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Barry and Hong,<br>
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Thank you. <br>
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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.
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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.</div>
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Jiannan<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Barry Smith <bsmith@petsc.dev><br>
<b>Sent:</b> Tuesday, September 6, 2022 11:33 PM<br>
<b>To:</b> Tu, Jiannan <Jiannan_Tu@uml.edu><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Using matrix-free with KSP</font>
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<span style="font-weight:bold">CAUTION:</span> This email was sent from outside the UMass Lowell network.</div>
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<div class="">On Sep 6, 2022, at 11:00 PM, Tu, Jiannan <<a href="mailto:Jiannan_Tu@uml.edu" class="">Jiannan_Tu@uml.edu</a>> wrote:</div>
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<span class="" style="font-size:12pt">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="x_Apple-converted-space"> </span></span></div>
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DMDA automatically sets up the <span class="" style="font-size:12pt; font-family:Calibri,sans-serif">ISLocaltoGlobalMapping() so you should not need to.</span>
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<span class="" style="font-size:12pt">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></div>
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<div> 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.</div>
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<div> Barry</div>
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<span class="" style="font-size:12pt">Thank you very much for your advice.</span></div>
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<span class="" style="font-size:12pt">Jiannan</span></div>
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