Thank you very much. Could you please recommend me some articles or books which I can find the idea to compute the integral in real space for assembling system? I think it would be really helpful for me. Best regards,
Vào Th 5, 11 thg 4, 2019 vào lúc 12:49 Wolfgang Bangerth < [email protected]> đã viết: > 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 > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > www: http://www.math.colostate.edu/~bangerth/ > > -- > The deal.II project is located at http://www.dealii.org/ > For mailing list/forum options, see > https://groups.google.com/d/forum/dealii?hl=en > --- > You received this message because you are subscribed to the Google Groups > "deal.II User Group" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > For more options, visit https://groups.google.com/d/optout. > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
