| Author | Message | ||
     Michael Daly (mdaly) Junior Member Username: mdaly Post Number: 3 Registered: 12-2004 |
I have a question about 2 examples. In "plates.pde", the electric field has a very weak dependence on the dielectric constant. For example, When I change eps in region 2 from 7 to 700, the electric field is basically the same. When I change the dielectric constant in "fieldmap.pde", the electric field changes much more. I assume this is from solving the adjoint equation. Could you explain this method or refer me to more sources regarding the adjoint equation? Thanks. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 320 Registered: 06-2003 |
The difference between these two problems is strictly geometric. In "Plates.pde", the plate voltage is fixed. The potential therefore has to tend to a uniform transition between the two levels. The only thing the dielectric constant can do is vary the depth of the end effects. In "fieldmap.pde", by contrast, the floating dielectric can vary all the way from uniform voltage to uniform gradient, depending on the dielectric constant. The adjoint equation is there only to generate the field lines. It does not modify the solution to the field equation. Unfortunately, I don't know a good reference on adjoint equations, and I have forgotten most of what little I once knew. |