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<p class="MsoNormal"><span style="font-size:11.0pt">That’s great to know.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Most cases we will deal with sparse matrix problems, so LU might not be so bad.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">-Ling<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="color:black">From:
</span></b><span style="color:black">Barry Smith <bsmith@petsc.dev><br>
<b>Date: </b>Friday, March 29, 2024 at 2:46 PM<br>
<b>To: </b>Zou, Ling <lzou@anl.gov><br>
<b>Cc: </b>Zhang, Hong <hzhang@mcs.anl.gov>, petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject: </b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-line-height-alt:.75pt"><span style="font-size:1.0pt;color:white">Generically you see the ~[DOF]^3 for dense matrix factorizations. For sparse, depending on the problem and space dimension 1, 2, or 3 you do much better than ~[DOF]^3
dof. Iterative solvers when working well offer the possibility of ~[DOF] <o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"> Generically you see the <span style="font-size:11.0pt">~[DOF]^3 for dense matrix factorizations. For sparse, depending on the problem and space dimension 1, 2, or 3 you do much better than ~[DOF]^3 dof. Iterative solvers when working
well offer the possibility of ~[DOF] which is why they are needed for very large problems.</span><o:p></o:p></p>
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<p class="MsoNormal">On Mar 29, 2024, at 3:29<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling via petsc-users <petsc-users@mcs.anl.gov> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Note that [Wall Time] ~ [DOF]^1.333, instead of being ~[DOF]^3.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">The [DOF]^3 rule was the scary part that I wanted to avoid LU.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>petsc-users <<a href="mailto:petsc-users-bounces@mcs.anl.gov">petsc-users-bounces@mcs.anl.gov</a>> on behalf of Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Friday, March 29, 2024 at 2:06 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>>, Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Hong, are these results somewhat expected? I don’t see any speed up for using 2 processors (maybe I don’t have 2 processors?).</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Option</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Wall Time (sec)</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">7.442</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">mpiexec -n 2 -pc_type lu</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">9.112</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -pc_factor_mat_solver_type mumps</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">8.748</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">mpiexec -n 2 -pc_type lu -pc_factor_mat_solver_type mumps</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">9.013</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">For different size problems</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -m 1000 -n 1000</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">7.442</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -m 750 -n 750</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">3.142</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -m 500 -n 500</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">1.007</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -m 250 -n 250</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">0.150</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-pc_type lu -m 100 -n 100</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">0.016</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><image001.png></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>petsc-users <<a href="mailto:petsc-users-bounces@mcs.anl.gov">petsc-users-bounces@mcs.anl.gov</a>> on behalf of Zou, Ling via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Friday, March 29, 2024 at 12:50 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">I cannot believe that I typed: make ex<span style="color:black;background:yellow">0</span>2</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thanks, it works.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Friday, March 29, 2024 at 12:43 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>>,<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:1.0pt;color:white">cd src/ksp/ksp/tutorials make ex2 On Mar 29, 2024, at 1:</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">10 PM, Zou,
Ling <lzou@</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">anl.</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">gov>
wrote: Hong, thanks! That’s great to know. I’d like to try the ex2 tutorial case locally to see how it performs. I have already installed PETSc 3.</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">20.</span><span style="font-size:1.0pt;font-family:"Arial",sans-serif;color:white"> </span><span style="font-size:1.0pt;color:white">5</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> cd <span style="font-size:11.0pt">src/ksp/ksp/tutorials</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> make ex2 </span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">On Mar 29, 2024, at 1:10<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>> wrote:<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Hong, thanks! That’s great to know.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">I’d like to try the ex2 tutorial case locally to see how it performs. I have already installed PETSc 3.20.5 on my Mac.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Here shows the very last step of installation.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">make PETSC_DIR=/Users/lingzou/Downloads/petsc-3.20.5 PETSC_ARCH=arch-opt check</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Running PETSc check examples to verify correct installation</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Using PETSC_DIR=/Users/lingzou/Downloads/petsc-3.20.5 and PETSC_ARCH=arch-opt</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">C/C++ example src/snes/tutorials/ex19 run successfully with 1 MPI process</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">C/C++ example src/snes/tutorials/ex19 run successfully with 2 MPI processes</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="s1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Completed PETSc check examples</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">I found myself not knowing how to compile petsc/src/ksp/ksp/tutorials/ex2.c</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Do we have a page for how to do that?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Best,</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Thursday, March 28, 2024 at 4:59 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>>, Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Ling,<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">MUMPS<span class="apple-converted-space"> </span><span style="font-size:10.0pt"><a href="https://urldefense.us/v3/__https:/mumps-solver.org/index.php__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLIwl86Bvw$"><span style="font-size:12.0pt">https://mumps-solver.org/index.php</span></a></span> ,
superlu and superlu_dist<span class="apple-converted-space"> </span><span style="font-size:10.0pt"><a href="https://urldefense.us/v3/__https:/portal.nersc.gov/project/sparse/superlu/__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLIHcCP4HQ$"><span style="font-size:12.0pt">https://portal.nersc.gov/project/sparse/superlu/</span></a><o:p></o:p></span></p>
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<p class="MsoNormal">are sparse LU solvers, i.e., they produce SPARSE LU matrix factors. For many applications, they can solve<span class="apple-converted-space"> </span><span style="font-size:11.0pt;color:#242424;background:white">1 million DOF</span> easily
even in sequential mode. For example <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">petsc/src/ksp/ksp/tutorials <span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">./ex2 -pc_type lu -pc_factor_mat_solver_type mumps -m 1000 -n 1000 -ksp_monitor_true_residual<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> 0 KSP preconditioned resid norm 1.000000000000e+03 true resid norm 6.330876716538e+01 ||r(i)||/||b|| 1.000000000000e+00<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> 1 KSP preconditioned resid norm 9.976801056860e-09 true resid norm 3.908107755078e-10 ||r(i)||/||b|| 6.173090916254e-12<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Norm of error 9.98582e-09 iterations 1<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">MUMPS LU solves this matrix of size 1.e6 in one iteration (takes few sec on my laptop).<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">As Barry suggests, try mumps first. If it fails or it is too slow, then explore other solvers available in PETSc<span class="apple-converted-space"> </span><span style="font-size:10.0pt"><a href="https://urldefense.us/v3/__https:/petsc.org/release/overview/linear_solve_table/__;!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLKPDawFmw$"><span style="font-size:12.0pt">https://petsc.org/release/overview/linear_solve_table/</span></a><o:p></o:p></span></p>
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<p class="MsoNormal">From my experiments, MUMPS is faster and more robust than superlu/superlu_dist, yet it consumes slightly more memory.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">See<span class="apple-converted-space"> </span><span style="font-size:10.0pt"><a href="https://urldefense.us/v3/__https:/petsc.org/release/manual/ksp/*using-external-linear-solvers__;Iw!!G_uCfscf7eWS!b4SLVXTUaKyR1_NPGNEtGinrk2pTkW9odwoiYKcTjslyDUQxuhihIs1ZLqrh2z33R3C5VLJJEKMXKA$"><span style="font-size:12.0pt">https://petsc.org/release/manual/ksp/#using-external-linear-solvers</span></a></span> on
how to install mumps with petsc.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Hong<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span class="apple-converted-space"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">Zou,
Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Sent:</b><span class="apple-converted-space"> </span>Thursday, March 28, 2024 2:34 PM<br>
<b>To:</b><span class="apple-converted-space"> </span>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Cc:</b><span class="apple-converted-space"> </span>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>>;<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:</b><span class="apple-converted-space"> </span>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thank you. Those are great suggestions. Although I mentioned 1 million DOF, but we rarely go there, so maybe stick with what is working now, and meanwhile seeking helps from literatures.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="xmsonormal" style="margin-bottom:12.0pt"><b>From:<span class="apple-converted-space"> </span></b>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Date:<span class="apple-converted-space"> </span></b>Thursday, March 28, 2024 at 2:26 PM<br>
<b>To:<span class="apple-converted-space"> </span></b>Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>><br>
<b>Cc:<span class="apple-converted-space"> </span></b>Zhang, Hong <<a href="mailto:hzhang@mcs.anl.gov">hzhang@mcs.anl.gov</a>>,<span class="apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><span class="apple-converted-space"> </span><<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
<b>Subject:<span class="apple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:1.0pt;color:white">You may benefit from a literature search on your model AND preconditioners to see what others have used. But I would try PETSc/MUMPS on the biggest size you want and see how it goes (better it runs
for a little longer and you don't waste months<span class="apple-converted-space"> </span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> You may benefit from a literature search on your model AND preconditioners to see what others have used. But I would try PETSc/MUMPS on the biggest size you want and see how it goes (better it runs for a little longer and you don't waste
months trying to find a good preconditioner).<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">On Mar 28, 2024, at 2:20<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling <<a href="mailto:lzou@anl.gov">lzou@anl.gov</a>> wrote:<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thank you, Barry.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Yes, I have tried different preconditioners, but in a naïve way, i.e., looping through possible options using `-pc_type <option>` command line.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">But no, not in a meaningful way because the lack of understanding of the connection between physics (the problem we are dealing with) to math (the correct combination of those preconditioners).</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="xmsonormal" style="margin-bottom:12.0pt"><b>From:<span class="xapple-converted-space"> </span></b>Barry Smith <<span style="font-size:10.0pt"><a href="mailto:bsmith@petsc.dev"><span style="font-size:12.0pt">bsmith@petsc.dev</span></a></span>><br>
<b>Date:<span class="xapple-converted-space"> </span></b>Thursday, March 28, 2024 at 1:09 PM<br>
<b>To:<span class="xapple-converted-space"> </span></b>Zou, Ling <<span style="font-size:10.0pt"><a href="mailto:lzou@anl.gov"><span style="font-size:12.0pt">lzou@anl.gov</span></a></span>><br>
<b>Cc:<span class="xapple-converted-space"> </span></b>Zhang, Hong <<span style="font-size:10.0pt"><a href="mailto:hzhang@mcs.anl.gov"><span style="font-size:12.0pt">hzhang@mcs.anl.gov</span></a></span>>,<span class="xapple-converted-space"> </span><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span><span class="xapple-converted-space"> </span><<span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span>><br>
<b>Subject:<span class="xapple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:1.0pt;color:white">1 million is possible for direct solvers using PETSc with the MUMPS direct solver when you cannot get a preconditioner to work well for your problems. ILU are not very robust preconditioners and
I would not rely on them. Have you investigated<span class="xapple-converted-space"> </span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> 1 million is possible for direct solvers using PETSc with the MUMPS direct solver when you cannot get a preconditioner to work well for your problems.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> ILU are not very robust preconditioners and I would not rely on them. Have you investigated other preconditioners in PETSc, PCGAMG, PCASM, PCFIELDSPLIT or some combination of these preconditioners work for many problems, though certainly
not all.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">On Mar 28, 2024, at 1:14<span style="font-family:"Arial",sans-serif"> </span>PM, Zou, Ling <<span style="font-size:10.0pt"><a href="mailto:lzou@anl.gov"><span style="font-size:12.0pt">lzou@anl.gov</span></a></span>> wrote:<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Thank you, Barry.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Yeah, this is unfortunate given that the problem we are handling is quite heterogeneous (in both mesh and physics).</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">I expect that our problem sizes will be mostly smaller than 1 million DOF, should LU still be a practical solution? Can it scale well if we choose to run the problem in a parallel way?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">PS1:<span class="xapple-converted-space"> </span></span>-ksp_norm_type unpreconditioned did not work as the true residual did not go down, even with 300 linear iterations.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">PS2: what do you think if it will be beneficial to have more detailed discussions (e.g., a presentation?) on the problem we are solving to seek more advice?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="xmsonormal" style="margin-bottom:12.0pt"><b>From:<span class="xapple-converted-space"> </span></b>Barry Smith <<span style="font-size:10.0pt"><a href="mailto:bsmith@petsc.dev"><span style="font-size:12.0pt">bsmith@petsc.dev</span></a></span>><br>
<b>Date:<span class="xapple-converted-space"> </span></b>Thursday, March 28, 2024 at 11:14 AM<br>
<b>To:<span class="xapple-converted-space"> </span></b>Zou, Ling <<span style="font-size:10.0pt"><a href="mailto:lzou@anl.gov"><span style="font-size:12.0pt">lzou@anl.gov</span></a></span>><br>
<b>Cc:<span class="xapple-converted-space"> </span></b>Zhang, Hong <<span style="font-size:10.0pt"><a href="mailto:hzhang@mcs.anl.gov"><span style="font-size:12.0pt">hzhang@mcs.anl.gov</span></a></span>>,<span class="xapple-converted-space"> </span><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span><span class="xapple-converted-space"> </span><<span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span>><br>
<b>Subject:<span class="xapple-converted-space"> </span></b>Re: [petsc-users] Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:1.0pt;color:white">This is a bad situation, the solver is not really converging. This can happen with ILU() sometimes, it so badly scales things that the preconditioned residual decreases a lot but the true residual
is not really getting smaller. Since your matrices<span class="xapple-converted-space"> </span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> This is a bad situation, the solver is not really converging. This can happen with ILU() sometimes, it so badly scales things that the preconditioned residual decreases a lot but the true residual is not really getting smaller. Since
your matrices are small best to stick to LU.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> You can use -ksp_norm_type unpreconditioned to force the convergence test to use the true residual for a convergence test and the solver will discover that it is not converging.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"> Barry<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">On Mar 28, 2024, at 11:43<span style="font-family:"Arial",sans-serif"> </span>AM, Zou, Ling via petsc-users <<span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span>>
wrote:<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Hong, thanks! That makes perfect sense.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">A follow up question about ILU.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">The following is the performance of ILU(5). Note that each KPS solving reports converged but as the output shows, the preconditioned residual does while true residual does not. Is there any way this performance
could be improved?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Background: the preconditioning matrix is finite difference generated, and should be exact.</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">-Ling</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Time Step 21, time = -491.75, dt = 1</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">NL
Step =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">0, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">6.98749E+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">0
KSP preconditioned resid norm 1.684131526824e+04 true resid norm 6.987489798042e+01 ||r(i)||/||b|| 1.000000000000e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1
KSP preconditioned resid norm 5.970568556551e+02 true resid norm 6.459553545222e+01 ||r(i)||/||b|| 9.244455064582e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">2
KSP preconditioned resid norm 3.349113985192e+02 true resid norm 7.250836872274e+01 ||r(i)||/||b|| 1.037688366186e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">3
KSP preconditioned resid norm 3.290585904777e+01 true resid norm 1.186282435163e+02 ||r(i)||/||b|| 1.697723316169e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">4
KSP preconditioned resid norm 8.530606201233e+00 true resid norm 4.088729421459e+01 ||r(i)||/||b|| 5.851499665310e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Linear
solve converged due to CONVERGED_RTOL iterations 4</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">NL
Step =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">4.08788E+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">0
KSP preconditioned resid norm 1.851047973094e+03 true resid norm 4.087882723223e+01 ||r(i)||/||b|| 1.000000000000e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1
KSP preconditioned resid norm 3.696809614513e+01 true resid norm 2.720016413105e+01 ||r(i)||/||b|| 6.653851387793e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">2
KSP preconditioned resid norm 5.751891392534e+00 true resid norm 3.326338240872e+01 ||r(i)||/||b|| 8.137068663873e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">3
KSP preconditioned resid norm 8.540729397958e-01 true resid norm 8.672410748720e+00 ||r(i)||/||b|| 2.121492062249e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Linear
solve converged due to CONVERGED_RTOL iterations 3</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">NL
Step =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">2, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">8.67124E+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">0
KSP preconditioned resid norm 5.511333966852e+00 true resid norm 8.671237519593e+00 ||r(i)||/||b|| 1.000000000000e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1
KSP preconditioned resid norm 1.174962622023e+00 true resid norm 8.731034658309e+00 ||r(i)||/||b|| 1.006896032842e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">2
KSP preconditioned resid norm 1.104604471016e+00 true resid norm 1.018397505468e+01 ||r(i)||/||b|| 1.174454630227e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">3
KSP preconditioned resid norm 4.257063674222e-01 true resid norm 4.023093124996e+00 ||r(i)||/||b|| 4.639583584126e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">4
KSP preconditioned resid norm 1.023038868263e-01 true resid norm 2.365298462869e+00 ||r(i)||/||b|| 2.727751901068e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">5
KSP preconditioned resid norm 4.073772638935e-02 true resid norm 2.302623112025e+00 ||r(i)||/||b|| 2.655472309255e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">6
KSP preconditioned resid norm 1.510323179379e-02 true resid norm 2.300216593521e+00 ||r(i)||/||b|| 2.652697020839e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">7
KSP preconditioned resid norm 1.337324816903e-02 true resid norm 2.300057733345e+00 ||r(i)||/||b|| 2.652513817259e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">8
KSP preconditioned resid norm 1.247384902656e-02 true resid norm 2.300456226062e+00 ||r(i)||/||b|| 2.652973374174e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">9
KSP preconditioned resid norm 1.247038855375e-02 true resid norm 2.300532560993e+00 ||r(i)||/||b|| 2.653061406512e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">10
KSP preconditioned resid norm 1.244611343317e-02 true resid norm 2.299441241514e+00 ||r(i)||/||b|| 2.651802855496e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">11
KSP preconditioned resid norm 1.227243209527e-02 true resid norm 2.273668115236e+00 ||r(i)||/||b|| 2.622080308720e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">12
KSP preconditioned resid norm 1.172621459354e-02 true resid norm 2.113927895437e+00 ||r(i)||/||b|| 2.437861828442e-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">13
KSP preconditioned resid norm 2.880752338189e-03 true resid norm 1.076190247720e-01 ||r(i)||/||b|| 1.241103412620e-02</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Linear
solve converged due to CONVERGED_RTOL iterations 13</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">NL
Step =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">3, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1.59729E-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">0
KSP preconditioned resid norm 1.676948440854e+03 true resid norm 1.597288981238e-01 ||r(i)||/||b|| 1.000000000000e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1
KSP preconditioned resid norm 2.266131510513e+00 true resid norm 1.819663943811e+00 ||r(i)||/||b|| 1.139220244542e+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">2
KSP preconditioned resid norm 2.239911493901e+00 true resid norm 1.923976907755e+00 ||r(i)||/||b|| 1.204526501062e+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">3
KSP preconditioned resid norm 1.446859034276e-01 true resid norm 8.692945031946e-01 ||r(i)||/||b|| 5.442312026225e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">Linear
solve converged due to CONVERGED_RTOL iterations 3</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
</div>
</div>
</div>
</div>
</div>
<div>
<div>
<div>
<div>
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<p class="MsoNormal" style="background:black"><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">NL
Step =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">4, fnorm =</span></span><span class="xapple-converted-space"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white"> </span></span><span class="xs1"><span style="font-size:9.0pt;font-family:"Andale Mono";color:white">1.59564E-01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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KSP preconditioned resid norm 1.509663716414e+03 true resid norm 1.595641817504e-01 ||r(i)||/||b|| 1.000000000000e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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KSP preconditioned resid norm 1.995956587709e+00 true resid norm 1.712323298361e+00 ||r(i)||/||b|| 1.073125108390e+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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KSP preconditioned resid norm 1.994336275847e+00 true resid norm 1.741263472491e+00 ||r(i)||/||b|| 1.091262119975e+01</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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KSP preconditioned resid norm 1.268035008497e-01 true resid norm 8.197057317360e-01 ||r(i)||/||b|| 5.137153731769e+00</span></span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="xmsonormal" style="margin-bottom:12.0pt"><b>From:<span class="xapple-converted-space"> </span></b>Zhang, Hong <<span style="font-size:10.0pt"><a href="mailto:hzhang@mcs.anl.gov"><span style="font-size:12.0pt">hzhang@mcs.anl.gov</span></a></span>><br>
<b>Date:<span class="xapple-converted-space"> </span></b>Wednesday, March 27, 2024 at 4:59 PM<br>
<b>To:<span class="xapple-converted-space"> </span></b><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span><span class="xapple-converted-space"> </span><<span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:12.0pt">petsc-users@mcs.anl.gov</span></a></span>>,
Zou, Ling <<span style="font-size:10.0pt"><a href="mailto:lzou@anl.gov"><span style="font-size:12.0pt">lzou@anl.gov</span></a></span>><br>
<b>Subject:<span class="xapple-converted-space"> </span></b>Re: Does ILU(15) still make sense or should just use LU?<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Ling,<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">ILU(level) is used for saving storage space with more computations. Normally, we use level=1 or 2. It does not make sense to use level 15. If you have sufficient space, LU would be the best.<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal">Hong<span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> petsc-users <</span><span style="font-size:10.0pt"><a href="mailto:petsc-users-bounces@mcs.anl.gov"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">petsc-users-bounces@mcs.anl.gov</span></a></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">>
on behalf of Zou, Ling via petsc-users <</span><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">petsc-users@mcs.anl.gov</span></a></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">><br>
<b>Sent:</b> Wednesday, March 27, 2024 4:24 PM<br>
<b>To:</b> </span><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">petsc-users@mcs.anl.gov</span></a></span><span class="xapple-converted-space"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> </span></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"><</span><span style="font-size:10.0pt"><a href="mailto:petsc-users@mcs.anl.gov"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">petsc-users@mcs.anl.gov</span></a></span><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">><br>
<b>Subject:</b> [petsc-users] Does ILU(15) still make sense or should just use LU?</span><span style="font-size:10.0pt"><o:p></o:p></span></p>
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<p><span style="font-size:11.0pt;font-family:Helvetica">Hi, I’d like to avoid using LU, but in some cases to use ILU and still converge, I have to go to ILU(15), i.e., `-pc_factor_levels 15`. Does it still make sense, or should I give it up and switch to LU?</span><span style="font-size:13.5pt;font-family:Helvetica"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt;font-family:Helvetica"> </span><span style="font-size:13.5pt;font-family:Helvetica"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt;font-family:Helvetica">For this particular case, ~2k DoF, and both ILU(15) and LU perform similarly in terms of wall time.</span><span style="font-size:13.5pt;font-family:Helvetica"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt;font-family:Helvetica"> </span><span style="font-size:13.5pt;font-family:Helvetica"><o:p></o:p></span></p>
<p><span style="font-size:11.0pt;font-family:Helvetica">-Ling</span><span style="font-size:13.5pt;font-family:Helvetica"><o:p></o:p></span></p>
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