| Author | Message | |||
     shi liang (caleb_shi) Member Username: caleb_shi Post Number: 6 Registered: 12-2004 |
Hi, Sir. last time you said :"FlexPDE uses Newton-Raphson iteration automatically whenever the problem is nonlinear. You don't have to do anything." if we have 2 equations to be solved in flexpde. 1) the schrodinger equation, with V, phi, E 2) poisson equation, with V, phi and E V with boundary specified. Can this be solved automatically by Flexpde?
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 304 Registered: 06-2003 |
Your script requests an eigenvalue calculation, but the equations are nonlinear. Your term V*Phi requires the product of eigenfunctions. FlexPDE cannot solve nonlinear eigenvalue problems. My remarks about automatic Newton iteration apply only to direct solution of PDE's. The best I can suggest is to solve the PDE system directly, with lamda as a parameter. Use STAGEs and sweep through values of lambda as a parameter study. Solution of a linear eigenvalue problem of similar characteristics might give you a range of lambdas to search. | |||
| Md. Gaffar (gaffareee) New member Username: gaffareee Post Number: 1 Registered: 04-2009 |
dear sir, is the poisson equation become time dependent? | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1239 Registered: 06-2003 |
The "Poisson Equation" Div(grad(phi)) = F is a special case of the more general "Diffusion Equation" dt(phi)=div(k*grad(phi))+source. Professor Backstrom discusses these (and the Schroedinger Equation as well) in his book "Simple Fields of Physics by Finite Element Analysis", available by link from our Bookstore page www.pdesolutions.com/bookstore.html. | |||
| Md. Gaffar (gaffareee) New member Username: gaffareee Post Number: 2 Registered: 04-2009 |
Dear dr. Nelson, thanks for the reply.i am going to describe what exactly i am looking for. i think you can help me out. any device can be solved with self consistent poisson-schrodinger solver with flex pde but in fdtd mode i need a time dependent schrodinger and poisson equation for simulation. Dear sir, i have searched for diffusion equation from your kind information but unfortunately i did not find it. can you send me the related pages in the following address gaffareeebuet@gmail.com thanks in advance. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1241 Registered: 06-2003 |
Search Wikipedia for "Diffusion Equation", and look at our sample problems (among many): V5: Samples | Time_Dependent | Misc | Diffusion.pde Samples | Time_Dependent | Chemistry | Chemburn.pde V6: Samples | Applications | Misc | Diffusion.pde Samples | Applications | Chemistry | Chemburn.pde |
particals in two dimensions