On 4/10/19 7:59 PM, Phạm Ngọc Kiên wrote:
>
> In finite element method, we transform the integral from the physical to the
> reference coordinate system.
> Thus to compute \int \varphi_i(x) \varphi_j(x) dx in a physical cell, I
> will need:
> \varphi_i(x_q), \varphi_j(x_q), and JxW in reference cell to compute the
> integral by quadrature formula.
> The term |det J(x_q)| is to change dx in physical coordinates into d( \hat x)
> in reference coordinates so that we can compute the integral in reference
> cell.
> However, in my code fe_values[vec[block_index_i]].value(i, q_point) is the
> shape function in physical coordinate system.
Correct. In deal.II, you do the integration in real space. You don't need to
do the transformation back to the reference cell. (Of course, this happens
somewhere internally to the library, but it is not something you need to worry
about.)
> If I use:
> sum of quadrature point { fe_values[vec[block_index_i]].value(i, q_point) *
> fe_values[vec[block_index_j]].value(j, q_point) *fe_values.JxW(q_point) }
> It means that I am using the shape functions in physical coordinate system to
> compute the integral instead of those in reference one.
Yes. And that's correct.
Best
WB
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Wolfgang Bangerth email: [email protected]
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