[petsc-users] Elasticity tensor in ex52

[Miguel Angel Salazar de Troya]

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 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
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