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

[Christophe Ortiz]

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 ?

Christophe


>
>   Thanks,
>
>      Matt
>
>
>> Is it a long vector like (u0, u1, ..., umx-1 , v0, v1, ..., vmx-1) ?
>> Or is it (u0, v0, u1, v1, u2, v2, ....., umx-1, vmx-1) ?
>>
>> I don't understand the order of the components of the Jacobian and how to
>> fill the matrix in that case.
>>
>> For instance, for the first row of the Jacobian, should I calculate
>> dFu0/du0, dFu0/dFu1, ...., dFu0/dumx-1, dFu0/dv0, dFu0/dv1.....
>>
>> or
>>
>> dFu0/du0, dFu0/dv0, dFu0/du1, dFu0/dv1, ....
>>
>> And then, which subroutine should I use to fill in the Matrix ? Simply
>> MatSetValues ?
>>
>> Many thanks in advance for your help.
>>
>> 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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