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    <div class="moz-cite-prefix">Matt and Jed<br>
      <br>
      But it does appear to work well in practice (as in I get the
      correct solution). Based on what I have tried, LSC (with GAMG on
      00) is the only solver I am able to use on relatively large
      problems with non trivial geometries (e.g., see my original
      email). <br>
      <br>
      So why is that? <br>
      <br>
      I will experiment with your other suggestions.<br>
      <br>
      Thanks,<br>
      <br>
      Tabrez<br>
      <br>
      <br>
      On 10/28/2014 09:55 AM, Matthew Knepley wrote:<br>
    </div>
    <blockquote
cite="mid:CAMYG4GnmDOi1-r1SBSLi3N+Sy1QhEevMTxmFjTU6+RGkmFw2yQ@mail.gmail.com"
      type="cite">
      <div dir="ltr">
        <div class="gmail_extra">
          <div class="gmail_quote">On Tue, Oct 28, 2014 at 9:49 AM,
            Tabrez Ali <span dir="ltr"><<a moz-do-not-send="true"
                href="mailto:stali@geology.wisc.edu" target="_blank">stali@geology.wisc.edu</a>></span>
            wrote:<br>
            <blockquote class="gmail_quote" style="margin:0 0 0
              .8ex;border-left:1px #ccc solid;padding-left:1ex">
              <div bgcolor="#FFFFFF" text="#000000">
                <div>Matt<br>
                  <br>
                  The system is certainly not singular (checked using
                  -pc_type svd -pc_svd_monitor). It also gives the
                  correct solution (compared to the analytical solution
                  for a trivial problem).</div>
              </div>
            </blockquote>
            <div><br>
            </div>
            <div>Something is very wrong with the preconditioner then.
              Move back to full Schur complement with a tight tolerance</div>
            <div>on the solver for S. This should converge in 1 iterate
              with a good true residual. Perhaps there is something
              wrong</div>
            <div>with LSC for your system. It is not guaranteed to work
              for all saddle points.</div>
            <div><br>
            </div>
            <div>  Matt</div>
            <div> </div>
            <blockquote class="gmail_quote" style="margin:0 0 0
              .8ex;border-left:1px #ccc solid;padding-left:1ex">
              <div bgcolor="#FFFFFF" text="#000000">
                <div><span class="HOEnZb"><font color="#888888"><br>
                      Tabrez</font></span>
                  <div>
                    <div class="h5"><br>
                      <br>
                      On 10/28/2014 08:44 AM, Matthew Knepley wrote:<br>
                    </div>
                  </div>
                </div>
                <div>
                  <div class="h5">
                    <blockquote type="cite">
                      <div dir="ltr">
                        <div class="gmail_extra">
                          <div class="gmail_quote">On Tue, Oct 28, 2014
                            at 8:00 AM, Tabrez Ali <span dir="ltr"><<a
                                moz-do-not-send="true"
                                href="mailto:stali@geology.wisc.edu"
                                target="_blank">stali@geology.wisc.edu</a>></span>
                            wrote:<br>
                            <blockquote class="gmail_quote"
                              style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                              <div bgcolor="#FFFFFF" text="#000000">
                                <div>Matt<br>
                                  <br>
                                  With MUMPS it is indeed the same but
                                  not faster. E.g., see 1.txt and 2.txt<br>
                                </div>
                              </div>
                            </blockquote>
                            <div><br>
                            </div>
                            <div>There is a big problem here. This
                              system is never actually being solved.
                              Look at 1.txt:</div>
                            <div><br>
                            </div>
                            <div><span> 0 KSP preconditioned resid norm
                                9.320055451716e+05 true resid norm
                                1.755998647494e+02 ||r(i)||/||b||
                                1.000000000000e+00 </span></div>
                            <div><span>380 KSP preconditioned resid norm
                                9.034871458425e-05 true resid norm
                                3.118451181896e+09 ||r(i)||/||b||
                                1.775884728811e+07 </span></div>
                            <div><br>
                            </div>
                            <div>The preconditioned residual did drop 10
                              order of magnitude, but the true residual
                              (b - Ax) is still very very large.</div>
                            <div>This looks like the system is singular
                              and the preconditioner is masking this.
                              This needs to be figured out first.</div>
                            <div>I would go back to a small serial
                              problem, and make sure it is actually
                              being solved.</div>
                            <div><br>
                            </div>
                            <div>   Matt</div>
                            <div> </div>
                            <blockquote class="gmail_quote"
                              style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                              <div bgcolor="#FFFFFF" text="#000000">
                                <div> With GAMG, cg takes forever (see
                                  4.txt). For reference GAMG with
                                  preonly is attached again (3.txt)<br>
                                  <br>
                                  All logs include
                                  -fieldsplit_0_ksp_monitor.<br>
                                  <br>
                                  Also, the true residual shows small
                                  oscillations. Is that normal?<br>
                                  <br>
                                  Tabrez<br>
                                  <br>
                                  <br>
                                  On 10/28/2014 07:08 AM, Matthew
                                  Knepley wrote:<br>
                                </div>
                                <blockquote type="cite">
                                  <div dir="ltr">
                                    <div class="gmail_extra">
                                      <div class="gmail_quote">On Tue,
                                        Oct 28, 2014 at 5:39 AM, Tabrez
                                        Ali <span dir="ltr"><<a
                                            moz-do-not-send="true"
                                            href="mailto:stali@geology.wisc.edu"
                                            target="_blank">stali@geology.wisc.edu</a>></span>
                                        wrote:<br>
                                        <blockquote class="gmail_quote"
                                          style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                                          <div bgcolor="#FFFFFF"
                                            text="#000000">
                                            <div>Mark<br>
                                              <br>
                                              When I replace
                                              "-fieldsplit_0_ksp_type
                                              preonly" with
                                              "-fieldsplit_0_ksp_type
                                              cg" then it becomes very
                                              slow (had to kill it).<br>
                                            </div>
                                          </div>
                                        </blockquote>
                                        <div><br>
                                        </div>
                                        <div>That means something in the
                                          setup is wrong. It should be
                                          about the same or faster. Run
                                          with -fieldsplit_0_ksp_monitor</div>
                                        <div>so we can see what is
                                          happening.</div>
                                        <div><br>
                                        </div>
                                        <div>   Matt</div>
                                        <div> </div>
                                        <blockquote class="gmail_quote"
                                          style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                                          <div bgcolor="#FFFFFF"
                                            text="#000000">
                                            <div> With MUMPS , i.e.,
                                              with
                                              '-fieldsplit_0_pc_type lu
                                              -fieldsplit_0_pc_factor_mat_solver_package

                                              mumps
                                              -fieldsplit_0_ksp_type
                                              preonly' it works fine but
                                              takes more time, and will
                                              be an issue for larger
                                              problems. The output for
                                              this run is attached.<br>
                                              <br>
                                              I will work on passing
                                              rigid body modes (as Matt
                                              mentioned) but short of
                                              that what is the best set
                                              of options for solving the
                                              following problem (i.e.,
                                              linear elasticity with
                                              constraints):<br>
                                              <br>
                                              <tt>|K cG'| | u | = |F|</tt><tt><br>
                                              </tt><tt>|G  0 | |l/c|  
                                                |d|</tt><br>
                                              <br>
                                              where c is a scaling
                                              factor (so that cG' terms
                                              are more or less of the
                                              same order as K)? The
                                              constraints are used to
                                              impose slip between
                                              surfaces and so on.<br>
                                              <br>
                                              Tabrez<br>
                                              <br>
                                              On 10/27/2014 01:17 PM,
                                              Mark Adams wrote:<br>
                                            </div>
                                            <blockquote type="cite">
                                              <div dir="ltr">The null
                                                space for GAMG is not
                                                critical but useful for
                                                elasticity.  If you in
                                                fact have an indefinite
                                                operator (eg, not
                                                "pinned)  the you need
                                                to use an iterative
                                                coarse grid solver.  You
                                                are
                                                using '-fieldsplit_0_pc_type
                                                gamg
                                                -fieldsplit_0_ksp_type
                                                preonly'.  And you have
                                                a hard elasticity
                                                problem.  You are going
                                                to want to start with a
                                                stronger solver. Use cg
                                                instead of preonly.  As
                                                Matt said start with
                                                MUMPS, then go to
                                                CG/GAMG, then you can
                                                see how far you can cut
                                                the _0_ solver down.
                                                <div>Mark</div>
                                              </div>
                                              <div class="gmail_extra"><br>
                                                <div class="gmail_quote">On
                                                  Thu, Oct 23, 2014 at
                                                  11:51 AM, 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-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                                                    <div dir="ltr">
                                                      <div
                                                        class="gmail_extra">
                                                        <div
                                                          class="gmail_quote"><span>On

                                                          Thu, Oct 23,
                                                          2014 at 10:48
                                                          AM, Tabrez Ali
                                                          <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:stali@geology.wisc.edu"
                                                          target="_blank">stali@geology.wisc.edu</a>></span>
                                                          wrote:<br>
                                                          <blockquote
                                                          class="gmail_quote"
                                                          style="margin:0px
                                                          0px 0px
0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                                                          <div
                                                          text="#000000"
bgcolor="#ffffff"> Matt<br>
                                                          <br>
                                                          On 10/23/2014
                                                          09:54 AM,
                                                          Matthew
                                                          Knepley wrote:
                                                          <blockquote
                                                          type="cite">
                                                          <div dir="ltr">
                                                          <div
                                                          class="gmail_extra">
                                                          <div
                                                          class="gmail_quote">On


                                                          Thu, Oct 23,
                                                          2014 at 9:27
                                                          AM, Tabrez Ali
                                                          <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:stali@geology.wisc.edu"
                                                          target="_blank">stali@geology.wisc.edu</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
                                                          bgcolor="#FFFFFF"
                                                          text="#000000">
                                                          <div>Matt<br>
                                                          <br>
                                                          Sorry about
                                                          that (I always
                                                          forget it).
                                                          The output for
                                                          the smallest
                                                          problem is now
                                                          attached (see
                                                          log.txt). I am
                                                          also attaching
                                                          some results
                                                          that compare
                                                          results
                                                          obtained using
                                                          FS/LSC and the
                                                          direct solver
                                                          (MUMPS), again
                                                          for the
                                                          smallest
                                                          problem. The
                                                          difference, as
                                                          you can see is
                                                          insignificant
                                                          O(1E-6).<br>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          <div><br>
                                                          </div>
                                                          <div>1) How do
                                                          you use MUMPS
                                                          if you have a
                                                          saddle point</div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          I simply used
                                                          -pc_type lu
                                                          -pc_factor_mat_solver_package
                                                          mumps.<br>
                                                          <br>
                                                          <blockquote
                                                          type="cite">
                                                          <div dir="ltr">
                                                          <div
                                                          class="gmail_extra">
                                                          <div
                                                          class="gmail_quote">
                                                          <div><br>
                                                          </div>
                                                          <div>2) You
                                                          can see from
                                                          the output
                                                          that something
                                                          is seriously
                                                          wrong with the
                                                          preconditioner.

                                                          It looks like
                                                          it has a null
                                                          space.</div>
                                                          <div>    Did
                                                          you add the
                                                          elastic null
                                                          modes to GAMG?
                                                          Without this,
                                                          it is not
                                                          going to work.
                                                          We have helper
                                                          functions for
                                                          this:</div>
                                                          <div><br>
                                                          </div>
                                                          <div>  <a
                                                          moz-do-not-send="true"
href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMPlexCreateRigidBody.html"
target="_blank">http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/DM/DMPlexCreateRigidBody.html</a></div>
                                                          <div><br>
                                                          </div>
                                                          <div>you could
                                                          just copy that
                                                          code. And then
                                                          use</div>
                                                          <div><br>
                                                          </div>
                                                          <div>  <a
                                                          moz-do-not-send="true"
href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetNearNullSpace.html"
target="_blank">http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetNearNullSpace.html</a></div>
                                                          <div><br>
                                                          </div>
                                                          <div>I don't
                                                          see it in the
                                                          output, so I
                                                          think this is
                                                          your problem.</div>
                                                          <div><br>
                                                          </div>
                                                          <div>In order
                                                          to test, I
                                                          would first
                                                          use MUMPS as
                                                          the A00 solver
                                                          and get the
                                                          Schur stuff
                                                          worked out.
                                                          Then I would</div>
                                                          <div>replace
                                                          MUMPS with
                                                          GAMG and tune
                                                          it until I get
                                                          back my
                                                          original
                                                          convergence.</div>
                                                          </div>
                                                          </div>
                                                          </div>
                                                          </blockquote>
                                                          I will try
                                                          this with
                                                          MatNullSpaceCreateRigidBody.
                                                          Btw does it
                                                          matter if some
                                                          nodes are
                                                          pinned?<br>
                                                          </div>
                                                          </blockquote>
                                                          <div><br>
                                                          </div>
                                                          </span>
                                                          <div>No these
                                                          are null modes
                                                          of the
                                                          operator, not
                                                          of the
                                                          particular
                                                          problem.</div>
                                                          <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-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
                                                          <div
                                                          text="#000000"
bgcolor="#ffffff"> Tabrez<br>
                                                          <br>
                                                          <blockquote
                                                          type="cite">
                                                          <div dir="ltr">
                                                          <div
                                                          class="gmail_extra">
                                                          <div
                                                          class="gmail_quote">
                                                          <div><br>
                                                          </div>
                                                          <div>  Thanks,</div>
                                                          <div><br>
                                                          </div>
                                                          <div>    Matt</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
                                                          bgcolor="#FFFFFF"
                                                          text="#000000">
                                                          <div> Also, I
                                                          did pass
                                                          'upper' and
                                                          'full' to
                                                          '-pc_fieldsplit_schur_factorization_type'
                                                          but the
                                                          iteration
                                                          count doesn't
                                                          improve (in
                                                          fact, it
                                                          increases
                                                          slightly). The
                                                          attached log
                                                          is with
                                                          'upper'.<br>
                                                          <br>
                                                          Regards,<br>
                                                          <br>
                                                          Tabrez<br>
                                                          <br>
                                                          On 10/23/2014
                                                          07:46 AM,
                                                          Matthew
                                                          Knepley wrote:<br>
                                                          </div>
                                                          <blockquote
                                                          type="cite">
                                                          <div dir="ltr">
                                                          <div
                                                          class="gmail_extra">
                                                          <div
                                                          class="gmail_quote">On



                                                          Thu, Oct 23,
                                                          2014 at 7:20
                                                          AM, Tabrez Ali
                                                          <span
                                                          dir="ltr"><<a
moz-do-not-send="true" href="mailto:stali@geology.wisc.edu"
                                                          target="_blank">stali@geology.wisc.edu</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
                                                          bgcolor="#FFFFFF"
                                                          text="#000000">
                                                          Hello<br>
                                                          <br>
                                                          I am using the
                                                          following
                                                          options
                                                          (below) for
                                                          solving linear
                                                          elasticity/poroelasticity



                                                          problems
                                                          involving slip
                                                          between two
                                                          surfaces
                                                          involving
                                                          non-trivial
                                                          geometries,
                                                          i.e., elements
                                                          with high
                                                          aspect ratios,
                                                          large
                                                          contrasts in
                                                          material
                                                          properties
                                                          etc. The
                                                          constraints
                                                          are imposed
                                                          using Lagrange
                                                          Multipliers. <br>
                                                          <br>
                                                          A picture
                                                          (shows
                                                          displacement
                                                          magnitude) is
                                                          attached. The
                                                          boundary
                                                          nodes, i.e.,
                                                          the base and
                                                          the four side
                                                          are pinned.<br>
                                                          <br>
                                                          The following
                                                          options appear
                                                          to work well
                                                          for the saddle
                                                          point problem:<br>
                                                          <br>
                                                          <tt>-pc_type
                                                          fieldsplit
                                                          -pc_fieldsplit_type
                                                          schur
                                                          -pc_fieldsplit_detect_saddle_point
                                                          -fieldsplit_0_pc_type



                                                          gamg
                                                          -fieldsplit_0_ksp_type
                                                          preonly
                                                          -fieldsplit_1_pc_type
                                                          lsc
                                                          -fieldsplit_1_ksp_type
                                                          preonly
                                                          -pc_fieldsplit_schur_fact_type
                                                          lower
                                                          -ksp_monitor</tt><br>
                                                          <br>
                                                          However, the
                                                          number of
                                                          iterations
                                                          keep on
                                                          increasing
                                                          with the
                                                          problems size
                                                          (see attached
                                                          plot), e.g.,<br>
                                                          <br>
                                                          <tt>120K
                                                          Tets        <b>507</b>
                                                          Iterations
                                                          (KSP Residual
                                                          norm
                                                          8.827362494659e-05)</tt><tt>
                                                          in  17 secs on
                                                            3 cores<br>
                                                          </tt><tt>1
                                                          Million Tets 
                                                          <b>1374</b>
                                                          Iterations
                                                          (KSP Residual
                                                          norm
                                                          7.164704416296e-05)</tt><tt>
                                                          in 117 secs
                                                          on  20 cores<br>
                                                          </tt><tt>8
                                                          Million Tets 
                                                          <b>2495</b>
                                                          Iterations
                                                          (KSP Residual
                                                          norm
                                                          9.101247550026e-05)
                                                          in 225 secs on
                                                          160 cores</tt><br>
                                                          <br>
                                                          So what other
                                                          options should
                                                          I try to
                                                          improve solver
                                                          performance?
                                                          Any
                                                          tips/insights
                                                          would be
                                                          appreciated as
                                                          preconditioning


                                                          is black magic
                                                          to me.<br>
                                                          </div>
                                                          </blockquote>
                                                          <div><br>
                                                          </div>
                                                          <div>For
                                                          reports,
                                                          always run
                                                          with </div>
                                                          <div><br>
                                                          </div>
                                                          <div> 
                                                          -ksp_view
                                                          -ksp_monitor_true_residual
-ksp_converged_reason</div>
                                                          <div><br>
                                                          </div>
                                                          <div>so that
                                                          we can see
                                                          exactly what
                                                          you used.</div>
                                                          <div><br>
                                                          </div>
                                                          <div>I believe
                                                          the default is
                                                          a diagonal
                                                          factorization.
                                                          Since your
                                                          outer iterates
                                                          are
                                                          increasing, I
                                                          would
                                                          strengthen
                                                          this</div>
                                                          <div>to either
                                                          upper or full</div>
                                                          <div><br>
                                                          </div>
                                                          <div> 
                                                          -pc_fieldsplit_schur_factorization_type
                                                          <upper,
                                                          full></div>
                                                          <div><br>
                                                          </div>
                                                          <div>  Thanks,</div>
                                                          <div><br>
                                                          </div>
                                                          <div>     
                                                          Matt </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
                                                          bgcolor="#FFFFFF"
                                                          text="#000000">
                                                          Thanks in
                                                          advance.<span><font
color="#888888"><br>
                                                          <br>
                                                          Tabrez<br>
                                                          </font></span></div>
                                                          </blockquote>
                                                          </div>
                                                          <br>
                                                          <br
                                                          clear="all">
                                                          <span><font
                                                          color="#888888">
                                                          <span><font
                                                          color="#888888">
                                                          <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 </font></span></font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></blockquote>
                                                          <span><font
                                                          color="#888888">
                                                          <br>
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></blockquote>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          <br>
                                                          <br
                                                          clear="all">
                                                          <span><font
                                                          color="#888888">
                                                          <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</font></span></font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></blockquote>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></blockquote>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                        <span><font
                                                          color="#888888">
                                                          <div>
                                                          <div><br>
                                                          <br
                                                          clear="all">
                                                          <span><font
                                                          color="#888888">
                                                          <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 </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></div>
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></font></span></div>
                                                      <span><font
                                                          color="#888888">
                                                          <span><font
                                                          color="#888888">
                                                          </font></span></font></span></div>
                                                    <span><font
                                                        color="#888888">
                                                        <span><font
                                                          color="#888888">
                                                          </font></span></font></span></blockquote>
                                                  <span><font
                                                      color="#888888"> <span><font
color="#888888"> </font></span></font></span></div>
                                                <span><font
                                                    color="#888888"> <span><font
                                                        color="#888888">
                                                        <br>
                                                      </font></span></font></span></div>
                                              <span><font
                                                  color="#888888"> </font></span></blockquote>
                                            <span><font color="#888888">
                                                <br>
                                              </font></span></div>
                                          <span><font color="#888888"> </font></span></blockquote>
                                        <span><font color="#888888"> </font></span></div>
                                      <span><font color="#888888"> <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 </font></span></div>
                                  </div>
                                </blockquote>
                                <br>
                              </div>
                            </blockquote>
                          </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>
                    </blockquote>
                    <br>
                  </div>
                </div>
              </div>
            </blockquote>
          </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>
    </blockquote>
    <br>
  </body>
</html>