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<p style="margin-top:0;margin-bottom:0">I think I find the problem but I do not know how to solve it. I believe the problem is in line 112 of code which is the derivative of aYdot[i][j] in y-direction:<br>
</p>
<p style="margin-top:0;margin-bottom:0"><span> Pyt=(aYdot[j+1][i].p-aYdot[j-1][i].p)/(2.0*user->hy);</span></p>
<p style="margin-top:0;margin-bottom:0"><span></span><span>in here I used 2 processors and the error is exactly in the middle of the domain in y-direction where I believe
<span>aYdot[j-1][i].p</span> belongs to the other processor. <br>
</span></p>
<p style="margin-top:0;margin-bottom:0"><span><br>
</span></p>
<p style="margin-top:0;margin-bottom:0"><span>It is interesting that I have this problem because always when discretizing derivatives, points can belong to different processors and it does not normally cause any problem (at least I did not have such problem
when there were only spacial derivatives in <span>FormFunction calculations of <span>
DMDATSSetIFunctionLocal</span></span>. Can you please help me what I should do?<br>
</span></p>
<p style="margin-top:0;margin-bottom:0"><span>Sepideh<br>
</span><span></p>
<div><span><br>
</span></div>
</span><span></span><span></span><span></span><span></span><br>
<p></p>
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<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Sepideh Kavousi<br>
<b>Sent:</b> Monday, April 16, 2018 9:22:31 PM<br>
<b>To:</b> Matthew Knepley<br>
<b>Cc:</b> petsc-users@mcs.anl.gov<br>
<b>Subject:</b> Re: [petsc-users] error running parallel on cluster</font>
<div> </div>
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<p style="margin-top:0; margin-bottom:0">I run with valgrind with the following command:</p>
<p style="margin-top:0; margin-bottom:0"><span>/work/skavou1/petsc/debug/bin/mpiexec -np 2 valgrind --tool=memcheck -q --num-callers=20 --log-file=valgrind.log.%p ./one.out -malloc off -ts_monitor -snes_fd_color -ts_max_snes_failures -1 -ts_type beuler -pc_type
bjacobi -snes_linesearch_type nleqerr -snes_type newtontr -ksp_gmres_restart 31 -sub_pc_type ilu -snes_monitor -snes_converged_reason -ksp_monitor</span><br>
</p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0">the valgringoutput is as following:</p>
<p style="margin-top:0; margin-bottom:0"></p>
<div>==39396== Invalid read of size 8<br>
==39396== at 0x402679: FormFunction (one.c:212)<br>
==39396== by 0x611AA5F: TSComputeIFunction_DMDA (dmdats.c:79)<br>
==39396== by 0x61349BD: TSComputeIFunction (ts.c:830)<br>
==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649)<br>
==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569)<br>
==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203)<br>
==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105)<br>
==39396== by 0x60246C0: SNESSolve (snes.c:4312)<br>
==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176)<br>
==39396== by 0x6237CA8: TSStep_Theta (theta.c:216)<br>
==39396== by 0x6153380: TSStep (ts.c:3548)<br>
==39396== by 0x615559D: TSSolve (ts.c:3731)<br>
==39396== by 0x403C95: main (one.c:303)<br>
==39396== Address 0x83f5158 is 8 bytes before a block of size 7,200 alloc'd<br>
==39396== at 0x4A05588: memalign (vg_replace_malloc.c:727)<br>
==39396== by 0x4D87516: PetscMallocAlign (mal.c:42)<br>
==39396== by 0x4D88DE0: PetscMallocA (mal.c:397)<br>
==39396== by 0x50AB230: VecGetArray2d (rvector.c:2167)<br>
==39396== by 0x589437E: DMDAVecGetArray (dagetarray.c:73)<br>
==39396== by 0x611A8ED: TSComputeIFunction_DMDA (dmdats.c:74)<br>
==39396== by 0x61349BD: TSComputeIFunction (ts.c:830)<br>
==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649)<br>
==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569)<br>
==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203)<br>
==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105)<br>
==39396== by 0x60246C0: SNESSolve (snes.c:4312)<br>
==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176)<br>
==39396== by 0x6237CA8: TSStep_Theta (theta.c:216)<br>
==39396== by 0x6153380: TSStep (ts.c:3548)<br>
==39396== by 0x615559D: TSSolve (ts.c:3731)<br>
==39396== by 0x403C95: main (one.c:303)<br>
==39396== <br>
==39396== Invalid read of size 8<br>
==39396== at 0x402689: FormFunction (one.c:212)<br>
==39396== by 0x611AA5F: TSComputeIFunction_DMDA (dmdats.c:79)<br>
==39396== by 0x61349BD: TSComputeIFunction (ts.c:830)<br>
==39396== by 0x623DD1C: SNESTSFormFunction_Theta (theta.c:649)<br>
==39396== by 0x615E599: SNESTSFormFunction (ts.c:4569)<br>
==39396== by 0x600C84E: SNESComputeFunction (snes.c:2203)<br>
==39396== by 0x60A34B6: SNESSolve_NEWTONTR (tr.c:105)<br>
==39396== by 0x60246C0: SNESSolve (snes.c:4312)<br>
==39396== by 0x6237346: TSTheta_SNESSolve (theta.c:176)<br>
==39396== by 0x6237CA8: TSStep_Theta (theta.c:216)<br>
==39396== by 0x6153380: TSStep (ts.c:3548)<br>
==39396== by 0x615559D: TSSolve (ts.c:3731)<br>
==39396== by 0x403C95: main (one.c:303)<br>
==39396== Address 0x18 is not stack'd, malloc'd or (recently) free'd<br>
==39396== <br>
</div>
<p></p>
<p style="margin-top:0; margin-bottom:0">Thanks,</p>
<p style="margin-top:0; margin-bottom:0">Sepideh<br>
</p>
</div>
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Matthew Knepley <knepley@gmail.com><br>
<b>Sent:</b> Monday, April 16, 2018 8:44:43 PM<br>
<b>To:</b> Sepideh Kavousi<br>
<b>Cc:</b> petsc-users@mcs.anl.gov<br>
<b>Subject:</b> Re: [petsc-users] error running parallel on cluster</font>
<div> </div>
</div>
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<div class="x_x_gmail_extra">
<div class="x_x_gmail_quote">On Mon, Apr 16, 2018 at 9:39 PM, Sepideh Kavousi <span dir="ltr">
<<a href="mailto:skavou1@lsu.edu" target="_blank">skavou1@lsu.edu</a>></span> wrote:<br>
<blockquote class="x_x_gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
<div dir="ltr">
<div id="x_x_m_-1220196563703675155divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:#000000; font-family:Calibri,Helvetica,sans-serif">
<p style="margin-top:0; margin-bottom:0">this is not used forghost points . my code is :</p>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>1) You are using ghost points, since you use i-1 as an index</div>
<div><br>
</div>
<div>2) I was wrong. X_t should also be ghosted.</div>
<div><br>
</div>
<div>Run under valgrind.</div>
<div><br>
</div>
<div> Thanks,</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="x_x_gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
<div dir="ltr">
<div id="x_x_m_-1220196563703675155divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:#000000; font-family:Calibri,Helvetica,sans-serif">
<p style="margin-top:0; margin-bottom:0"></p>
<div> for (j=info2->ys;j<info2->ys+<wbr>info2->ym;j++){<br>
for (i=info2->xs;i<info2->xs+<wbr>info2->xm;i++){<br>
if (i==0) {aF[j][i].U=aY[j][i+1].U-aY[j]<wbr>[i].U ; aF[j][i].p=aY[j][i+1].p-aY[j][<wbr>i].p ;}<br>
else if (i==info2->mx-1) {aF[j][i].U=aY[j][i-1].U-aY[j]<wbr>[i].U ; aF[j][i].p=aY[j][i].p-aY[j][i-<wbr>1].p ;}<br>
else if (j==0) {aF[j][i].U=aY[j+1][i].U-aY[j]<wbr>[i].U; aF[j][i].p=aY[j+1][i].p-aY[j][<wbr>i].p ;}<br>
else if (j==info2->my-1) {aF[j][i].U=aY[j-1][i].U-aY[j]<wbr>[i].U ; aF[j][i].p=aY[j][i].p-aY[j-1][<wbr>i].p ;}<br>
else {<br>
//derivatives of U and p<br>
Px=(aY[j][i+1].p-aY[j][i-1].<wbr>p)/(2.0*user->hx);<br>
Py=(aY[j+1][i].p-aY[j-1][i].<wbr>p)/(2.0*user->hy);<br>
Pxx=((aY[j][i+1].p+aY[j][i-1]<wbr>.p-2.0*aY[j][i].p)/(hx2));<br>
Pxy=((aY[j+1][i+1].p+aY[j-1][<wbr>i-1].p-aY[j+1][i-1].p-aY[j-1][<wbr>i+1].p)/(4.0*hxy));<br>
Pyy=((aY[j+1][i].p+aY[j-1][i]<wbr>.p-2.0*aY[j][i].p)/hy2);<br>
Pxt=(aYdot[j][i+1].p-aYdot[j]<wbr>[i-1].p)/(2.0*user->hx);<br>
Pyt=(aYdot[j+1][i].p-aYdot[j-<wbr>1][i].p)/(2.0*user->hy);<br>
<br>
<br>
if (((Px*Px)+(Py*Py))>0.0 ) { //<br>
theta=PetscAtanReal(Py/Px);<br>
thetax=(Px*Pxy-Py*Pxx)/((Px*<wbr>Px)+(Py*Py));<br>
thetay=(Px*Pyy-Py*Pxy)/((Px*<wbr>Px)+(Py*Py));<br>
}<br>
else { <br>
theta=PETSC_PI*0.5;<br>
thetax=0.0;<br>
thetay=0.0;<br>
}<br>
e=(1.0+user->epsilon*cos(4.0*<wbr>theta));;<br>
ep=-(4.0*user->epsilon*sin(4.<wbr>0*theta));<br>
epp=-(4.0*user->epsilon*4.0*<wbr>cos(4.0*theta));<br>
<br>
<br>
<br>
Ux=(aY[j][i+1].U-aY[j][i-1].<wbr>U)/(2.0*user->hx);<br>
Uy=(aY[j+1][i].U-aY[j-1][i].<wbr>U)/(2.0*user->hy);<br>
Uxx=((aY[j][i+1].U+aY[j][i-1]<wbr>.U-2.0*aY[j][i].U)/(hx2));<br>
Uyy=((aY[j+1][i].U+aY[j-1][i]<wbr>.U-2.0*aY[j][i].U)/hy2);<br>
<br>
U1=user->D*user->tau_0/(user-<wbr>>W*user->W);<br>
U2= ((Px*Px+Py*Py)>0.0) ? user->a_p/sqrt(Px*Px+Py*Py) : 0.0 ;<br>
//U2=0.0;<br>
P1= (user->W*user->hy*j-user->Vp*<wbr>user->tau_0*t)/user->lT;<br>
<br>
aF[j][i].U=(U1*(-0.5*(Ux*Px+<wbr>Uy*Py)+0.5*(1-aY[j][i].p)*(<wbr>Uxx+Uyy))+U2*(1+(1-user->k)*<wbr>aY[j][i].U)*(Pxt*Px+Pyt*Py+<wbr>aYdot[j][i].p*(Pxx+Pyy))+U2*(<wbr>1-user->k)*aYdot[j][i].p*(Ux*<wbr>Px+Uy*Py)+0.5*(1+(1-user->k)*<wbr>aY[j][i].U)*aYdot[j][i].p-0.5*<wbr>(1+user->k-(1-user->k)*aY[j][<wbr>i].p)*aYdot[j][i].U)*hx2;<br>
<br>
aF[j][i].p=( e*e*(Pxx+Pyy)+2.0*e*ep*(<wbr>thetax*Px+thetay*Py)+(e*epp+<wbr>ep*ep)*(thetay*Px-thetax*Py)+(<wbr>aY[j][i].p-aY[j][i].p*aY[j][i]<wbr>.p*aY[j][i].p)-user->lambda*(<wbr>aY[j][i].p*aY[j][i].p-1)*(aY[<wbr>j][i].p*aY[j][i].p-1)*(aY[j][<wbr>i].U+P1)-(1-(1-user->k)*P1)*(<wbr>1.0+4.0*user->epsilon*cos(4.0*<wbr>theta))*(1.0+4.0*user-><wbr>epsilon*cos(4.0*theta))*aYdot[<wbr>j][i].p
)*hx2 ;<br>
<br>
}<br>
}</div>
<p></p>
<p style="margin-top:0; margin-bottom:0">Sepideh<br>
</p>
</div>
<hr style="display:inline-block; width:98%">
<div id="x_x_m_-1220196563703675155divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>><br>
<b>Sent:</b> Monday, April 16, 2018 8:36:37 PM<br>
<b>To:</b> Sepideh Kavousi<br>
<b>Cc:</b> <a href="mailto:petsc-users@mcs.anl.gov" target="_blank">petsc-users@mcs.anl.gov</a><br>
<b>Subject:</b> Re: [petsc-users] error running parallel on cluster</font>
<div> </div>
</div>
<div>
<div dir="ltr">
<div class="x_x_m_-1220196563703675155x_gmail_extra">
<div class="x_x_m_-1220196563703675155x_gmail_quote">On Mon, Apr 16, 2018 at 9:20 PM, Sepideh Kavousi
<span dir="ltr"><<a href="mailto:skavou1@lsu.edu" target="_blank">skavou1@lsu.edu</a>></span> wrote:<br>
<blockquote class="x_x_m_-1220196563703675155x_gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
<div dir="ltr">
<div id="x_x_m_-1220196563703675155x_m_734736110172724093divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<div>Hello,</div>
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
I am solving a PDE where I have the spacial derivtive of the time derivative of a variable. In the
<span>DMDATSSetIFunctionLocal</span> function I defined d(dY/dt)/dx as:</div>
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<span>(aYdot[j][i+1].p-aYdot[j][i-1]<wbr>.p)/(2.0*user->hx)</span></div>
</div>
</div>
</blockquote>
<div><br>
</div>
<div>I do not think that you get ghosted Ydot in that function.</div>
<div><br>
</div>
<div> Matt</div>
<div> </div>
<blockquote class="x_x_m_-1220196563703675155x_gmail_quote" style="margin:0 0 0 .8ex; border-left:1px #ccc solid; padding-left:1ex">
<div dir="ltr">
<div id="x_x_m_-1220196563703675155x_m_734736110172724093divtagdefaultwrapper" dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<span>on my workstation, it is working but on the cluster it gives an error. I can not run with debugger on the cluster but I have checked and the error is related to this part and I do not have any problem on cluster when running in series. Can you please
help me about it. <br>
</span></div>
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<span><br>
</span></div>
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<span>the error is:</span></div>
<div dir="ltr" style="font-size:12pt; color:rgb(0,0,0); font-family:Calibri,Helvetica,sans-serif,"EmojiFont","Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols">
<span>
<div>0]PETSC ERROR: Caught signal number 11 SEGV: Segmentation Violation, probably memory access out of range<br>
[0]PETSC ERROR: Try option -start_in_debugger or -on_error_attach_debugger<br>
[0]PETSC ERROR: or see <a href="http://www.mcs.anl.gov/petsc/documentation/faq.html#valgrind" target="_blank">
http://www.mcs.anl.gov/petsc/d<wbr>ocumentation/faq.html#valgrind</a><br>
[0]PETSC ERROR: or try <a href="http://valgrind.org" target="_blank">http://valgrind.org</a> on GNU/linux and Apple Mac OS X to find memory corruption errors<br>
[0]PETSC ERROR: likely location of problem given in stack below<br>
[0]PETSC ERROR: --------------------- Stack Frames ------------------------------<wbr>------<br>
[0]PETSC ERROR: Note: The EXACT line numbers in the stack are not available,<br>
[0]PETSC ERROR: INSTEAD the line number of the start of the function<br>
[0]PETSC ERROR: is given.<br>
[0]PETSC ERROR: [0] TSComputeIFunction_DMDA line 63 /ddnB/work/skavou1/petsc/src/t<wbr>s/utils/dmdats.c<br>
[0]PETSC ERROR: [0] TS user implicit function line 829 /ddnB/work/skavou1/petsc/src/t<wbr>s/interface/ts.c<br>
[0]PETSC ERROR: [0] TSComputeIFunction line 815 /ddnB/work/skavou1/petsc/src/t<wbr>s/interface/ts.c<br>
[0]PETSC ERROR: [0] SNESTSFormFunction_Theta line 640 /ddnB/work/skavou1/petsc/src/t<wbr>s/impls/implicit/theta/theta.c<br>
[0]PETSC ERROR: [0] SNESTSFormFunction line 4564 /ddnB/work/skavou1/petsc/src/t<wbr>s/interface/ts.c<br>
[0]PETSC ERROR: [0] SNES user function line 2202 /ddnB/work/skavou1/petsc/src/s<wbr>nes/interface/snes.c<br>
[0]PETSC ERROR: [0] SNESComputeFunction line 2187 /ddnB/work/skavou1/petsc/src/s<wbr>nes/interface/snes.c<br>
[0]PETSC ERROR: [0] SNESSolve_NEWTONTR line 90 /ddnB/work/skavou1/petsc/src/s<wbr>nes/impls/tr/tr.c<br>
[0]PETSC ERROR: [0] SNESSolve line 4203 /ddnB/work/skavou1/petsc/src/s<wbr>nes/interface/snes.c<br>
[0]PETSC ERROR: [0] TSTheta_SNESSolve line 175 /ddnB/work/skavou1/petsc/src/t<wbr>s/impls/implicit/theta/theta.c<br>
[0]PETSC ERROR: [0] TSStep_Theta line 191 /ddnB/work/skavou1/petsc/src/t<wbr>s/impls/implicit/theta/theta.c<br>
[0]PETSC ERROR: [0] TSStep line 3526 /ddnB/work/skavou1/petsc/src/t<wbr>s/interface/ts.c<br>
[0]PETSC ERROR: [0] TSSolve line 3668 /ddnB/work/skavou1/petsc/src/t<wbr>s/interface/ts.c<br>
[0]PETSC ERROR: --------------------- Error Message ------------------------------<wbr>------------------------------<wbr>--<br>
[0]PETSC ERROR: Signal received<br>
[0]PETSC ERROR: See <a href="http://www.mcs.anl.gov/petsc/documentation/faq.html" target="_blank">
http://www.mcs.anl.gov/petsc/d<wbr>ocumentation/faq.html</a> for trouble shooting.<br>
[0]PETSC ERROR: Petsc Release Version 3.9.0, unknown <br>
[0]PETSC ERROR: ./one.out on a debug named mike1 by skavou1 Mon Apr 16 20:11:44 2018<br>
[0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++ --with-fc=gfortran --download-mpich --download-fblaslapack<br>
[0]PETSC ERROR: #1 User provided function() line 0 in unknown file<br>
application called MPI_Abort(MPI_COMM_WORLD, 59) - process 0<br>
==29057== <br>
==29057== HEAP SUMMARY:<br>
==29057== in use at exit: 560,151 bytes in 383 blocks<br>
==29057== total heap usage: 8,734 allocs, 8,351 frees, 4,449,350 bytes allocated<br>
==29057== <br>
==29057== LEAK SUMMARY:<br>
==29057== definitely lost: 0 bytes in 0 blocks<br>
==29057== indirectly lost: 0 bytes in 0 blocks<br>
==29057== possibly lost: 0 bytes in 0 blocks<br>
==29057== still reachable: 560,151 bytes in 383 blocks<br>
==29057== suppressed: 0 bytes in 0 blocks<br>
==29057== Rerun with --leak-check=full to see details of leaked memory<br>
==29057== <br>
==29057== For counts of detected and suppressed errors, rerun with: -v<br>
==29057== ERROR SUMMARY: 0 errors from 0 contexts (suppressed: 8 from 6)<br>
<br>
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<span>Thanks,</span></div>
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<span>Sepideh<span class="x_x_HOEnZb"><font color="#888888"><br>
</font></span></span></div>
<span class="x_x_HOEnZb"><font color="#888888"></font></span></div>
<span class="x_x_HOEnZb"><font color="#888888"></font></span></div>
<span class="x_x_HOEnZb"><font color="#888888"></font></span></blockquote>
<span class="x_x_HOEnZb"><font color="#888888"></font></span></div>
<span class="x_x_HOEnZb"><font color="#888888"><br>
<br clear="all">
<div><br>
</div>
-- <br>
<div class="x_x_m_-1220196563703675155x_gmail_signature">
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<div>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><br>
</div>
<div><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~<wbr>knepley/</a><br>
</div>
</div>
</div>
</div>
</div>
</font></span></div>
</div>
</div>
</div>
</blockquote>
</div>
<br>
<br clear="all">
<div><br>
</div>
-- <br>
<div class="x_x_gmail_signature">
<div dir="ltr">
<div>
<div dir="ltr">
<div>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><br>
</div>
<div><a href="http://www.caam.rice.edu/~mk51/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><br>
</div>
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