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<p class="MsoNormal">I tried the matrix-free method. Since the number of the unknown is large, say 50000, then the number of matrix elements is 50000^2, which is greater than the max number represented by the 32-bit int. PETSC gives an error message: “Mesh
of 50000 by 50000 by 1 (dof) is too large for 32 bit indices.”<o:p></o:p></p>
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<p class="MsoNormal">I know using the 64-bit int option when compiling PETSC can avoid this error. However, it seems that 64-bit int makes the PETSC relatively slow. I wonder why the matrix-free method still counts the total number of matrix elements even though
they are not stored. Any other ways around it?<o:p></o:p></p>
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<p class="MsoNormal">Thank you,<o:p></o:p></p>
<p class="MsoNormal">Jiannan<o:p></o:p></p>
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<p class="MsoNormal"><b>From:</b> Barry Smith <bsmith@petsc.dev> <br>
<b>Sent:</b> Tuesday, May 24, 2022 2:13 PM<br>
<b>To:</b> Tu, Jiannan <Jiannan_Tu@uml.edu><br>
<b>Cc:</b> petsc-users@mcs.anl.gov<br>
<b>Subject:</b> Re: [petsc-users] Using matrix-free with KSP<o:p></o:p></p>
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<p class="MsoNormal"><b><span style="color:red">This e-mail originated from outside the UMass Lowell network.</span></b>
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<p class="MsoNormal"> You can use MatCreateMFFD <a href="https://urldefense.com/v3/__https:/petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d10-zlXkw$">https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/</a>
MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix to KSP. Note you will need to use -pc_type none or provide your own custom preconditioner with <a href="https://urldefense.com/v3/__https:/petsc.org/main/docs/manualpages/PC/PCSHELL/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d1cA4fKGw$">https://petsc.org/main/docs/manualpages/PC/PCSHELL/</a><o:p></o:p></p>
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<p class="MsoNormal">On May 24, 2022, at 1:21 PM, 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">I want to use a matrix-free matrix to solve a large linear equation system because the matrix is too large to be stored. Petsc user manual describes matrix-free method for SNES with examples. The matrix-free
matrices section explains how to set up such a matrix, but I can't find any example of matrix-free method with KSP. <span style="color:black;background:white">I am wondering how to apply the method to KSP iterative solver in parallel.</span><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black;background:white">I greatly appreciate your help for me to understand this topic. </span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black;background:white">Jiannan Tu</span><span style="font-size:12.0pt"><o:p></o:p></span></p>
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