[petsc-users] How to construct Jacobian for multicomponent problem ?

[Matthew Knepley]

On Wed, Sep 25, 2013 at 4:55 AM, Christophe Ortiz <
christophe.ortiz at ciemat.es> wrote:

>
>
>
> On Wed, Sep 25, 2013 at 1:46 PM, Matthew Knepley <knepley at gmail.com>wrote:
>
>> On Wed, Sep 25, 2013 at 4:40 AM, Christophe Ortiz <
>> christophe.ortiz at ciemat.es> wrote:
>>
>>> Hi Matt,
>>> Thanks for your prompt reply.
>>>
>>> On Wed, Sep 25, 2013 at 1:34 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> On Wed, Sep 25, 2013 at 4:31 AM, Christophe Ortiz <
>>>> christophe.ortiz at ciemat.es> wrote:
>>>>
>>>>> Hi guys,
>>>>>
>>>>> Please apologize if this question has already been raised in previous
>>>>> posts.
>>>>>
>>>>> I am developing a code in fortran 90 to solve a 1D multicomponent
>>>>> problem.
>>>>> For instance, something like
>>>>>
>>>>> u_t = u_xx + R(u,v)
>>>>> v_t = v_xx + R(u,v)
>>>>>
>>>>> I have already implemented this for one component (u) and using DMDA.
>>>>> So far no problem. It works fine.
>>>>>
>>>>> Now I am trying to implement several components per node. Following
>>>>> example ex22f.F, for the residual function I would have for node i (1D)
>>>>>
>>>>> F(1,i) = ....
>>>>> F(2,i) = ....
>>>>>
>>>>> Now, I am not quite sure to understand how to construct the Jacobian
>>>>> when there are various components. In this case, how is the vector in PETSc
>>>>> ?
>>>>>
>>>>
>>>> The Jacobian is a matrix, and the rows are ordered in the same way as
>>>> in the residual function. The columns are the same as the rows.
>>>>
>>>
>>> Yes, I understand this for one component. My question is when you have
>>> dof > 1. For a multicomponent problem you can write the residual function
>>> as an array:
>>>
>>> F(1,i) =...           (component 1)
>>> F(2,i) = ...          (component 2)
>>>
>>> Since there is only one Jacobian for the whole system, how are the
>>> components of the Jacobian ordered in that case ? Is it first the
>>> components of u, then the components of v ?
>>>
>>
>> The ordering of the rows (and columns) of the Jacobian match the rows of
>> the residual EVEN in the multicomponent case.
>>
>>    Matt
>>
>>
>
> Ok. But what I still don't understand is the ordering of the residual in
> the multicomponent case. Let's say dof=2, components u and v. Which is the
> correct ordering in the following ?
>
> Fu0, Fu1, Fu2,...Fumx-1, Fv0, Fv1, Fv2, ...Fvmx-1
>
> or
>
> Fu0, Fv0, Fu1, Fv1, Fu2, Fv2, ...    ?
>

This one.


> It is this point that is not clear to me.
>
> Also, which subroutine do you advice to use to fill in the Matrix ?
> MatSetValues ? MatSetValuesBlocked ?
>

MatSetValuesStencil.

   Matt


> Christophe
>
>
>



-- 
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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