div class="gmail_quote">
                            <div>I have used the MAC scheme with
                              indexing as shown in:  fig 7.5, page 96
                              of: <a moz-do-not-send="true"
href="http://books.google.co.uk/books?id=W83gxp165SkC&printsec=frontcover&dq=Introduction+to+Numerical+Geodynamic+Modelling&hl=en&sa=X&ei=v6TmUaP_L4PuOs3agJgE&ved=0CDIQ6AEwAA"
                                target="_blank">http://books.google.co.uk/books?id=W83gxp165SkC&printsec=frontcover&dq=Introduction+to+Numerical+Geodynamic+Modelling&hl=en&sa=X&ei=v6TmUaP_L4PuOs3agJgE&ved=0CDIQ6AEwAA</a><br>
                              <br>
                              Thus I have a DM with 4 dof but there are
                              several "ghost values" set to 0.<br>
                            </div>
                            <div>Would this cause any problem when using
                              the multigrid ? (This has worked fine when
                              not using the multigrid.)</div>
                          </div>
                        </div>
                      </div>
                    </blockquote>
                    <div><br>
                    </div>
                  </div>
                  <div>I don't know exactly how you have implemented
                    this. These should be rows of the identity.</div>
                  <div class="im">
                    <div> </div>
                    <blockquote class="gmail_quote" style="margin:0px
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                      <div dir="ltr">
                        <div class="gmail_extra">
                          <div class="gmail_quote">
                            <blockquote class="gmail_quote"
                              style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
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                                <div class="gmail_extra">
                                  <div class="gmail_quote">
                                    <div>I do this problem in the
                                      tutorial with</div>
                                    <div>a constant viscosity.</div>
                                  </div>
                                </div>
                              </div>
                            </blockquote>
                            <div><br>
                            </div>
                            <div>Which tutorial are you referring to ?
                              Could you please provide me the link
                              please ? </div>
                          </div>
                        </div>
                      </div>
                    </blockquote>
                    <div><br>
                    </div>
                  </div>
                  <div>
                    There are a few on the PETSc Tutorials page, but you
                    can look at this</div>
                  <div><br>
                  </div>
                  <div>  <a moz-do-not-send="true"
href="http://www.geodynamics.org/cig/community/workinggroups/short/workshops/cdm2013/presentations/SessionIV_Solvers.pdf"
                      target="_blank">http://www.geodynamics.org/cig/community/workinggroups/short/workshops/cdm2013/presentations/SessionIV_Solvers.pdf</a></div>
                  <div><br>
                  </div>
                  <div>for a step-by-step example of a saddle-point
                    problem at the end.</div>
                  <div><br>
                  </div>
                  <div>    Matt</div>
                  <div>
                    <div class="h5">
                      <div> </div>
                      <blockquote class="gmail_quote" style="margin:0px
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                        <div dir="ltr">
                          <div class="gmail_extra">
                            <div class="gmail_quote"><br>
                              <blockquote class="gmail_quote"
                                style="margin:0px 0px 0px
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                                  <div class="gmail_extra">
                                    <div class="gmail_quote">
                                      <div><br>
                                      </div>
                                      <div>    Matt</div>
                                      <div>
                                        <div>
                                          <div> </div>
                                          <blockquote
                                            class="gmail_quote"
                                            style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                            <div dir="ltr">
                                              <div class="gmail_extra">
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                                                  <blockquote
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                                                    style="margin:0px
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0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                                    <div dir="ltr">
                                                      <div
                                                        class="gmail_extra">
                                                        <div
                                                          class="gmail_quote">
                                                          <div>
                                                          <div>
                                                          </div>
                                                          </div>
                                                          <div>   Matt</div>
                                                          <div>
                                                          <div>
                                                          <div><br>
                                                          </div>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:0px
                                                          0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                                          <div dir="ltr">
                                                          <div
                                                          class="gmail_extra">
                                                          <br>
                                                          </div>
                                                          <div
                                                          class="gmail_extra">but
                                                          I get the
                                                          following
                                                          errror:<br>
                                                          <br>
                                                          [0]PETSC
                                                          ERROR:
                                                          ---------------------
                                                          Error Message
------------------------------------<br>
                                                          [0]PETSC
                                                          ERROR: Null
                                                          argument, when
                                                          expecting
                                                          valid pointer!<br>
                                                          [0]PETSC
                                                          ERROR: Null
                                                          Object:
                                                          Parameter # 2!<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          ------------------------------------------------------------------------<br>
                                                          [0]PETSC
                                                          ERROR: Petsc
                                                          Release
                                                          Version 3.4.2,
                                                          Jul, 02, 2013
                                                          <br>
                                                          [0]PETSC
                                                          ERROR: See
                                                          docs/changes/index.html
                                                          for recent
                                                          updates.<br>
                                                          [0]PETSC
                                                          ERROR: See
                                                          docs/faq.html
                                                          for hints
                                                          about trouble
                                                          shooting.<br>
                                                          [0]PETSC
                                                          ERROR: See
                                                          docs/index.html
                                                          for manual
                                                          pages.<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          ------------------------------------------------------------------------<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          src/AdLemMain
                                                          on a
                                                          arch-linux2-cxx-debug
                                                          named edwards
                                                          by bkhanal Fri
                                                          Jul 26
                                                          14:23:40 2013<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          Libraries
                                                          linked from
                                                          /home/bkhanal/Documents/softwares/petsc-3.4.2/arch-linux2-cxx-debug/lib<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          Configure run
                                                          at Fri Jul 19
                                                          14:25:01 2013<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          Configure
                                                          options
                                                          --with-cc=gcc
                                                          --with-fc=g77
                                                          --with-cxx=g++
                                                          --download-f-blas-lapack=1
                                                          --download-mpich=1
                                                          -with-clanguage=cxx
--download-hypre=1<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          ------------------------------------------------------------------------<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          MatPtAP() line
                                                          8166 in
                                                          /home/bkhanal/Documents/softwares/petsc-3.4.2/src/mat/interface/matrix.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          PCSetUp_MG()
                                                          line 628 in
                                                          /home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/mg/mg.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          PCSetUp() line
                                                          890 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSPSetUp()
                                                          line 278 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSPSolve()
                                                          line 399 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          PCApply_FieldSplit_Schur()
                                                          line 807 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/impls/fieldsplit/fieldsplit.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          PCApply() line
                                                          442 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/pc/interface/precon.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSP_PCApply()
                                                          line 227 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/include/petsc-private/kspimpl.h<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSPInitialResidual()
                                                          line 64 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itres.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSPSolve_GMRES()
                                                          line 239 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/impls/gmres/gmres.c<br>
                                                          [0]PETSC
                                                          ERROR:
                                                          KSPSolve()
                                                          line 441 in
/home/bkhanal/Documents/softwares/petsc-3.4.2/src/ksp/ksp/interface/itfunc.c<br>
                                                          <br>
                                                          </div>
                                                          <div
                                                          class="gmail_extra"><br>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          </div>
                                                          </div>
                                                        </div>
                                                        <br>
                                                        <br clear="all">
                                                        <span><font
                                                          color="#888888"><span><font
color="#888888">
                                                          <div>
                                                          <div><br>
                                                          </div>
                                                          -- <br>
                                                          What most
                                                          experimenters
                                                          take for
                                                          granted before
                                                          they begin
                                                          their
                                                          experiments is
                                                          infinitely
                                                          more
                                                          interesting
                                                          than any
                                                          results to
                                                          which their
                                                          experiments
                                                          lead.<br>
                                                          -- Norbert
                                                          Wiener
                                                          </div>
                                                          </font></span></font></span></div>
                                                    </div>
                                                    <span><font
                                                        color="#888888">
                                                      </font></span></blockquote>
                                                </div>
                                                <span><font
                                                    color="#888888"><br>
                                                  </font></span></div>
                                            </div>
                                            <span><font color="#888888">
                                              </font></span></blockquote>
                                        </div>
                                      </div>
                                    </div>
                                    <span><font color="#888888">
                                        <div>
                                          <div><br>
                                            <br clear="all">
                                            <div><br>
                                            </div>
                                            -- <br>
                                            What most experimenters take
                                            for granted before they
                                            begin their experiments is
                                            infinitely more interesting
                                            than any results to which
                                            their experiments lead.<br>
                                            -- Norbert Wiener
                                          </div>
                                        </div>
                                      </font></span></div>
                                </div>
                              </blockquote>
                            </div>
                            <br>
                          </div>
                        </div>
                      </blockquote>
                    </div>
                  </div>
                </div>
                <div>
                  <div class="h5"><br>
                    <br clear="all">
                    <div><br>
                    </div>
                    -- <br>
                    What most experimenters take for granted before they
                    begin their experiments is infinitely more
                    interesting than any results to which their
                    experiments lead.<br>
                    -- Norbert Wiener
                  </div>
                </div>
              </div>
            </div>
          </blockquote>
        </div>
        <br>
      </div>
    </blockquote>
    <br>
  </body>
</html>