>>> *That might not easily be possible with our PETSc interfaces.*
*PETSc has the concept of MatShell, which is in essence what deal.II'sLinearOperator is: A class that implements a matrix-vector operation,without giving access to individual matrix elements. You could trywhether you can implement something derived from MatrixBase that is aMatShell operation in the same way as the existing classes derived fromMatrixBase model other types of PETSc matrices.* *I don't know how difficult that would be, though.* Ok. I see. Seems like using ARPACK might be easier then. >>> You can do that, but I believe that it's also possible to work with the original system where one of the two matrices is only semidefinite. I have redone it with the original system, but it seems that PETSc is complaining about missing diagonal entry. *[0]PETSC ERROR: Object is in wrong state* *[0]PETSC ERROR: Matrix is missing diagonal entry 3* I presume this happens due to a zero block in one (or both) of the original matrices. Hmmm, should I then just explicitly see all zero diagonal values to 0.0. Anton. On Wednesday, August 25, 2021 at 12:20:38 PM UTC-6 Wolfgang Bangerth wrote: > On 8/25/21 11:53 AM, Anton Ermakov wrote: > > I I¯ A 0 ¯I *eigenvalue + I¯ 0 B ¯ I I * eigenvector =0 > > I I_ 0 0 _I I_ C D _I I > > ¯ ¯ > > where eigenvector consists of a vector displacement and a scalar > > pressure perturbation: > > > > eigenvector = transpose([U P]) > > > > It seems from the literature (e.g., Wang & Bathe 1997) that it is > > standard to rewrite this system to eliminate the pressure variable: > > > > eigenvalue * A * U - B * D^-1 * C * U = 0 > > > > or > > > > eigenvalue * A * U + M * U = 0 > > > > with M = - B * D^-1 * C and P = -D^-1 * C * U > > You can do that, but I believe that it's also possible to work with the > original system where one of the two matrices is only semidefinite. > > > What I am having trouble with is how to efficiently represent matrix > > products and inverses that go into matrix M. All the matrices (A, B, C, > > D) are sparse, but due to the inverse, it seems that M will be a full > > matrix and it might be unaffordable to store it in the memory. There was > > a discussion on a similar topic here: > > > > https://groups.google.com/g/dealii/c/5P_fv0zg7jg/m/CPYcYrbsDQAJ > > > > It seems that LinearOperator was used in that discussion to manipulate > > the matrix products and inverses, which seemed like an approach to > > follow if you use ARPACK eigensolvers. However, I am using SLEPc and it > > seems the inputs to SLEPc solvers would have to be objects of class > > PETScWrappers::MatrixBase > > < > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dealii.org%2Fcurrent%2Fdoxygen%2Fdeal.II%2FclassPETScWrappers_1_1MatrixBase.html&data=04%7C01%7CWolfgang.Bangerth%40colostate.edu%7Ce376b299e56c44690ada08d967f13673%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C637655108014800275%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=QQLBoH27O1sZ6GMXDatmucrxAye8edSeN3XNqAybONI%3D&reserved=0>. > > > > > > > > So, my question is how to prepare such a matrix M involving matrix > > products and matrix inverse efficiently and represent it as > > PETScWrappers::MatrixBase > > That might not easily be possible with our PETSc interfaces. > > PETSc has the concept of MatShell, which is in essence what deal.II's > LinearOperator is: A class that implements a matrix-vector operation, > without giving access to individual matrix elements. You could try > whether you can implement something derived from MatrixBase that is a > MatShell operation in the same way as the existing classes derived from > MatrixBase model other types of PETSc matrices. > > I don't know how difficult that would be, though. > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/88a0aebf-86dd-436f-8f56-8aef2edae4d8n%40googlegroups.com.
