> On 20 Apr 2023, at 10:28 PM, Zhang, Hong <[email protected]> wrote: > > Pierre, > 1) Is there any hope to get PDIPDM to use a MatNest? > > KKT matrix is indefinite and ill-conditioned, which must be solved using a > direct matrix factorization method.
But you are using PCBJACOBI in the paper you attached? In any case, there are many such systems, e.g., a discretization of Stokes equations, that can be solved with something else than a direct factorization. > For the current implementation, we use MUMPS Cholesky as default. To use > MatNest, what direct solver to use, SCHUR_FACTOR? I do not know how to get it > work. On the one hand, MatNest can efficiently convert to AIJ or SBAIJ if you want to stick to PCLU or PCCHOLESKY. On the other hand, it allows to easily switch to PCFIELDSPLIT which can be used to solve saddle-point problems. > 2) Is this fixed > https://lists.mcs.anl.gov/pipermail/petsc-dev/2020-September/026398.html ? > I cannot get users to transition away from Ipopt because of these two missing > features. > > The existing pdipm is the result of a MS student intern project. None of us > involved are experts on the optimization solvers. We made a straightforward > parallelization of Ipopt. It indeed needs further work, e.g., more features, > better matrix storage, convergence criteria... To our knowledge, parallel > pdipm is not available other than our pdipm. Ipopt can use MUMPS and PARDISO internally, so it’s in some sense parallel (using shared memory). Also, this is not a very potent selling point. My users that are satisfied with Ipopt as a "non-parallel" black box don’t want to have to touch part of their code just to stick it in a parallel black box which is limited to the same kind of linear solver and which has severe limitations with respect to Hessian/Jacobian/constraint distributions. Thanks, Pierre > We should improve our pdipm. > Hong > >> On 20 Apr 2023, at 5:47 PM, Zhang, Hong via petsc-users >> <[email protected] <mailto:[email protected]>> wrote: >> >> Karthik, >> We built a KKT matrix in TaoSNESJacobian_PDIPM() (see >> petsc/src/tao/constrained/impls/ipm/pdipm.c) which assembles several small >> matrices into a large KKT matrix in mpiaij format. You could take the same >> approach to insert P and P^T into your K. >> FYI, I attached our paper. >> Hong >> >> From: petsc-users <[email protected] >> <mailto:[email protected]>> on behalf of Matthew Knepley >> <[email protected] <mailto:[email protected]>> >> Sent: Thursday, April 20, 2023 5:37 AM >> To: Karthikeyan Chockalingam - STFC UKRI >> <[email protected] >> <mailto:[email protected]>> >> Cc: [email protected] <mailto:[email protected]> >> <[email protected] <mailto:[email protected]>> >> Subject: Re: [petsc-users] question about MatSetLocalToGlobalMapping >> >> On Thu, Apr 20, 2023 at 6:13 AM Karthikeyan Chockalingam - STFC UKRI via >> petsc-users <[email protected] <mailto:[email protected]>> wrote: >> Hello, >> >> I created a new thread, thought would it be more appropriate (and is a >> continuation of my previous post). I want to construct the below K matrix >> (which is composed of submatrices) >> >> K = [A P^T >> P 0] >> >> Where K is of type MatMPIAIJ. I first constructed the top left [A] using >> MatSetValues(). >> >> Now, I would like to construct the bottom left [p] and top right [p^T] using >> MatSetValuesLocal(). >> >> To use MatSetValuesLocal(), I first have to create a local-to-global >> mapping using ISLocalToGlobalMappingCreate. I have created two mapping >> row_mapping and column_mapping. >> >> I do not understand why they are not the same map. Maybe I was unclear >> before. It looks like you have two fields, say phi and lambda, where lambda >> is a Lagrange multiplier imposing some constraint. Then you get a saddle >> point like this. You can imagine matrices >> >> (phi, phi) --> A >> (phi, lambda) --> P^T >> (lambda, phi) --> P >> >> So you make a L2G map for the phi field and the lambda field. Oh, you are >> calling them row and col map, but they are my phi and lambda >> maps. I do not like the row and col names since in P they reverse. >> >> Q1) At what point should I declare MatSetLocalToGlobalMapping – is it just >> before I use MatSetValuesLocal()? >> >> Okay, it is good you are asking this because my thinking was somewhat >> confused. I think the precise steps are: >> >> 1) Create the large saddle point matrix K >> >> 1a) We must call >> https://petsc.org/main/manualpages/Mat/MatSetLocalToGlobalMapping/ on it. In >> the simplest case, this just maps >> the local rows numbers [0, Nrows) to the global rows numbers >> [rowStart, rowStart + Nrows). >> >> 2) To form each piece: >> >> 2a) Extract that block using >> https://petsc.org/main/manualpages/Mat/MatGetLocalSubMatrix/ >> >> This gives back a Mat object that you subsequently restore using >> https://petsc.org/main/manualpages/Mat/MatRestoreLocalSubMatrix/ >> >> 2b) Insert values using >> https://petsc.org/main/manualpages/Mat/MatSetValuesLocal/ >> >> The local indices used for insertion here are indices relative >> to the block itself, and the L2G map for this matrix >> has been rewritten to insert into that block in the larger >> matrix. Thus this looks like just calling MatSetValuesLocal() >> on the smaller matrix block, but inserts correctly into the >> larger matrix. >> >> Therefore, the code you write code in 2) could work equally well making the >> large matrix from 1), or independent smaller matrix blocks. >> >> Does this make sense? >> >> Thanks, >> >> Matt >> >> I will use MatSetLocalToGlobalMapping(K, row_mapping, column_mapping) to >> build the bottom left [P]. >> >> >> Q2) Can now I reset the mapping as MatSetLocalToGlobalMapping(K, >> column_mapping, row_mapping) to build the top right [P^T]? >> >> >> Many thanks! >> >> Kind regards, >> Karthik. >> >> >> >> >> >> >> >> >> >> >> >> -- >> What most experimenters take for granted before they begin their experiments >> is infinitely more interesting than any results to which their experiments >> lead. >> -- Norbert Wiener >> >> https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/> >> <IET Generation Trans Dist - 2022 - Sundermann - Parallel primal‐dual >> interior point method for the solution of dynamic.pdf>
