[petsc-users] Question about how to use DS to do the discretization

[Stefano Zampini]

Take a look at
https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/snes/tutorials/ex11.c?ref_type=heads__;!!G_uCfscf7eWS!er4CI8GIe7OCWvCmRKQpZt6FOz1QYvbuZOdf2Fm7pvMGee3I9M5bhjNytv42F9C17NpBy0i6mTfgEmQfUR_QOqwC7gC6pYk$ 
and the discussion at the beginning (including the reference to the
original paper)

On Sat, Mar 23, 2024, 15:03 Gong Yujie <yc17470 at connect.um.edu.mo> wrote:

> Dear PETSc group, I'm reading the DS part for the discretization start
> from SNES ex17. c which is a demo for solving linear elasticity problem. I
> have two questions for the details. The first question is for the residual
> function. Is the residual
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> Dear PETSc group,
>
> I'm reading the DS part for the discretization start from SNES ex17.c
> which is a demo for solving linear elasticity problem. I have two questions
> for the details.
>
> The first question is for the residual function. Is the residual
> calculated as this? The dot product is a little weird because of the
> dimension of the result.
> Here \sigma is the stress tensor, \phi_i is the test function for the i-th
> function (Linear elasticity in 3D contains three equations).
>
> The second question is how to derive the Jacobian of the system (line 330
> in ex17.c). As shown in the PetscDSSetJacobian, we need to provide function
> g3() which I think is a 4th-order tensor with size 3*3*3*3 in this linear
> elasticity case. I'm not sure how to get it. Are there any references on
> how to get this Jacobian?
>
> I've checked about the comment before this Jacobian function (line 330 in
> ex17.c) but don't know how to get this.
>
> Thanks in advance!
>
> Best Regards,
> Yujie
>
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