[petsc-users] Simple question regarding dense matrix algebra using elemental

[Matthew Knepley]

On Mon, Apr 13, 2015 at 12:20 PM, Preyas Shah <shah.preyas at gmail.com> wrote:

> Another beginner's querry:
>
> ​I worked out an example that "combines"
> mat/examples/tests/ex145.c
>  /ksp/ksp/examples/tutorials/ex2.c
> /ksp/ksp/examples/tutorials/ex30.c
>
> Please see attached code sample. The code compiles but does not solve the
> system correctly. I would like to know what changes I would need to
> ​implement to get it working right. Thanks!
>

Check the residual as well (rhs - MM sol). This should be small. Its
possible you have not set
the exact solution correctly, or the discretization error is large, or the
condition number is large.

  Thanks,

     Matt


> P.S.  Feel free to include the (corrected) code sample in the
> test/tutorial folders of the development version.
>
> On Sun, Apr 12, 2015 at 7:47 PM, Hong <hzhang at mcs.anl.gov> wrote:
>
>> You can either use elemental directly, or use petsc-elemental interface.
>> An example can be found at
>> ~petsc/src/mat/examples/tests/ex145.c
>>
>> You may use petsc KSP interface instead. I just modified
>> ~petsc/src/ksp/ksp/examples/tutorials/ex2.c
>> so this example can be run with elemental with runtime options
>> mpiexec -n 3 ./ex2 -pc_type lu -pc_factor_mat_solver_package elemental
>> -mat_type elemental
>> Norm of error 2.81086e-15 iterations 1
>>
>> Please using petsc-dev (master branch) for petsc-elemental interface.
>>
>> Hong
>>
>> On Sun, Apr 12, 2015 at 6:57 PM, Preyas Shah <shah.preyas at gmail.com>
>> wrote:
>>
>>> Hi,
>>>
>>> I have been recently investigating the use of Petsc for solving a PDE
>>> related to my research and web search suggests that I should use petsc with
>>> elemental.
>>>
>>> So far, I was required to solve a matrix equation Ax=b where A was dense
>>> (with number of non zeros =0) but the size of the matrix was order
>>> 5000x5000. I employed the standard serial LU solver from Gnu Scientific
>>> Library and obtained a decent runtime that served my needs.
>>>
>>> Now I am investigating the same problem in a particularly singular limit
>>> of one parameters in my PDE. As a result, to obtain grid convergence on the
>>> physical domain, I am forced to go to sizes of A beyond 30000x30000. I am
>>> trying to find a good library that can solve such dense systems in
>>> **parallel**. Petsc says its capable of doing dense linear algebra but my
>>> web search hasn't shown me any examples where dense equations are solved in
>>> **parallel**. A webpage showing a minimum working example would be enough.
>>> Or any other advice :)
>>>
>>> Thanks for your time!
>>> ​~Preyas
>>>
>>>
>>
>
>
> --
> ~
> Preyas
>
> Doctoral Researcher, MechE, Stanford Univ.
>
> *"Can a man still be brave if he's afraid?".**"That is the only time he
> can be brave."-- George R R Martin*
> *"To learn who rules over you, simply find out who you are not allowed to
> criticize." -- Voltaire*
> *"First they ignore you, then they laugh at you, then they fight you, then
> you win" -- Gandhi*
>



-- 
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
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