| Author | Message | |||
     Masashi Machida (machida) New member Username: machida Post Number: 1 Registered: 06-2004 |
Hello, I'm trying to solve an electrical filed generated by an electrically charged particle in a pipe. I got good results with potential:V, but not with derivative values, Dx(V) and Dz(Dx(V)).   In order to obtain smoother curves, I decreased ERRLIM to 1e-9 and had an error message, "memory overflow". Do someone know how I can overcome this problem? Thanks in advice. Machida
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 160 Registered: 06-2003 |
The problem is essentially one of providing enough mesh density at the location you want to observe. Because of the small size of your source, you have a steep 1/r falloff of V, and at the position you want to observe, both the potential and the field have fallen to less than 1 percent of the peak values in the problem. So FlexPDE is not as interested in the details as you are. The mesh generator in FlexPDE version 3 uses a fairly rudimentary mesh generation policy in the Z dimension, which does not provide enough cells along the pipe wall to resolve the field. One thing you might do is introduce several fictitious layers near Z=0 to force finer mesh cells. This kind of problem is handled much better by FlexPDE version 4 than by version 3. First, because it is no longer necessary to extend the source throughout Z, and second, because you have more control over the mesh density than in version 3. I have attached a plot from version 4. Notice that although the trace is smoother, the basic features (max excursion and integral) are not terribly different from the version 3 result. One thing you must remember is that in the finite element method, the solution is approximated by an assembly of patches, in each of which the solution is interpolated by a low-order polynomial. The default basis in FlexPDE is quadratic, so derivatives like the electric field are always represented by linear patches (which are not guaranteed to be continuous). Second derivatives are always stair-steps across the mesh. You can select cubic interpolation, which increases the flexibility of the interpolation, but you pay for it in an increased number of nodes. If you would like to try version 4, download and install it and send us the computer ID from the Help|Register dialog, together with a request for a 30-day trial license.  | |||
| Masashi Machida (machida) New member Username: machida Post Number: 2 Registered: 06-2004 |
Thanks, Robert. I will try to introduce fictious layers. I have already installed version 4 with 30-day trial license. But it failes mesh generation. Maybe my script is not suitable to version 4. Could you send me your pde file "EFinPIPE-364v4.pde". Masashi Machida | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 163 Registered: 06-2003 |
The primary advantage of version 4 in problems like this is that you don't need to extend the tiny circle throughout Z. To take advantage of this feature, you need to make the sphere a LIMITED REGION. The V4 problem I ran is attached.
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| Masashi Machida (machida) Junior Member Username: machida Post Number: 3 Registered: 06-2004 |
Thank you very much for your help. Your script teaches me a lot. I'll try. Masashi Machida |
electrical field in pipe