Than you for your response! and if I may ask for some advise:
I tried to give some additional constrains for electirc field E (I must admit that it wasn't good idea) to avoid another unphysical results. General physical poin of view is that I should have this kind of a situation: [image: str.png] The Ex in the middle should go from 0 to -1e7 or -1e6 in the middle of device and then go back to zero but my results (for Ex) look rather like this: [image: results.png] Where all Ex values, over all domain is almost -9e7 and it drops a little in the middle (as it should, but not from such a big value). I couldn't find any mistake in my implementation so I've dicided to change boundary condition to enforce electric filed E to be 0. Do you have an intuition what I'm making wrong? Probably I can subtract the values on the boundary from all of the results but I don't think it is proper way to deal with this problem. W dniu środa, 4 września 2019 18:17:23 UTC+2 użytkownik Wolfgang Bangerth > napisał: >> >> >> Konrad, >> >> > I am trying to solve 2D transient problem in semiconductor devices and >> > I'm stuck with application of Dirichlet boundary values via >> > ConstrainMatrix or AffineMatrix (in the last version of this library) >> > >> > >> > The program (which I am rewriting) solves consecutively two equation: >> > (i) for a given charge density it solves Poisson equation, and than >> (ii) >> > the continuity equation to find the densities in next step. >> > >> > The poisson equation looks like this: >> > >> > >> > eq.png >> > >> > This is a formulation of mixed finite element problem with phi as >> > electric potential and E = (Ex, Ey) as a vector of electric field. >> >> I suspect you have already found that out (even though you don't state >> it in your email) that this is *exactly* the problem step-20 solves. >> >> >> > The geometry (as well as boundary conditions) is quite simple: >> >> This doesn't work. You can't impose boundary conditions on *both* Phi >> and E at the left and right sides. It would be equivalent to imposing >> both Dirichlet and Neumann values for the non-mixed Laplace equation. >> >> >> > I have choosen this kind of boundary conditions because: >> > >> > - the potential is applied on the left side of device >> > >> > - Interesting things (non-zero carrier densities) shound appeard only >> > near the interface of two domains so I assumed that Ex=0, Ey=0 on >> > Dirichlet boundaries >> >> This assumption is unphysical. From your first equation, it is clear >> that (up to some constant), E=-grad Phi. So if E=0 at the boundary, >> you'd have grad Phi=0 AND ALSO Phi=something on these boundaries. >> >> >> >> > Unfortunately when I look at the output the E value on Dirichlet >> > boundary only x-component Ex is 0, but not Ey. >> >> That's because for the R-T element, the degrees of freedom at a face are >> only the normal component of the vector. That's the only thing you can >> constrain, i.e., you can only prescribe E.n=something, but not the >> tangential component. >> >> 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/e4256a3e-b1a3-4c90-86f0-7752dfad99fd%40googlegroups.com.
