<table cellspacing="0" cellpadding="0" border="0" ><tr><td valign="top" style="font: inherit;"><DIV>Hi Charles</DIV>
<DIV>&nbsp;</DIV>
<DIV>Max. is around 12. I guess it has to be close to 1 or 2. Is that the only reason for nonconvergence of&nbsp;the nonlinear solver? </DIV>
<DIV>&nbsp;</DIV>
<DIV>CUBIT&gt; quality volume all Condition No. global</DIV>
<DIV>&nbsp;Hex quality, 24360 elements:<BR>------------------------------------<BR>&nbsp;&nbsp; Function Name&nbsp;&nbsp;&nbsp; Average&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Dev&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Minimum&nbsp;&nbsp; (id)&nbsp;&nbsp;&nbsp; Maximum&nbsp; (id)<BR>&nbsp;-----------------&nbsp; ---------&nbsp;&nbsp;&nbsp; ---------&nbsp;&nbsp;&nbsp; --------------&nbsp;&nbsp;&nbsp; -------------<BR>&nbsp;&nbsp; Condition No.&nbsp;&nbsp;&nbsp; 1.118e+00&nbsp;&nbsp;&nbsp; 3.692e-01&nbsp;&nbsp;&nbsp; 1.000e+00 (2846)&nbsp;&nbsp;&nbsp; 1.231e+01 (24023)</DIV>
<DIV>&nbsp;</DIV>
<DIV>In that case, I have no option but to refine the mesh throughout which will give me a huge number of cells. Then I won't be able to run it on my machine, for sure.</DIV>
<DIV>&nbsp;</DIV>
<DIV></DIV>
<DIV>Can I use Pylith's refine mesh capability to help me here? Can it refine selectively in&nbsp;one material region?</DIV>
<DIV></DIV>
<DIV>&nbsp;</DIV>
<DIV>Thanks and regards</DIV>
<DIV>Birendra</DIV>
<DIV><BR>--- On <B>Mon, 11/26/12, Charles Williams <I>&lt;willic3@gmail.com&gt;</I></B> wrote:<BR></DIV>
<BLOCKQUOTE style="BORDER-LEFT: rgb(16,16,255) 2px solid; PADDING-LEFT: 5px; MARGIN-LEFT: 5px"><BR>From: Charles Williams &lt;willic3@gmail.com&gt;<BR>Subject: Re: [CIG-SHORT] Dynamic faulting under gravity<BR>To: "Birendra jha" &lt;bjha7333@yahoo.com&gt;<BR>Cc: cig-short@geodynamics.org<BR>Date: Monday, November 26, 2012, 3:32 AM<BR><BR>
<DIV id=yiv577914371>
<DIV>Hi Birendra,
<DIV><BR></DIV>
<DIV>What sort of maximum condition number values are you getting? &nbsp;There still appear to be some very flat cells in your mesh.</DIV>
<DIV><BR></DIV>
<DIV>Cheers,</DIV>
<DIV>Charles</DIV>
<DIV><BR></DIV>
<DIV><BR>
<DIV>
<DIV>On 25/11/2012, at 5:53 PM, Birendra jha wrote:</DIV><BR class=yiv577914371Apple-interchange-newline>
<BLOCKQUOTE type="cite">
<DIV>Hi all<BR><BR>I removed gravity (and initial stress), improved the aspect ratio of my grid (condition number is much better now), still the nonlinear solver is not converging (linear solver converges in &lt;50 iterations). SNES Function Norm decreases for first 2 iterations then increases (from 2.8E-02 to 3.08E-02 in 4 iterations).<BR><BR>I have the attached the 3 files necessary to run the problem.<BR><BR>Problem description: a slanted fault in a box domain. Dynamic fault. Static friction model with 0 cohesion.<BR>Boundary condition: roller boundary on -x, +y, -y. Dirichlet displacement on +x of -1 cm to apply compression on the fault.<BR><BR>Please help!<BR><BR>Thanks and regards<BR>Birendra<BR><BR>--- On Thu, 11/22/12, Brad Aagaard &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=baagaard@usgs.gov" rel=nofollow target=_blank ymailto="mailto:baagaard@usgs.gov">baagaard@usgs.gov</A>&gt; wrote:<BR><BR>
<BLOCKQUOTE type="cite">From: Brad Aagaard &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=baagaard@usgs.gov" rel=nofollow target=_blank ymailto="mailto:baagaard@usgs.gov">baagaard@usgs.gov</A>&gt;<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Subject: Re: Dynamic faulting under gravity<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">To: "Birendra jha" &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=bjha7333@yahoo.com" rel=nofollow target=_blank ymailto="mailto:bjha7333@yahoo.com">bjha7333@yahoo.com</A>&gt;<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Cc: <A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=cig-short@geodynamics.org" rel=nofollow target=_blank ymailto="mailto:cig-short@geodynamics.org">cig-short@geodynamics.org</A><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Date: Thursday, November 22, 2012, 3:18 AM<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Birendra,<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">You have very flat hex cells in your mesh. This results in a<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">very poorly <BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">conditioned system. I think this prevents getting a decent<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">guess for the <BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">slip, so the nonlinear solve fails to converge.<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">It looks like you are trying to resolve very small scale<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">geometric <BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">features with a coarse hexahedral mesh. I think you will<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">need a mesh <BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">with much closer to cube-like cells to get the nonlinear<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">solve to converge.<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Regards,<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">Brad<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">On 11/20/2012 11:32 AM, Birendra jha wrote:<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Hi,<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">With that, the linear solver converges but nonlinear<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">solver didn't converge in 100 iterations.<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">To improve the gravity modeling, I also modified the<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">boundary conditions such that now I have zero normal<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">displacement on +x,-x,+y,-y,-z faces except the fault nodes<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">on +y,-y,-z faces. With this setup, in absence of fault<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">model in pylith, the case runs fine with almost 0<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">displacement everywhere except on the fault nodes which are<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">free. This is as expected. But with fault friction, it does<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">not converge. The unconverged solution also shows large<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">displacements on the fault nodes, I am just not sure if the<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">numbers are accurate.<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">The modified files are attached.<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Thanks<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Birendra<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">--- On Tue, 11/20/12, Brad Aagaard &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=baagaard@usgs.gov" rel=nofollow target=_blank ymailto="mailto:baagaard@usgs.gov">baagaard@usgs.gov</A>&gt;<BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">wrote:<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">From: Brad Aagaard &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=baagaard@usgs.gov" rel=nofollow target=_blank ymailto="mailto:baagaard@usgs.gov">baagaard@usgs.gov</A>&gt;<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Subject: Re: Dynamic faulting under gravity<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">To: "Birendra jha" &lt;<A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=bjha7333@yahoo.com" rel=nofollow target=_blank ymailto="mailto:bjha7333@yahoo.com">bjha7333@yahoo.com</A>&gt;<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Cc: <A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=cig-short@geodynamics.org" rel=nofollow target=_blank ymailto="mailto:cig-short@geodynamics.org">cig-short@geodynamics.org</A><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Date: Tuesday, November 20, 2012, 10:28 PM<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Birendra,<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">The linear solve did not converge. If the linear<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">solves<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">within the<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">nonlinear solve doesn't converge, the nonlinear<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">solve won't<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">converge.<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">You are using ASM for the preconditioner. Try using<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">the<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">field split<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">preconditioner with ML on the elastic part and the<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">custom<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">fault<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">preconditioner. See examples/3d/tet4/step04 for<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">PETSc<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">settings.<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Brad<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">On 11/19/2012 09:36 PM, Birendra jha wrote:<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Dear all<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">I have a relatively simple case of a slanted<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">fault<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">plane (along y axis) inside a layered box. I am<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">using<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">FaultCohesiveDyn with static friction model (please<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">see the<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">attached file). +x, -x boundaries are fixed in x,y<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">directions and bottom is fixed in z direction. y<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">faces are<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">free.<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">I have gravity on and I use<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">initial_stress.spatialdb<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">with a density of 2400 kg/m3.<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">The nonlinear solver is not converging. Can you<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">please<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">help? What am I missing? There are four thin layers<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">in the<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">grid sandwiched between thick layers above and<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">below. Is<BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">that the problem?<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">I am using the Pylith 1.8.0 windows binary.<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Thanks and regards<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">Birendra<BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite">
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE></BLOCKQUOTE>
<BLOCKQUOTE type="cite"><BR></BLOCKQUOTE>
<BLOCKQUOTE type="cite"></BLOCKQUOTE><SPAN>&lt;faultedgrid3.zip&gt;</SPAN>_______________________________________________<BR>CIG-SHORT mailing list<BR><A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=CIG-SHORT@geodynamics.org" rel=nofollow target=_blank ymailto="mailto:CIG-SHORT@geodynamics.org">CIG-SHORT@geodynamics.org</A><BR>http://geodynamics.org/cgi-bin/mailman/listinfo/cig-short<BR></DIV></BLOCKQUOTE></DIV><BR>
<DIV><SPAN style="WIDOWS: 2; TEXT-TRANSFORM: none; TEXT-INDENT: 0px; LETTER-SPACING: normal; BORDER-COLLAPSE: separate; FONT: medium Helvetica; WHITE-SPACE: normal; ORPHANS: 2; COLOR: rgb(0,0,0); WORD-SPACING: 0px" class=yiv577914371Apple-style-span><SPAN style="WIDOWS: 2; TEXT-TRANSFORM: none; TEXT-INDENT: 0px; LETTER-SPACING: normal; BORDER-COLLAPSE: separate; FONT: 12px Helvetica; WHITE-SPACE: normal; ORPHANS: 2; COLOR: rgb(0,0,0); WORD-SPACING: 0px" class=yiv577914371Apple-style-span>
<DIV style="WORD-WRAP: break-word">
<DIV>
<DIV style="MARGIN: 0px"><FONT style="FONT: 12px Helvetica" size=3 face=Helvetica>Charles A. Williams</FONT></DIV>
<DIV style="MARGIN: 0px">Scientist<BR>GNS Science<BR>1 Fairway Drive, Avalon<BR>PO Box 30368<BR>Lower Hutt &nbsp;5040<BR>New Zealand<BR>ph (office): 0064-4570-4566<BR>fax (office): 0064-4570-4600</DIV>
<DIV style="MARGIN: 0px"><A href="http://us.mc1650.mail.yahoo.com/mc/compose?to=C.Williams@gns.cri.nz" rel=nofollow target=_blank ymailto="mailto:C.Williams@gns.cri.nz">C.Williams@gns.cri.nz</A></DIV></DIV></DIV></SPAN></SPAN></DIV><BR></DIV></DIV></DIV></BLOCKQUOTE></td></tr></table>