50,000 * 50,000 > 2^31 (roughly 2 billion) hence we cannot represent even the length of a vector using 32 bit integers; just to do "book keeping" of dimensions requires using 64 bit integers. Using 64 bit integers should not slow PETSc significantly, especially in matrix-free mode.
> On May 30, 2022, at 7:33 PM, Tu, Jiannan <jiannan...@uml.edu> wrote: > > 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 50,000 by 50,000 by 1 (dof) is too large for 32 bit indices.” > > 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? > > Thank you, > Jiannan > > From: Barry Smith <bsm...@petsc.dev <mailto:bsm...@petsc.dev>> > Sent: Tuesday, May 24, 2022 2:13 PM > To: Tu, Jiannan <jiannan...@uml.edu <mailto:jiannan...@uml.edu>> > Cc: petsc-users@mcs.anl.gov <mailto:petsc-users@mcs.anl.gov> > Subject: Re: [petsc-users] Using matrix-free with KSP > > This e-mail originated from outside the UMass Lowell network. > > You can use MatCreateMFFD > https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/ > <https://urldefense.com/v3/__https:/petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d10-zlXkw$> > MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix > to KSP. Note you will need to use -pc_type none or provide your own custom > preconditioner with https://petsc.org/main/docs/manualpages/PC/PCSHELL/ > <https://urldefense.com/v3/__https:/petsc.org/main/docs/manualpages/PC/PCSHELL/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d1cA4fKGw$> > > > > > On May 24, 2022, at 1:21 PM, Tu, Jiannan <jiannan...@uml.edu > <mailto:jiannan...@uml.edu>> wrote: > > 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. I am wondering how to apply the method to KSP > iterative solver in parallel. > > I greatly appreciate your help for me to understand this topic. > > Jiannan Tu
