[petsc-users] Questions about AMG and Jacobian Contruction

Smith, Barry F. bsmith at mcs.anl.gov
Sun Jul 14 11:44:51 CDT 2019

> On Jul 14, 2019, at 5:22 AM, Yingjie Wu via petsc-users <petsc-users at mcs.anl.gov> wrote:
> Respected PETSc developers:
> Hi,
> I have some questions about some functions of AMG and the construction time of Jacobian matrix in the process of using. Please help me to answer them.
> 1. I see some functions about AMG in the list of PETSc functions. I wonder if DMDA is necessary to construct vectors when using AMG precondition. (Because the geometry described in my PDE is irregular,it contains a lot of pipes and connections,

   You might take a look at DMNetwork, this a specialized DM for network problems which it sounds like you have. Of course you don't have to use DMNetwork, you can manage the network data structure yourself.

   We've found that the additive Schwarz methods (PCASM) or even block Jacobi PCBJACOBI often work well for network problems, better than GAMG. GAMG doesn't know anything about the structure of networks, it is for PDEs on meshes, so there is no reason to think it would work particularly well for network problems.


> instead of using DMDA to manage vectors, I define discrete solution vectors by myself.)
> 2. As far as I know, besides V-cycle, AMG method also needs auxiliary matrix B and transfer matrix P (transfer matrix from fine mesh to coarse mesh). Are these transformation matrices built-in or can they be provided by users in PETSc?
> 3. At present, in my program, I use -snes_mf_operator to solve the non-linear PDE problem. Although I do not directly construct Jacobian matrix, it is also expensive to construct preconditioning matrix (provided by users). Can I control the update and decomposition time of the preconditioning matrix, such as updating the preconditioning matrix every two Newton steps and then ILU factorization? Can these controls be implemented in SNESMonitor?
> Thanks,
> Yingjie

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