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<p class="MsoNormal"><span class="DefaultFontHxMailStyle"><span style="font-size:12.0pt">Barry,<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="DefaultFontHxMailStyle"><span style="font-size:12.0pt"><o:p> </o:p></span></span></p>
<p class="MsoNormal"><span class="DefaultFontHxMailStyle"><span style="font-size:12.0pt">Thank you very much.<o:p></o:p></span></span></p>
<p class="MsoNormal"><span class="DefaultFontHxMailStyle"><span style="font-size:12.0pt"><o:p> </o:p></span></span></p>
<p class="MsoNormal">DMDASetBlockFills() needs two input arrays specifying sparsity pattern. In my case, I have 26 components at each grid. Is it correct that I need to have two arrays of 26x26 elements with value 1 for coupling and 0 for no coupling? Also
how to determine when the value should be 1 or 0? Each component involves 7 stencils (i-1, j, k), (I, j, k), (i+1, j, k), (I, j-1, k), (I, j+1, k), (I, j, k-1), and (I, j, k+1), and couples with several other components.<o:p></o:p></p>
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<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal">Sent from <a href="https://go.microsoft.com/fwlink/?LinkId=550986">
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<p class="MsoNormal" style="border:none;padding:0in"><b>From: </b><a href="mailto:bsmith@petsc.dev">Barry Smith</a><br>
<b>Sent: </b>Wednesday, September 7, 2022 11:53 AM<br>
<b>To: </b><a href="mailto:Jiannan_Tu@uml.edu">Tu, Jiannan</a><br>
<b>Cc: </b><a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a><br>
<b>Subject: </b>Re: [petsc-users] Using matrix-free with KSP</p>
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span style="font-size:12.0pt;color:black"> This email was sent from outside the UMass Lowell network.</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal">DMDASetBlockFills() or DMDASetBlockFillsSparse() (they are just different ways of providing the same information) will help you here enormously, your type of case is exactly what they were designed for.<o:p></o:p></p>
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<p class="MsoNormal"> Barry<o:p></o:p></p>
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<p class="MsoNormal">On Sep 7, 2022, at 10:47 AM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu">Jiannan_Tu@uml.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Barry and Hong,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Thank you.<span class="apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">There are 26 components at each grid and there are not fully coupled in terms of stiff functions. Mutual coupling is among about 6 components.<span class="apple-converted-space"> </span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">I would prefer not using matrix-free since the Jacobina is not difficult to calculate and only up to 10 non-zeros at each row. I'll try DMDASetBlockFills() or DMDASetBlockFillsSparse() and see how they can
reduce the memory usage.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Jiannan<o:p></o:p></span></p>
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<p class="MsoNormal"><b>From:</b><span class="apple-converted-space"> </span>Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>><br>
<b>Sent:</b><span class="apple-converted-space"> </span>Tuesday, September 6, 2022 11:33 PM<br>
<b>To:</b><span class="apple-converted-space"> </span>Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu">Jiannan_Tu@uml.edu</a>><br>
<b>Cc:</b><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] Using matrix-free with KSP<span style="font-size:13.5pt;font-family:"Helvetica",sans-serif">
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<p class="MsoNormal" style="line-height:16.0pt;background:#FFCACA"><b><span style="font-size:12.0pt;color:black">CAUTION:</span></b><span class="apple-converted-space"><span style="font-size:12.0pt;color:black"> </span></span><span style="font-size:12.0pt;color:black">This
email was sent from outside the UMass Lowell network.</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif">On Sep 6, 2022, at 11:00 PM, Tu, Jiannan <</span><a href="mailto:Jiannan_Tu@uml.edu"><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif">Jiannan_Tu@uml.edu</span></a><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif">>
wrote:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">I am using TS IMEX to solve a large DAE system. The DAE is obtained by applying finite FV method to 3-D multi-specie ion/neutral fluids equations with magnetic induction equation. The Jacobian for stiff part
is formed by using MatSetValuesStencil(). The Jacobian matrix is very sparse, no more than 10 non-zeros on each row. MatSetValuesStencil requires local to global mapping by calling ISLocaltoGlobalMapping(). Could you please instruct me how to use local to
global mapping?<span class="xapple-converted-space"> </span></span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif"> DMDA automatically sets up the </span><span style="font-size:12.0pt">ISLocaltoGlobalMapping() so you should not need to.</span><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif">
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<p class="MsoNormal"><span style="font-size:12.0pt">I also tried using DMCreateMatrix() to create the Jacobian. While local to global mapping is not necessary, the matrix takes too much memory and requires 64-bit indices. I would prefer to take the advantage
of sparsity of the Jacobian, pre-allocate the matrix to use as less as possible memory so that the code can be run on a multi-core desktop.</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif"> If using matrix-free does not work for you because the linear solves do not converge or converge too slowly. Then you might be able to decrease the memory used in the matrix.
The DMCreateMatrix() does take advantage of sparsity and tries to preallocate only what it needs. Often what it preallocates is the best possible, but for multicomponent problems it has to assume there is full coupling within all the degrees of freedom that
live at each at each grid point. How many components live at each grid point in your model and are they not all coupled to each other in the equations? If they are not fully coupled you can use either DMDASetBlockFills() or DMDASetBlockFillsSparse() to indicate
the reduced coupling that actually exists for you model.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:13.5pt;font-family:"Helvetica",sans-serif"> Barry<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Thank you very much for your advice.</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Jiannan</span><o:p></o:p></p>
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