[petsc-users] Elasticity tensor in ex52

[Miguel Angel Salazar de Troya]

Thanks for your response. Now I understand a bit better your
implementation, but I am still confused. Is the g3 function equivalent to
the f_{1,1} function in the matrix in equation (3) in this paper:
http://arxiv.org/pdf/1309.1204v2.pdf ? If so, why would it have terms that
depend on the trial fields? I think this is what is confusing me.


On Sat, Apr 19, 2014 at 11:35 AM, Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Apr 18, 2014 at 1:23 PM, Miguel Angel Salazar de Troya <
> salazardetroya at gmail.com> wrote:
>
>> Hello everybody.
>>
>> First, I am taking this example from the petsc-dev version, I am not sure
>> if I should have posted this in another mail-list, if so, my apologies.
>>
>> In this example, for the elasticity case, function g3 is built as:
>>
>> void g3_elas(const PetscScalar u[], const PetscScalar gradU[], const
>> PetscScalar a[], const PetscScalar gradA[], const PetscReal x[],
>> PetscScalar g3[])
>> {
>>   const PetscInt dim   = spatialDim;
>>   const PetscInt Ncomp = spatialDim;
>>   PetscInt       compI, d;
>>
>>   for (compI = 0; compI < Ncomp; ++compI) {
>>     for (d = 0; d < dim; ++d) {
>>       g3[((compI*Ncomp+compI)*dim+d)*dim+d] = 1.0;
>>     }
>>   }
>> }
>>
>> Therefore, a fourth-order tensor is represented as a vector. I was
>> checking the indices for different iterator values, and they do not seem to
>> match the vectorization that I have in mind. For a two dimensional case,
>> the indices for which the value is set as 1 are:
>>
>> compI = 0 , d = 0      ----->     index = 0
>> compI = 0 , d = 1      ----->     index = 3
>> compI = 1 , d = 0      ----->     index = 12
>> compI = 1 , d = 1      ----->     index = 15
>>
>> The values for the first and last seem correct to me, but they other two
>> are confusing me. I see that this elasticity tensor (which is the
>> derivative of the gradient by itself in this case) would be a four by four
>> identity matrix in its matrix representation, so the indices in between
>> would be 5 and 10 instead of 3 and 12, if we put one column on top of each
>> other.
>>
>
> I have read this a few times, but I cannot understand that you are asking.
> The simplest thing I can
> respond is that we are indexing a row-major array, using the indices:
>
>   g3[ic, id, jc, jd]
>
> where ic indexes the components of the trial field, id indexes the
> derivative components,
> jc indexes the basis field components, and jd its derivative components.
>
>    Matt
>
>
>> I guess my question is then, how did you vectorize the fourth order
>> tensor?
>>
>> Thanks in advance
>> Miguel
>>
>> --
>> *Miguel Angel Salazar de Troya*
>> Graduate Research Assistant
>> Department of Mechanical Science and Engineering
>> University of Illinois at Urbana-Champaign
>> (217) 550-2360
>> salaza11 at illinois.edu
>>
>>
>
>
> --
> 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
>



-- 
*Miguel Angel Salazar de Troya*
Graduate Research Assistant
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
(217) 550-2360
salaza11 at illinois.edu
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