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

[Christophe Ortiz]

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, ...    ?

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 ?

Christophe
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