[petsc-users] petsc-users Digest, Vol 26, Issue 30

[Matthew Knepley]

On Sun, Feb 13, 2011 at 8:12 PM, Kontsantinos Kontzialis <
ckontzialis at lycos.com> wrote:

> Message: 1
>> Date: Sat, 12 Feb 2011 16:12:36 -0600
>> From: Matthew Knepley<knepley at gmail.com>
>> Subject: Re: [petsc-users] Guidelines for solving the euler equations
>>        with an implicit matrix free approach
>> To: PETSc users list<petsc-users at mcs.anl.gov>
>> Message-ID:
>>        <AANLkTimus8N2jUu7Bvu0TZe59dr4FTpoJFh+m0QQUN-V at mail.gmail.com>
>> Content-Type: text/plain; charset="iso-8859-1"
>>
>> On Fri, Feb 11, 2011 at 10:37 AM, Kontsantinos Kontzialis<
>> ckontzialis at lycos.com>  wrote:
>>
>>  Dear Petsc team,
>>>
>>>  I'm new in Petsc and I'm trying to solve the euler equations of fluid
>>> dynamics
>>> using an implicit matrix free approach with a spatial discontinues
>>> galerkin
>>> discretization.
>>> I need some directions about how can I solve the following system:
>>>
>>> (M/dt+dR/du)*DU=R
>>>
>>> where R denotes the residual of the system and dR/du the residual
>>> jacobian.
>>> Please help.
>>>
>>>  Petsc provides linear algebra and nonlinear solvers. This is fine once
>> you
>> have discretized.
>> It sounds like you will use DG:
>>
>>   a) on a structured or unstructured grid?
>>
>> The PETSc DA supports structured grids in any dimension. After this, you
>> want to use the
>> TS object to present your system. There are many examples in the TS, e.g.
>> ex10 for
>> radiation-diffusion or ex14 for hydrostatic ice flow.
>>
>> Once you have your problem producing the correct residual and Jacobian, we
>> can talk
>> about solvers.
>>
>>    Matt
>>
>>
>>  Kostas
>>>
>>>  Mat,
>
> Thank you for your reply. I have done the discretization and the residual
> and jacobian are computes correctly. Furthermore, I managed to do some
> calculation using TS but with an explicit scheme. I need to work with an
> implicit time discretization and I have read in a quite few papers that they
> follow the matrix free approach.
>

Once you plug your Residual and Jacobian into the TS, you can start to try
out different solvers. Is this working?

  Thanks,

     Matt


> Thank you,
>
> Kostas
>



-- 
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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