| Author | Message | ||
     Takeyuki Ojima (tac) Member Username: tac Post Number: 13 Registered: 07-2005 |
Dear Sirs/Madame: In electromagnetic ploblems, there are uncontinuous variables on the interface of materials, which sometimes makes difficult to solve by FlexPDE or FEM. I would like to know whether or not it is possible to optionally construct nodes of mesh not on the interface but in each material a little bit distant from it. I think then FlexPDE can treat uncontinuous ploblems. I look forward to opinions. | ||
| Marek Nelson (mgnelson) Moderator Username: mgnelson Post Number: 8 Registered: 07-2007 |
1) Discontinuous variables like electric field are handled automatically if they are defined in terms of a potential function. Writing div(D) = div(eps*E) = div(eps*grad(V)) will conform to Maxwell's equations at material interfaces. Normal(E) will be discontinuous. A similar effect can be acheived with magnetic fields using the magnetic vector potential. See the supplementary applications manual "applications_em_r1.pdf" in the FlexPDE installation directory or online at www.pdesolutions.com/bookstore.html 2) FlexPDE can also deal with discontinuous variables using the CONTACT and JUMP statements. See "Discontinuous Variables" and "Contact Resistance" in the help manual. | ||
| Takeyuki Ojima (tac) Member Username: tac Post Number: 14 Registered: 07-2005 |
1) It is of course partially possible, particularly for static problems. The wave equation of electric or magnetic fields has however second order derivatives with respect to x,y,z and t, and then using potential functions for such problems bring third order ones, which makes more difficult to solve because of unknown boundary conditions in general. 2) This kind of discontinuity capable to be solved seems confined to a case of an explicitly known function of the discontinuity between both sides which is in general not the case for EM-wave problems. I have once failed in using these statements. | ||
| Marek Nelson (mgnelson) Moderator Username: mgnelson Post Number: 10 Registered: 07-2007 |
In some cases, it is possible to merely change the value declared as a FlexPDE variable to one which is continuous at material interfaces. For example, using displacement instead of electric field. Without knowing more about your specific equations, it is difficult to give a general answer. | ||
| Takeyuki Ojima (tac) Member Username: tac Post Number: 15 Registered: 07-2005 |
My initial posting did not come from any specific problem but just my easy idea like the FDTD method, in which boundary conditions are automatically met due to the structure of meshes and the location of variables including discontinuous ones for EM-wave problems. So my present challenge in FlexPDE is in a material-free space with electrically-charged particles only like a hydrogen atom or molecule, also including another difficulty though. |