Thank you so much. I appreciate your help.
On Monday, December 10, 2018 at 1:54:28 PM UTC-5, Wolfgang Bangerth wrote:
>
> On 12/10/18 11:25 AM, Jaman wrote:
> >
> > I have stuck in another piece of the weak form. I have an inner product
> (\grad
> > u^{n-1}:\grad u^n I, \grad v), where : is the contraction between the
> two
> > tensors, "I" is the identity matrix and v is the test function.
> >
> > I understand that scalar_product(old_time_gradient_values[q], grad_phi[
> j ])
> > will serve for the part \grad u^{n-1}:\grad u^n but how can I multiply
> it with
> > the identity matrix of the appropriate size so that I can take another
> > scalar_product to complete the contribution of it in the local_matrix? I
> hope
> > if this problem is solved I can move faster.
>
> You don't have to. The term
> scalar_product(old_time_gradient_values[q], grad_phi[ j ])
> is just a scalar number, so instead of multiplying it with I (resulting in
> a
> tensor) and then multiplying the tensor with grad v, you are better off
> writing this as
>
> (\grad u^{n-1}:\grad u^n I, \grad v)
> = \int [\grad u^{n-1}:\grad u^n] [I : \grad v]
>
> i.e., you now only need to know how to compute [I : \grad v]. But this is
> just
> the trace of grad v:
>
> = \int [\grad u^{n-1}:\grad u^n] [trace (\grad v)]
>
> Best
> W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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