[petsc-users] Fwd: nonzero prescribed boundary condition

[Hong Zhang]

amrit :
>
> If I run a program with the following runtime option (notice that I have not
> included -pc_type lu ), will the program use mumps to solve the linear
> system of equations directly, or does it  run with default gmres iterative
> solver? Why do we have to specify a preconditioner for a direct solver ?
>
>  -pc_factor_mat_solver_package mumps

You must include '-pc_type lu' to use mumps.
There are many preconditioners for solving linear system, lu is one of pcs,
and mumps is one of packages implement lu.

Hong

>
>
>> From: bsmith at mcs.anl.gov
>> Date: Thu, 8 Sep 2011 14:02:09 -0500
>> To: petsc-users at mcs.anl.gov
>> Subject: Re: [petsc-users] Fwd: nonzero prescribed boundary condition
>>
>>
>> Are you running with -ksp_converged_reason and -ksp_monitor_true_residual
>> to see if the iterative method is actually converging and how rapidly. Also
>> if you impose a tight tolerance on the iterative solver say with -ksp_rtol
>> 1.e-12 how much do the "solutions" differ, it should get smaller the smaller
>> you make this tolerance (in double precision you cannot expect to use a
>> tolerance less than 1.e-3 or 1.e-14)
>>
>> If your "big" matrix is very complicated and comes from no well understood
>> simulation it may be that it is very ill-conditioned, in that case you
>> either need to understand the underlying equations real well to develop an
>> appropriate preconditioner or just use parallel direct solvers (which get
>> slow for very large problems but can handle more ill-conditioning.n To use
>> the MUMPS parallel direct solver you can configure PETSc with
>> --download-mumps --download-scalapack --download-blacs and run the program
>> with -pc_type lu -pc_factor_mat_solver_package mumps
>>
>> Barry
>>
>>
>>
>> On Sep 8, 2011, at 12:57 PM, amrit poudel wrote:
>>
>> > After running my simulation multiple times on a multiprocessor computer
>> > I've just verified that using iterative solver (default gmres) in PETSc to
>> > solve a linear system of equations ( Cx=b) with more than 2 processors
>> > setting ALWAYS lead to erroneous result. Running identical code with
>> > identical setting except for the number of processors ( set this to 2)
>> > ALWAYS gives me correct result .
>> >
>> > I am really not sure what is the point behind including iterative
>> > solvers if they result into erroneous result on a multiprocessor computer.
>> > The result I get from multiprocessor computer is a complete garbage, so I am
>> > really not talking about small percentage of error here. Also, if somebody
>> > could enlighten why the iterative solvers are error prone on multiprocessors
>> > that will be highly appreciated.
>> >
>> > I am very hopeful that there is a way around to this problem, because
>> > PETSc is such a powerful and useful library that I really do not want to
>> > give up on this and start something else from scratch.
>> >
>> >
>> > Would you think that a DIRECT SOLVER would circumvent this problem? My
>> > problem is that I have a very large system of equations and the size of a
>> > sparse coefficient matrix is huge ( > 1e+8). I assemble this matrix in
>> > MATLAB, write to a binary file, and read it in PETSc. So I really need to be
>> > able to solve this system of equations in a cluster of computers (which
>> > inherently has multiprocessors and distributed memory setting). Does this
>> > mean I am completely out of luck with PETSc's iterative solver package and
>> > the only hope for me is the direct solver? I do have MUMPS downloaded and
>> > compiled with PETSc, so I will give that a try and see what results I
>> > obtain, but I am really surprised that iterative solvers are no good in a
>> > large multiprocessor settings.
>> >
>> > Any insights, suggestions/advice will be highly appreciated.
>> >
>> > Thanks.
>> >
>> > PS (I can attach my entire code, plots that compare the results obtained
>> > by solving Cx=b in 2 processors vs 12 or 6 processors if any body wants to
>> > take a look at it. I get garbage if I run iterative solver on 12 processors)
>>
>