Thank you very much I will dig deeper from your suggestion. Best regards, Pham Ngoc Kien
Vào Th 5, 28 thg 3, 2019 vào lúc 12:25 Wolfgang Bangerth < [email protected]> đã viết: > On 3/27/19 6:56 PM, Phạm Ngọc Kiên wrote: > > Yes, I know that the source should be integral over the edge of a cell, > not a > > single point on the cell. > > And I checked that if I take the integral over an edge of shape function > I > > will get 1 * inverse of edge length. > > However, we actually do compute the source term over a cell when > assembling > > the right hand side: > > F_i = \int_\Omega \phi_i(x) J(x) dx > > To compute it, we implement the Quadrature formula with its weights on > unit > > cell rather than the weights on and edge. > > In my limited knowledge, I think that J(x) should be non-zero if x is on > my > > source line, and be zero every where else in the cell. > > Well, but that's precisely a delta function then. J is a current > *density*, so > if you have a current density that only lives on an edge with a finite > length > but an infinitely small diameter, then the total current that is flowing > is > zero. If you say that J(x) is zero everywhere but on that edge, then no > current is flowing. Your model is just flawed in that case. > > If you want to restrict a *nonzero* current to just an edge, then you need > an > infinite current density, and in that case you would have > > F_i = \int_Omega phi_i(x) J(x) // J is current *density* > = \int_edge phi_i(x) j(x) // j is *current* > > where the second integral only extends over a one-dimensional edge. > > > > Should I set J(x) constant when computing F_i if dof i of the cell > relates to > > the source? > > You're asking the wrong person. If you are trying to model a physical > situation, then what J(x) is is a question of how that physical situation > looks like and is best described. Nobody but you can answer this -- it's > not a > mathematical question, but a modeling question. > > Best > W. > > -- > ------------------------------------------------------------------------ > 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.
