| Author | Message | |||
     ronehwa (ronehwa) New member Username: ronehwa Post Number: 1 Registered: 07-2005 |
I want to solve a Poisson equation Div(E)=(p-n) coupled to two drift equations dt(n)=exp(-(x-1)^2)+Div(n*E), and dt(p)=exp(-(x-1)^2)+0.1*Div(p*E), where E(x,t) is the electric field, and n(x,t), p(x,t) stand for the electron and hole in semiconductor. The range of the position x is from 0 and 10. How can I solve them using FlexPDE? any suggestion will be appreciated. Thanks. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 416 Registered: 06-2003 |
You could write the equations just as you have given them here. But since all these equations are first order, the system would probably behave badly. I suggest you use a potential variable (V, for example) instead of E and replace E by grad(V). Having done this, the implementation should be straightforward. See the User_Guide and example problems. | |||
| ronehwa (ronehwa) New member Username: ronehwa Post Number: 2 Registered: 07-2005 |
I found FlexPDE seems to be unable to solve this type of coupled equation. The error message always appear while running FlexPDE. The attachment is my script file. Can someone help me? Thanks.
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 417 Registered: 06-2003 |
You must have posted the wrong file. The one you showed is not syntactically acceptable to FlexPDE. 1) you appear to want a 1D problem, but you have not specified a 1D coordinate system. 2) you appear to want a time-dependent problem, but you have not given a time selection for plots. 3) You have used 2D boundary condition specifications, not 1D Point conditions. 4) the initial conditions give no clue as to the expected size of n and p, so you must provide a Treshold. 5) your initial and boundary conditions on phi are inconsistent. With phi=3 on the boundary, n=p=0 and an electrostatic equation, the correct initial condition on phi is a ramp from 3 to whatever the right boundary value will be when you specify it. I suggest you read through the User Guide and look at some of the sample problems. FlexPDE will have a lot better chance of solving "this type of coupled equation" if you conform to the script language and fully specify the problem. |
Convection+Poisson equation